A COMPLETE T REATISE ON PRACTICAL LAND-SURVEYING, $n J^tbttt Starts: Designed chiefly for the USE OF SCHOOLS AND PRIVATE STUDENTS. By A^NESBIT, ^ Land-Surveyor ; Master of the Classical, Commercial, and Mathematical Academy, Oxford-Street, Manchester ; and Author of "A Treatise on Practical Mensuration ;" "A Treatise on Practical Guaging;" " Keys to the Mensuration, and Guaging ;" "An Introduction to English Parsing, adapted to Murray's Grammar ;" and " A Treatise on Practical Arithmetic," &c. &c. THE SEVENTH EDITION, GREATLY ENLARGED BY NUMEROUS ADDITIONS AND IMPROVEMENTS; The whole illustrated by two hundred and fifty Practical * Examples, one hundred and sixty Wood Cuts, twelve Copper -plates, and an Engraven Field-Book of sixteen Pages. Sorts Printed by Thomas Wilson and Sons, High-Ousegate ; FOR LONGMAN, ORME, BROWN, GREEN, AND LONGMANS, rATERNOSTER-ROW, LONDON ; AND FOR WILSON AND SONS, YORK. 1839. ^ ~£ ./f + 5 Rev. FRANCIS WRANGHAM, M.A.F.R.S. Archdeacon of the East Riding of Yorkshire, Examining Chaplain to the Archbishop of York, fyc. fyc. EMINENTLY DISTINGUISHED FOR HIS HIGH LITERARY ATTAINMENTS, ZEALOUS SUPPORT OF THE DOCTRINES OF CHRISTIANITY ; TO WHOM THE AUTHOR OF THIS WORK IS UNDER THE GREATEST OBLIGATION, THIS EFFORT TO RENDER A MOST VALUABLE SCIENCE FAMILIAR TO THE MEANEST CAPACITY; HUMBLY AND RESPECTFULLY INSCRIBED, BY HIS MUCH OBLIGED AND MOST OBEDIENT SERVANT, A. NESBIT. Ml re* at Stationers' ffealt INTRODUCTION. 1 he various works which so imperfect a being as man is able to perform, and the great advances which he is capable of making In the arts and sciences, are astonishing. He comes into the world devoid both of strength and of reflection ; nor are the powers of his body more rapidly developed, than those of his mind. But however ingenious and active the individual may prove, when arrived at maturity, his efforts would generally be unavailing, if they were not combined with those of his fel- lows. His first improvements he acquires from the suggestions of his contemporaries, or from the works of his predecessors, whose rules and demonstrations have been the labour of ages. From the Old Testament, it appears, that the arts and sciences were cultivated to a certain extent, before the flood. Among the offspring of Cain, Jubal was the father of all such as handled the harp and organ ; and Tubal-Cain was the instructor of every artificer in brass and iron. According to Josephus, the poste- rity of Seth also observed the order of the heavens, and the course of the stars. The same author asserts, that the Assyrians and Chaldeans were the first, after the deluge, who applied themselves to the cultivation of the sciences. Their king, Belus, is said to have converted the tower of Babel into an observatory, and upon it to have made many astronomical discoveries. With regard to the origin of Land-Surveying, historians vary in their opinions. Diodorus, Herodotus, and Strabo, attribute the invention of it to the Egyptians ; whom they represent as constrained by the annual inundation of the Nile, removing or defacing their land-marks, to devise some method of ascertaining the ancient boundaries after the waters had retired. By Jose- phus, however, it is ascribed to the Hebrews. According to him, the arts and sciences of Egypt were derived from the pa- triarch Abraham, who conveyed them into that country, from Ur of the Chaldees. The science in question was originally called ' Geometry ;' but this being deemed too comprehensive a title for the men- suration of superficies, it was afterwards denominated ' The Art of Measuring Land.' From the banks of the Nile, it was carried into Greece by Thales, one of the seven wise men, born before Christ 640 years. This philosopher travelled into Egypt, and studied, under its sages, astronomy, geometry, and other branches of the mathe- matics ; but having given offence to king Amasis, by the free- b VI INTRODUCTION. dom of his remarks upon the conduct of princes, he returned home, and employed himself in communicating the knowledge which he had acquired. The great utility of Land-Surveying, without which it is impossible to conduct the affairs of civilized life, induced many of the most celebrated philosophers and mathematicians of an- tiquity to study its principles ; and to Thales, Pythagoras, So- crates, Plato, Aristotle, Euclid, Archimedes, &c. we are indebted for many substantial improvements. The ancient Romans, like- wise, 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 AVork, which, I hope, will be found to contain every necessary in- struction 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 obser- vations. Part the First contains such Definitions, Problems, and Theorems in Geometry, as I conceived to be indispensably ne- cessary in Land-Surveying. Those who desire to see the sub- ject more fully treated, are referred to the Elements of Simp- son, Emerson, Bonnycastle, Keith, Playfair, and Leslie ; to Simson's Euciid, Hutton's Course of Mathematics, and Rey- nard's Geometria Legitima. The last AVork is well adapted to the capacities of Youth ; and contains a number of Quccstiones Solvendw, 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, Cross- Staff, 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 Avith an account of the variation of the Needle, has been given, under the convic- INTRODUCTION. Vll tion 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 ac- quainted 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 frequently adopted by unskilful Surveyors, in computing the contents of Narrow Pieces of Land, and of Onsets. Methods leading to such erroneous results, ought to be discarded by every one who is ambitious 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 Equidis- tant Ordinates, which will be found more easy, expeditious, and accurate, than finding their areas by a succession of tri- angles 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, Avhen disputes took place concernino- 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 sur- veying 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 b 2 Vlll INTRODUCTION. 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 a Remark on the impropriety and injustice of returning the hypothenusal measure of Hills, uni- versally ; although it has been long and strenuously contended for, by Theoretical and Superficial Writers. This Remark, 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 sur- face that is measured, but the diminished quantity which would result, had the whole been reduced to a horizontal plane. This distinction is founded on the obvious principle, that since plants shoot up vertically, the vegetable produce of a swelling 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, com- prising 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 Penta- graph, which instrument far surpasses any other, for that pur- pose. Three different methods of embellishing Plans are given, con- taining directions for shading and colouring Meadows, Pas- tures, Corn-fields, Moors, Marshy Grounds, Sands, Rocks, Trees, Lakes, Rivers, Sea-Shores, Hills, Pleasure- Grounds, Gar- dens, 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 likewise given, in order to shew 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 illustrated by no fewer than nine copper- plates, fourteen wood-cuts, and a neatly engraven Field- Book; and it may not be improper to state, that the Estates INTRODUCTION. IX 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 Sur- veyors, they will please to recollect for whom the Work is de- signed. 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, illus- trated 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 «ver 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. As various customary measures prevail in different Counties, I have given General and Particular Rules for reducing them to statute -measure ; and vice versa. I have also introduced Scotch and Irish Land Measure ; by which the Work becomes adapted to every part of the United Kingdom. Part the Seventh 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 sur- veying, 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, win serve to exercise the genius of the Learner, after he has acquired a competent knowledge of the principles of surveying and di- viding Land, by carefully studying the former part of this Work. Such Questions tend to rouse the latent energies of youth j and to give them a relish for making interesting calcu- lations; and a delight in discovering unknown truths. They b3 X INTRODUCTION. 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. As the Theodolite is sometimes used in surveying Meres, "Woods, Roads, Rivers, and Canals, when angles cannot be taken by the Chain, I have given a description of that instrument ; but as neither it nor the Plane Table are ever used by Pro- fessional Surveyors, when they can avoid it ; and as this Trea- tise is confined chiefly to Chain Surveying, I have not given any directions for measuring either with the Plane Table or the Theodolite. Besides, the expense of these instruments places them out of the reach of a great number of those persons who may be desirous of learning Surveying ; and as most estates may be measured more correctly by the Chain only ; the method of surveying of these instruments would only have tended to enhance the price of this Work, without adding much to its real utility. Levelling is a subject in which Writers on Surveying gene- rally dabble ; but nothing that I have yet seen, deserves the name of a Treatise on Levelling. The only examples worthy of notice, are a few in Jones's Treatise on Mathematical Instru- ments, selected from the Works of Le Febvre. In preparing this Work for the Press, I felt a strong incli- nation to comply with the request of my Friends, by saying something on the subject of Levelling ; but on mature con- sideration, I found that the number of COpper-plates, and the quantity of letter-press necessary to do justice to the subject, would have too much increased the price of the present Work. However, if health and life should permit, I may, perhaps, at some future time, turn my attention to this desideratum. Having given a brief description of the contents of the fol- lowing Work ; it is only necessary to add, that I have endea- voured to treat the whole, to the best of my abilities, not only in a theoretical, but also in a practical manner. 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. INTRODUCTION. XI The engraven Field-Book, being detached from the Sur- veying, 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 ; con- sequently, no information that I conceived to be necessary, has been withheld. In order, however, to make a complete Sur- veyor, the Rules and Directions which I have laid down must be brought into actual use by Field Practice ; not only in mea- suring 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 in- curred, and that the forbearance which I have exercised towards the labours of others, will be exercised towards mine in return. A. NESBIT. Manchester, Aug. 1839. P. S. It may, perhaps, be proper to inform the young reader, that Professor Leslie, whose opinion I have quoted, in the former part of this Preface, concerning the method of measuring Hilly Ground, was late Professor of Mathematics, and is now Professor of Natural Philosophy, in the University of Edinburgh ; and has given to the world several valuable Works, which rank him with the first Mathematicians and Philosophers of the Age. Mr. NESBIT receives into his House a limited number of BOARDERS, for the purpose of Tuition. The Terms of the School and other particulars may be known, by applying to Mr. NESBIT, Oxford Street, Manchester. b 4 aabrrttsrmrnt TO THE SECOND EDITION. The flattering Testimonies which the Author has received, not only from many of the first Teachers and Mathematicians in the kingdom, but also from a considerable number of Pro- fessional Surveyors and Commissioners, concerning the merits of the First Edition of this AVork, have induced him to revise the whole ; and make every Addition and Improvement that he thought would render the Second Edition still more acceptable to his Friends and the Public. Accordingly, it will be found that this Edition is enriched with the addition of five new copper-plates ; forty wood-cuts ; one hundred and ten new questions : and exceeds the former Edition by one hundred and forty pages. And as a much smaller type has been chosen, both for the text and the notes, the ^v~ork, in its present form, contains nearly twice as much matter. The Improvements thus introduced, are dispersed through the whole of the TVork ; but it may be proper to observe, that the method of computing by Equidistant Ordinates ; and of measuring and planning Roads, Rivers, and Canals, did not appear in the former Edition ; and that Part the Fifth has been re-written ; and four of the most approved" methods of surveying large Estates, described ; and also illustrated by copper-plates. The use of the Parallel Ruler, in straightening crooked fences, has likewise been given, in twelve new Problems, comprising every case that can possibly occur in Practice. The description of the Pentagraph, and its use in copying and reducing Plans, have also been added ; together with three different methods of making and ornamenting finished Plans. Much new and valuable Information has been adduced on the method of conducting Inclosures. valuing land, &c. &c. ; and an Abstract of the General Inclosure Act inserted, which will tend greatly to elucidate the subject. Scotch and Irish Customary-Measures have likewise been given ; and also the method of measuring by the Gad ; and of making an estimation of the number of acres contained in a Common, County, or Kingdom. Part the Seventh, describing the method of surveying and planning Villages, Towns, and Cities; and of measuring, planning, and laying-out Building-Ground, is entirely new; and will, the Author is persuaded, be found of essential service to Learners. The Miscellaneous Questions, at the end of this Part, on sur- veving, parting-off, and dividing Land, may also be mentioned among the Additions and Improvements. Bradford, Yorkshire, July. 1820. A. NESBIT. C O N T E N T S. PART I. vJeometrical Definitions • •• ••• •• ... ... l Geometrical Problems ••• -•• •■• ... ... 11 Prob. 1 . To bisect a given line ... ... ... ... 1 1 2. To bisect a given angle ••• ... ... ... 12 3. To draw a line parallel to a given line ... ... ... \o 4. To erect a perpendicular from a given point, near the middle of a given line ... ... ... ... ... 13 5. To erect a perpendicular from a given point, near the end of a given line ... ... ... ... ... 13 6. From a given point, to let fall a perpendicular upon a given line ... ••• ... ... ... ,.. 14 7. To construct a triangle of three given lines ... ... 15 8. Having given the base and perpendicular, to construct a triangle 16 9. To describe a square, whose side shall be equal to a given right line-. ••• ... ... ... ... jg 10. To describe a rectangular parallelogram, whose length and breadth shall be equal to two given lines ... ... 17 11. Upon a given right line, to construct a rhombus ... ... 17 12. With two given right lines, as sides, to construct a rhomboid 18 1 3. With a given base and two given perpendiculars, to con- struct a trapezoid ... ... ... ... ... 13 14. With four given sides, to construct a quadrilateral figure, which has one right angle ... ... ... ... 19 15. With given transverse and conjugate diameters, to construct an ellipse-- ••• ... ... ... ... 19 16. To reduce a given trapezium, to a triangle of equal area ... 20 17. To reduce an irregular polygon of five sides, to a triangle of equal area •■• ••• • •• ... ... 21 18. To raise a perpendicular by a scale of equal parts ... 21 19. To make a right angle by the line of chords on the plane scale 22 20. To make an acute angle ... ... ... ... 22 21. To make an obtuse angle ... ... ... ... 23 22. To find the number of degrees contained in a given angle ... 23 23. To lay down a line making a given angle with the meridian line 24 24. Geometrical Theorems ... ... ... ... 26 PART II The Chain ... ... ... ... ... ... ... 32 The Cross- Staff ... ... ... ... ... ... 33 Xl> CONTENTS. Page. The Offset-Staff ... ... ... ... ... ... 34 The Compass ••• ••• ••■ • •• •• ..35 The Field-Book -•• ... ••• ••• ... ... 36 Directions to young Surveyors, when in the Field, &c. ... ... 37 Directions concerning Scales, laying down Figures, Sac. ... ... 40 PART III. To Survey with the Chain and Cross ... ... ... ... 42 A Table of lineal measures ■•• •-- • •• ... ... 43 A Table of square measures... ... ... ... —44 Prob. 1. Square fields ... ... ... ... ... 45 2. Rectangular fields ... ... ... ... ... 47 3. Triangular fields ... ... ... ... .. 48 4. Fields in the form of a trapezium ... ... ... 51 5. Fields comprehended under more than four straight sides ... 56 6. Fields comprehended under any number of crooked sides ... 66 7. Narrow pieces of land ... ... ... ... 86 8. Meres and woods ... .. ... ... ... 93 9. To find the area of a segment of a circle, or any, other curvi- lineal figure by means of equidistant ordinates .. . ... 97 10. To find the breadth of a river ... ... .. ... 107 1 1 . Lines, upon which there are impediments not obstructing the sight ... ... ... ..7 ... ... 108 1 2. Lines, upon which there are impediments obstructing the sight ... ... ... ... ... . . 109 PAR T IV. To Survey with the Chain only ... ... ... ... 110 MisceUaneous instructions ... .. ... ... ..110 Prob. 1. Triangular fields ... ... ... ... ... Ill 2. Fields in the form of a trapezium ... ... ... 122 3. Fields of more than four sides ... ... ... 142 4. Meres and Woods ... ... . . ... ... 162 5. To measure and plan roads, rivers, canals, &c. ... ... 165 6. To take distances by the chain and scale ... . . 169 7. To erect a perpendicular by the chain ... ... ... 170 8. From the plan of a field, and its true area, to discover the scale by which it has been constructed ... ... 171 To measure hilly ground ... ... ... ... ... 172 Methods used by Practical Surveyors, to reduce hypothenusal to hori- zontal lines ... ... ... ... ... 173 Method I. ... ... ... ... ... ... ... 173 A Table for reducing hypothenusal to horizontal lines ... . . 174 A Quadrant for taking the altitudes of hills, steeples, See. .. ... 175 CONTENTS. XV Page. To take the altitude of a hill with the Quadrant ■•• ••• -.176 To take the altitude of a steeple ... ••• ... ••• 176' Method II. ... ... ... ■■• ... ••• ... 176 To preserve the horizontal line by elevating the chain, in ascending or descending a hill ... ... ... ••• ••• 176 Method III. ••• • •• ••• ••• ••• • • 178 The description and use of King's Quadrant ... •• ••• 178 A Table, by which a Quadrant (invented by the Author) may be con- structed, answering the same purpose as King's •• 181 The construction of the above Table ... ... ••■ ... 182 The construction of the Author's Quadrant ••■ ••• ... 182 The method of proving it • • • • • • • • ■ • • • ... 1 84 The method of applying it in surveying •• • •-• ••• ... 185 Methods for finding the hypothenusal measure of hilly ground . . 186 A remark oil measuring hilly ground ... ... ••• ...191 PART V. To survey farms, large estates, or lordships ... ... ... 195 First method, by triangles ... ••• ... ••■ •• 195 Second method, by running lines nearly parallel to each other ... 198 Third method, by tie-lines, &c ... ... ... ...200 Fourth method, by running lines in the most advantageous manner, without regarding any particular method • • • • - • 200 Miscellaneous instructions relating to running lines, putting down stations, ranging the poles, measuring across valleys, observing the fences, &c. &c. ... ... ••• ••• ••• 201 General rules for planning large surveys ... ••• ... 204 Directions for planning the estate in Plate VIII. ... ... ... 206 Directions for planning the estate in Plate X. ... ... ... 207 Drawing pencils ... ... ... ... ... ... 209 To compute the contents of estates ... ... ... ... 210 The use of the parallel ruler, in reducing crooked fences to straight ones, in order to find the areas of fields by the method of casting ... 211 A general rule for the parallel ruler ... ... ... ... 227 A book of dimensions, castings, and areas, belonging to Plate VIII 228 Ditto, belonging to Plate X. ... ... ... ... ... 230 To transfer a rough plan to a clean sheet, in order to make a finished plan 231 Method I. by points ... ... ... ... ... ... 231 Method II. by tracing paper ... ... ... ... ... 231 Method III. by a copying-glass ... ... ... ... 232 Method IV. by similar squares ... ... ... ... 232 Method V. by the pentagraph •• • ... ... ... ... 234 A description of the pentagraph ... ... ... ... 235 in JTTENTS. The method of using the pentagraph, In copying and reducing plans . . To embellish or fiwMi plain Method I. To finish plans neatly with Indian ink and colours How to choose Indian ink Colours necessary for a Land-Surveyor ... MjmHH EL To finish plans highly with Indian ink and colours T. - ale and colour meado" ; PasttLT-e-rrr^iii C: "-fields ... Moors Marshy ground Sands, rocks, and loose stones Trees Lakes, rivers, and the sea-shore Hilly ground Fissure- rrrurls The elevations of buildings Method III. ... ... ... ..- To finish plans highly with Indian ink only Shadirg with the pen Penmanship... Ornaments on Plate IX. Ditto on Plate XI. ... Miscellaneous ins" "a ting to surveying, planning, eastiz r. luing, ice. &c. ... A :: rrier of the survey in Plate IX. that - 238 238 238 ., -, •241 241 ... .,. .-/. U - :-/ 244 245 ., :-- 248 .:. 250 25 ::. 251 233 PART VI. Directions for laying-out, parting-off, and dividing Land ; and for re- ducing Statute-Measure to Customary, and vice versa ; also Scofaft and Erieh Measures ... ... ... 251 SECTION I. Pbob. 1. To reduce acres, roods, and perches into square links 8 ; '. I : lay out, in a square, any quantity of land proposed Opomagma line, to make a rectangle, which shall contain any proposed quantity of land ... ... '.' 4. To lay out any given quantity of land in a rectangle, so that CONTENTS. XV11 Page, one of its sides shall be two, three, four, or any number of times as long as the other ... ... ... ... 26 1 Prod. 5. Upon a given base, to lay out a triangle that shall contain any given number of acres, &c. ... ... ... ... 262 6. Upon a given side, or base-line, to lay out a trapezium, which shall contain any number of acres ... ... ... 263 7. Upon a given base, to lay out a rhombus of any content less than the square of the base ... ... ... ... 266 8. To lay out any given quantity of land in a circle ... ... 267 9. To lay out any given quantity of land in a regular polygon ... 268 10. To lay out any given quantity of land in an ellipse, with a given diameter ... ... ... ... ... 270 1 1 . To part from a square or rectangle any proposed quantity of land, by a line parallel to one of its sides ... ... 272 12. To part from a square or rectangle any proposed quantity of land, either in a right-angled triangle or trapezoid, by a line drawn from any of the angles to either of the opposite sides 274 1 3. To part from a triangle, upon the base or longest side, any proposed quantity of land, by a line drawn from either of the angles at the base, to the opposite side ... ... 276 14. To part from a triangle any proposed quantity of land, by a line parallel to any of its sides ... ... ... 278 15. To part from a rectangle or triangle any proposed quantity of land, upon a line on which there are offsets, when the area of those offsets is to be considered as part of the portion to be parted off ... ... ... ... ... 279 16. To part from a trapezium, or any irregular polygon whatever, any proposed quantity of land, by a line drawn parallel to any of the sides, or by a line drawn from any of the angles, or from any assigned point in one of the sides, to any of the opposite sides ... ... ... . . ... 282 SECTION II. Prob. 1 . To divide a square or rectangle, either equally or unequally, among any number of persons, by lines parallel to one of its sides ... ... ... ... ... ... 291 2. To divide a triangular field, either equally or unequally, among any number of persons, by fences made from any of its angles to the opposite side ... ... ... ... 292 3. To divide a triangular field, either equally or unequally, among any number of persons, by fences proceeding from any as- signed point in one of its sides ... ... ... 295 4. To divide a triangular field, either equally or unequally, among any number of persons, by fences made parallel to one of its sides ... ... ... ... ... ... 297 XV111 CONTENT.-. Page. Prob. 5. To divide a trapezium, or an irregular polygon, either equally or unequally, among any number of persons, by fences made in a given direction ... ... ... ... 300 6. To divide a common or any quantity of land, of uniform value, among: any number of proprietors, in the proportion of their respective interests ... ... ... ... 304 7. To divide a common, X 2 = 12 — 6" 37. A regular polygon has all its sides and angles equal, "When they are unequal, the polygon is irregular. 38. A circle is a plane figure, bounded by a curved line, called the circumference, which is every where equidistant from a certain point within it, called the centre. Part I.) LAND-SURVEYING. 9 39. The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds. 40. The diameter of a circle is a right line drawn through the centre, and terminating in the circumference on each side ; as A B. 41. The radius of a circle is half the diameter, or it is a right line drawn from the centre to* the circumference ; as A B. 10 LAND-SURVEYING. (Part I. 42. An arc of a circle is any part of the circumference ; as the arc A B. 43. A chord is a right line joining the extremities of an arc ; as the line A B. 44. A segment is any part of a circle hounded by an arc and its chord. 45. A semicircle is half of a circle, or a segment cut off by the diameter ; as A B C. 46. A sector is any part of a circle bounded by an arc, and two radii. 47. A quadrant is the fourth part of a circle, or a sector bounded by an arc and two radii at right angles to each other ; as C D B. Corol. Hence a right angle is said to contain 90°. Note. — All Definitions and Rules should be committed to memory. GEOMETRICAL PROBLEMS. PROBLEM I. To bisect a given Line A B, in n From A and B as centres, with any radius greater than half A B, in your compasses, describe arcs cutting each other in m and n. Draw the line m C n, and it will bisect A B in 0. 12 LAND-SURVEYING. (Part. J. PROBLEM II. To bisect a given Angle A B C. B From the point B with any radius, describe the arc A C. From A and C with the same, or any other radius, make the intersection m. Draw the line B m, and it will bisect the aDgle A B C, as required. PROBLEM III. To draw a Line parallel to a given Line A B, at a given Distance. C i- o -N* m TO. From any two points, m and n, in the given line, with the given distance as a radius, describe the arcs r and o. Draw C D to touch these arcs, without cutting them, and it will be parallel to AB. Note. — This problem may be more readily performed by a parallel ruler. Part I.) LAND-SURVEYING. 13 PROBLEM IV. To erect a Perpendicular from a given Point C, near the Middle of a given Line A B. ?v m. n B On each side of the point C, take two equal distances, C m and C n ; from m and n as centres, with any radius greater than C m or C n, describe two arcs cutting each other in r. Draw the line C r, and it will he the perpendicular required. PROBLEM V. To erect a Perpendicular from a given Point C, near the End of a given Line A B. ,^m x* iix. C B From any point m, as a centre, with the radius or distance C m, describe an arc cutting the given line in C and n. Through n and m, draw a line cutting the arc in r. Draw the line C r, and it will be the perpendicular required. 14 LAND-SURVEYING. (Part I. PROBLEM VI. From a given Point C, to let fall a Perpendicular upon a given Line A B. A. m D a. B X* "With C as a centre, and any radius, a little exceeding the dis- tance of the given line, describe an are cutting A B in m and n. With the centres m and n, and the same or any radius, exceed- ing half their distance, describe arcs intersecting each other in r. — Draw the line C r ; and C D will be the perpendicular required. Note. — The last three problems may be easily performed by a square, or a plotting scale. Fart I.J LAND-SURVEYING. 15 PROBLEM VII. To make a Triangle with three given Lines, any two of ichich must he greater than the third. (Euclid, I. 22. J Let the given lines be A B=10, AC=8, and BC=6 chains. From any scale of equal parts, (which is to be understood as employed likewise in all the following problems,) lay off the base A B. With the centre A, and radius A C, describe an arc. With the centre B, and radius B C, describe another arc, cutting the former in C. Draw the lines A C and B C, and the triangle will be completed. Note. — Any trapezium may be constructed iu the same manner ; having the four sides, and one of the diagonals. 16 LAND-SURVEYING. (Part 7, PROBLEM VIII. Having given the Base, the Perpendicular, and the Place of the Perpendicular upon the Base, to construct a Triangle. Let the base A B=9, the perpendicular C D=5, and the distance A D=6 chains. C A D B Make A B equal to 9, and A D equal to 6. At D erect the perpendicular D C, which make equal to 5. Join A C and B C, and the figure will be completed. Note. — A trapezium may be constructed in a similar manner, by having one of the diagonals, the two perpendiculars let fall thereon from the oppo- site angles, and the places of these perpendiculars upon the diagonal. PROBLEM IX. To describe a Square, whose Side shall be equal to a given right Line. Let the given line A B=4 chains. :3> C A B Upon one extremity B of the given line, by Problem V. er the perpendicular B C, which make equal to A B. erect Tart 1.) LAND-SURVEYING. 17 With A and C as centres, and the radius A B, describe arcs cutting each other jn D. Draw the lines A D and C D, and the square will be completed. PROBLEM X. To describe a rectangular Parallelogram^ whose Length and Breadth shall be equal to two given Lines. Let the length AB = 8, and the breadth B C =: 4 chains. At B erect the perpendicular B 0, which make equal to 4. With A as a centre, and the radius B C, describe an arc ; and with C as a centre, and the radius A B, describe another arc, cutting the former in D. Draw the lines A D and C D, and the rectangle will be completed. PROBLEM XL Upon a given right Line to construct a regular Rhombus, Let the given line A B = 4 chains. 3> JC K A B Draw the line A B, equal to 4. With A and B as centres, and the radius A B, describe arcs cutting each other in D ; then c 1 8 l axd-nl'rve y : Purt I. --.-_ 3 and D as centres, and the same radius, make the Draw the lines AD.D C\ and B C. and the rhombus will be comple: PROBLEM XII. -~ ' ' ' -- 9 .crfren, to construct a Rhomboid* L - 1 :he given lines beABz:*. and BC = 4 chains. D / A b B Draw the fine A B, equal to 7. Take in yonr compasses the fine B C, and lay it from A I : Z — With A and E as centres, and the radius A R, make the intersection D. Then with B as a centre, and the same radius, describe an arc ; and with D as a centre,, and the radius A B. describe another arc, cutting the in C. Draw the lines A D. D C. and B G, and the will be PROBLEM XIII. Hazing tie Base and tie turo PerpmeKemiar 7 _ the base A B=7. and the perpendiculars B C and A D=u and 2 chains respecti _ B Part I.) LAND-SURVEYING. 19 Draw the base A B, equal to 7, and erect the perpendiculars B C equal to 3, and A D equal to 2 chains. Then join D C, and the trapezoid will be completed. PROBLEM XIV. Having the four Sides given, to construct a quadrilateral Figure, which has one right Angle. Let the sides A B=7, B C=4, C D—6, and D A=3 chains ; and let the angle at B be a right angle. A B Draw the line A B, equal to 7 ; and erect the perpendicular B C, equal to 4 chains. With C as a centre, and the radius C D, describe an arc ; and with A as a centre, and the radius D A, describe another arc, cutting the former in D. Draw the lines C D and D A, and the figure will be completed. PROBLEM XV. Having the transverse and conjugate Diameters given, to construct an Ellipsis. Let the transverse diameter A B = 7, and the conjugate diameter CD = 4 chains. 20 land-surveying. (Part I. Draw the two diameters to bisect each other perpendicularly in the centre o. With the radius A o, and the centre C or D, intersect A B, in F and f. — These points will be the foci of the ellipse. Take any point m, in the transverse diameter, and with F and f as centres, and the radius A m, describe the arcs G, G, g, g. Then -with the same centres, and the radius B m, describe arcs cutting the former in the points G, G, g, g : thus will you have four points in the circumference of the ellipse. After this, take a second point n, in the transverse diameter, and proceeding as before, you will determine other four points. — By the same method you may determine as many more as you please ; through all of which, with a steady hand, you must draw the circumference of the ellipse. jsote. — An ellipse may also be constructed as follows: Haying found the foci F, f, as before, take a thread equal in length to the transverse diameter A B, and fasten its ends, with two pins, in the points F, f ; then stretch the thread to its greatest extent ; and by moving a pencil round, within the thread, keeping it always tight you will trace out the curve of the ellipse. The principle upon which this construction is founded, may be seen in Prob, X. Part VL PROBLEM XVI. To reduce a given Trapezium A B C D, to a Triangle of equal Area. D C B E Draw the diagonal D B, and parallel to it draw C E, meeting A B produced in E. Join the points DE; so shall the triangle A D E be equal to the trapezium A B C D. Note . — This and the following Problem may be applied in finding the areas of trapeziums and irregular polygons by first reducingthemto triangles. Part I.) LAND-SURVEYING. 21 PROBLEM XVII. To reduce an irregular Polygon ABCDE, of Jive sides, to a Triangle of equal Area. C Extend the side A E, both ways tit pleasure ; and draw the diagonals C E, C A. Parallel to these diagonals draw the lines D F, and B G ; join the points C F, G G ; and G C F will be the triangle required. Note. — Any irregular polygon of more than five sides, may be brought to a triangle of equal area, by reducing it successively to a figure with one side less* until you bring it to a figure of three sides. Thus the trapezium A B C F, or G C D E is equal to the polygon A B C D E, as well as the triangle G C F. PROBLEM XVIII. To raise a Perpendicular from any point D, in a given Line A B, by a Scale of equal Parts. C f 5/ 30L m 3 c 3 D B 22 LAND-SURVEYING. (Part I. Make D m •=. 3 ; and from the points D and m, with the dis- tances 4 and .5, describe arcs intersecting each other in n. From D, through the points n, draw the line D C, and it will he the perpendicular required. Note. — This Problem may be performed by any other numbers in the same proportion ; but 3, 4, and 5, are the least whole numbers that will make a right-angled triangle. PROBLEM XIX. To make a right Angle by the Line of Chords on the plane Scale. JE. C D B Draw the unlimited line A B ; then take in your compasses 60° from the line of chords, and with A as a centre, describe the arc E D. Take 90° from the same scale, and set off that extent from D to C. Draw the line A C ; and CAD will be the angle required. PROBLEM XX. To make an acute Angle equal to any Number of Degrees ; sup- pose 33° 30'. E S D B Draw the unlimited line A B ; then take 60° in your com- passes, and with A as a centre, describe the arc E D, Then set off 90° from D to C ; and from C to G set off the excess above 90°, which is 35° 30'. Draw the line AG; and G A D will be the angle required. PROBLEM XXII. Tojind the Number of Degrees contained in any given AngWB A. C C With the chord of 60°, and A as a centre, describe the arc m n. Take the distance m n in your compasses, and apply it to the line of chords ; and it will show the number of degrees required. Note. — Angles may be more expeditiously laid down or measured by means of a semi-circle of brass called a Protractor, the arc of which is divided into 180 degrees. c 4 24 LAND-SURVEYING. 'Part I. PROBLEM XXIII. To lay dowcn a Line making a aire* Angle ttiik the or X&rtk and SoutA Lime. 1. Lt: if be required to lav down a line that ranges N. E . ™«lrmg an angle of 45°, with the meridian line. (See the Draw the meridian Ene A N ; and with the sweep 1 1 in your compasses, taken from the line of chords, and A as a centre, descrihe the arc B C. Set off the given angle 45°, from B : : C : draw the line AC^ and it will range X. E. Aafe.— If the Hue had ranged >". W, the angle must have bees set off on the other siio of the meridian A N : and AD would h*Te been the Part I.) LAND-SURVEYING. 25 2. Lay down a line that ranges S. W. b. W., making an angle of 56° 15', with the meridian line. Draw the meridian line A S ; and with the sweep of 60° describe the arc E F. Set off 56° 15' from E to F ; draw the line A F, and it will range S. W. b. W., as was required. Note 1. — If the line had ranged S. E.b.E., the angle must have been set off from E to G ; and A G would have been the direction of the line. 2. — This Problem will be found useful to young Surveyors, in laying down the first line, the range of which should be taken in the field by a compass. GEOMETRICAL THEOREMS. T'^Dz-. lay besee Elements of Euclid. Simpson, and Emerson. THEOREM I. I B two =:raight lines A B. C D. cut each other in the point E, the an^r A E C ^21 be equal to the angle DEB.andC E B to A E B. ' Ewr.il I. 15 Simpson La Emerxm L 2 J THEOREM II. He gmatori side ■:: evarj :riangle is opposite to the greatest i^r'-f-, 'iT:-::. I. IS, >':.;: . I. 13. E .. II. 4.^ THEOREM III. Let the right line E F fall upon the parallel right lines A B, C D ; the alternate angles A G- H. G H D are equal to each other j and the exterior angle E G B is eqaal to the interior and opposite, upon the same ride G H D : and the two interior angles B G H, G H D. upon the same side, are together equal to nvo right angles, (E :,-;. I. .? v L ?. -£*;/;, I. -i.^ E A i B G - D \ F Part I.) LAND-SURVEYING, 27 THEOREM IV. Let A B C be a triangle, and let one of its sides B C be pro- duced to D ; the exterior angle A C D is equal to the two in- terior and opposite angles CAB,ABC; also the three interior angles of every triangle are together equal to two right angles. (Euc. I. 32. Simp. I. 9. $ 10. Em. II. 1 $• 2 J THEOREM V. Let the parallelograms ABCD, DBCEbe upon the same base B C, and between the same parallels AE,BC; the paral- lelogram ABC D, is equal to the parallelogram D B C E. ( Euc. I 35. Simp. II. 2. Em. III. 6 J A D E THEOREM VI. Let the triangles A B C, D B C be upon the same base B C, and between the same parallels AD,BC; the triangle A B C is equal to the triangle D B C. (Euc. 1, 37. Simp. II. 2. Em. II. 10 J D 88 VKVEYING. Par: I THE REM VII. A B C be a right-angled triangle, Baring die right angle lare of the side 6 C is equal to the sum of the squares of the sides A B. A _Z" I ' Simp. II 5. .Cni.IL 81 THEOREM VIII. Let A I a circle, and B D C an angle of the centre, and B A C al ::r their base; the angle B D C is doable of die angle ba>: ::: : 5wny.in.io. £■*.!?. 12 THEOREM IX Let A B C be a semi -circle ; then the ■■ mi l i ii h, is a rish: angle, 'Ems. III. SI : B A B C in Ant Simp III . Part I.) LAND-SURVEYING. 29 THEOREM X. Let D E be drawn parallel to B C, one of the sides of the triangle ABC; then B D is to D A, as C E to E A. ( Euc. VI. 2. Simp. IV. 12. Em. II. 12 J A D B THEOREM XI. In the preceding figure, D E being parallel to B C, the trianoles A B C, A D E are equi-angular or similar ; therefore A B is to B C, as A D to D E ; and A B is to A C, as A D to A E. (Euc. VI. 4. Simp. IV. 12. Em. II. 13.J THEOREM XII. Let A B C be a right-angled triangle, having the right angle BAC; and from the point A let A D be drawn perpendicularly to the base B C ; the triangles A B D, A D C are similar to the whole triangle A B C, and to each other. Also the perpendicular ADisa mean proportional between the segments of the base ; and each of the sides is a mean proportional between the base and its segment adjacent to that side ; therefore B D is to D A, asD AtoDC;BCistoBA,asBAtoBD; andBCistoCA, as C A to C D. (Euc. VI. 8. Simp. IV. 19. Em. VI. 17 J THEOREM XIII. Let A B C, A D E be similar triangles, having the angle A common to both ; then the triangle A B C is to the triangle 30 land-surveying. (Part I. A D E, as the square of B C to the square of D E. That is similar triangles are to one another in the duplicate ratio of their homologous sides. ( jEuc.VI.19. Simp.IY. 24<. E?n.ll.l8.J THEOREM XIV. In any triangle ABC, double the square of a line C D, drawn from the vertex to the middle of the base A B, together with double the square of half the base A D or B D, is equal to the sum of the squares of the other sides A C, B C. (Simp. II. 11. Em. II. 28. J C THEOREM XV. In any parallelogram A B C D, the sum of the squares of the two diagonals A C, B D, is equal to the sum of the squares of all the four sides of the parallelogram. (Simp. II. 12. Em. III. 9. ) D C THEOREM XVI. All similar figures are in proportion to each other as the squares of their homologous sides. (Simp. IV. 26. Em. III. 20. ) THEOREM XVII. The circumferences of circles, and the arcs and chords of similar segments, are in proportion to each other, as the radii or diameters of the circles. (Em. IV. 8^-9.^ Part I.) LAND-SURVEYING. 31 THEOREM XVIII. Circles are to each other as the squares of their radii, diame- ters, or circumferences. (Em. IV. 35. ) THEOREM XIX. Similar polygons described in circles, are to each other, as the circles in which they are inscribed ; or as the squares of the diameters of those circles. ( Em. IV. 36. ) THEOREM XX. All similar solids are to each other, as the cubes of their like dimensions. (Em. VI. 24.J LAND-SURVEYING. A Description of the Chain, Cross-Staff, Offset-Staff, Compass, and Field-Book ; also Directions and Cau- tions to young Surveyors, when in the Field, fyc. THE CHAIN. JLjand is commonly measured with a Chain, invented by Mr, Gunter, which is known by the name of " Gunter's Chain." It is 4 poles, 22 yards, or 66 feet in length, and divided into 100 equal parts, called links ; each link being 7.92 inches. At every tenth link from each end, is fixed a piece of brass, with notches or points; that at 10 links having one notch or point; at 20, two ; at 30, three ; and at 40, four points. At 50, or the middle, is a large, round, plain piece of brass. The chain being thus marked, the links may be easily counted from either end ; the mark at 90, 80, &c. being the same as that at 10, 20, &c. Part of the first link, at each end, is made into a large ring or bow, for the ease of holding it in the hand. The chain should always exceed 22 yards, by an inch and half, or two inches ; because, in surveying, it is almost impos- sible to go in a direct line, or to keep the chain perfectly stretched. Long arrows likewise keep the ends of the chain a considerable distance from the ground ; the lines, consequently, will be made longer than they are in reality. Part II) LAND-SURVEYING. 33 Chains, when new, are seldom a proper length ; they ought always, therefore, to be examined ; as should those, likewise, which are stretched by frequent use. Note 1. — In folding up the chain, it is most expeditious to begin at the middle, and fold it up double. When you wish to unfold it, take both the handles in your left-hand, and the other part of the chain in your right ; then throw it from you, taking care to keep hold of the handles. You must then adjust the links before you proceed to measure. 2. — Chains, which have three rings between each link, are much better than those which have only two ; as they are not so apt to twist. THE CROSS-STAFF. The Cross-Staff is an instrument used in the field by sur- veyors, to erect perpendiculars, and may very easily be made in the following manner. Procure a piece of board about 6 inches square, either of sycamore, box, or mahogany. Draw the two diagonals ; and at their extremities fix four small studs or pins, which will serve as sights to direct to any object or angle. Or, instead of studs or pins, you may saw two fine grooves at right-angles, about a quarter of an inch deep, in the board. This being fixed upon a staff, of a convenient length for use, pointed with iron at the bottom to enter the ground readily, the instrument is called a cross-staff. Note 1. — The cross must be fixed upon the staff by a screw, in such a man- ner that it may be easily turned without moving the staff. 2. — The cross may be made of a circular piece of board ; you must then draw two diameters crossing each other at right-angles. The fourth part of a square, or of a circle, will answer the purpose equally well. 3. — Great care ought to be taken in making this instrument, as its accuracy depends on the sights, or grooves being at right-angles with each other. D 34 land-surveying. (Part lis b c \ /] a / \ 1 11 Suppose a b c d, to represent a cross, and the groove a c to be directed to an object at m ; then, "will the groove b d point to another at n. Reverse the direction of the grooves, so that b d may be in the direction of m; then, if a c be in the direction of n, the instrument is correct. THE OFFSET-STAFF. The Offset-Staff is an instrument used to measure short distances ; and may be in length. 10, 12, or 15 links. It would be advisable to number the links from each end, on opposite sides, with the figures, 1, 2, 3, Sec. as the staff, thus marked, will be more convenient for use. Note. — As the Cross-Staff is sometimes thought incommodious, a small pocket-cross may be so contrived as to be readily fixed, upon occasion, to the Offset-staff. This may be most expeditiously accomplished by means of a hole made through the cross, admitting the top of the staff, to the eighth link, counting from the bottom or piked end ; at which place there must be attached a small shoulder, upon which the cross will rest. Plate I. of. tic and / ///r ? //>',//,' '//////'// sv/f//fSf'//// ///////r.j ' ^rithtlioMrricliaii. Part II) LAND-SURVEYING. 35 THE COMPASS. The Compass is an instrument used by surveyors, to point out the range or direction of lines ; and also to shew the bear- ings of objects. The circumference of the card of the compass contains 360°, and is divided into thirty-two equal parts, called Points, each containing 11° 15'. Of these, the four principal (namely East, West, North, and South) are called Cardinal Points ; from which the names of the others are derived. To the under-side of the card, and in the direction of its north and south lines, is attached a magnetic bar of hardened steel, called the Needle, by which the north-point is directed toward the northern part of the horizon ; and the other points, conse- quently, to their corresponding ones in the heavens. The card and needle are suspended on an upright pin, called the Supporter, which is fixed in the bottom of a brass, or wooden, box ; and the whole is covered with a plate of glass to prevent the action of the wind upon the card. Although the compass is divided into thirty-two points, yet surveyors reduce them to eight, namely, the four cardinal, or chief points ; and the four midway between them ; viz. the north-east, north-west, south-east, and south-west, which may be expressed by their initial letters, as E., W. 5 N., S. ; N E., N TV., S E., S. W. Note 1. — A small pocket-compass may be procured for about five shillings, which will answer the purpose of a surveyor ; but for the sake of those who may not possess such an instrument, the following methods of finding a meri- dian line, &c. are given. When a surveyor enters a field, let him call that side, which is next the sun rising, east ; then will the opposite side be west ; and, in measuring from the east to the west, he will have the north on his right-hand, and the south on his left. If his direction should lie between any two of the above points, as for example, between the north and the west, he may call the range of the line north-west, &c. This method will suffice, when a correct plan is not required. A true meridian, or north and south line, may be found by observing which line or fence points accurately toward the sun at noon, he being then upon the meridian, or full south. Lines, at right-angles to this meridian line, are east and west. d 2 36 land-surveying. (Part II. 2. — The north point of the compass does not point exactly to the north-point of the horizon ; but inclines, in some places toward the east, and in others to- ward the west ; and this inclination is called the variation of the compass. In most parts of England, the variation is, at this time, more than 24° westerly ; so that the true range of any line, or the bearing of any object, will be above two points more toward the east than what is indicated by the conr This wonderful phenomenon has perplexed our greatest philosophers ; neither Halley, nor the immortal Newton, having been able satisfactorily to account for it. 3. — Some compasses have the cards attached to the bottom of the boxes, and the needles only are suspended upon pins. When this is the case, place the Compass in such a manner that the north -point of the needle may rest 24° to the west of the north-point of the card ; and you will thus make an allow- ance for the variation ; for in this situation of the Compass, all the points on the card, will be in their true positions. 4. — It is necessary sometimes to get the needle of the Compass retouched with the magnet, in order that it may traverse properly ; as the power of the magnet, on the needle, has a tendency in lapse of time, to decrease. THE FIELD-BOGK. Scarcely any two surveyors set down their field-notes exactly in the same manner. The method, however, now generally adopted, and which is certainly preferable to all others, is to begin at the bottom of the page and write upward. Each page of the book must be divided into three columns. In the middle column must be set down the distances on the chain-line at which any mark, oifset, or other observation is made : and in the right and left-hand columns respectively, those marks, o:Fse:>. an 1 observations must be entered. The crossings of fences, rivers, &c. may be denoted by lines drawn across the middle column, or part of the right and left- hand columns, opposite the distances on the chain-line, at which they are crossed ; and the comers of fields, and other remarkable turns in the fences, to which oixsets are taken, may be denoted by lines joining or lying in the same relation to the middle column, as the fences. &c. do to the chain-line. Part II.) LAND-SURVEYING. 37 Thus a tolerably accurate representation of the fences, &c. may be sketched in the held, which will very much assist the surveyor in drawing the plan. With respect to the characters used to denote stations, the letters of the alphabet will do very well, in small surveys ; but in those of a larger extent, numeral figures must be used, and the sign -f- (plus) placed before each figure ; thus, + 1, or -f 2, which may be read, station first, or cross first ; station one, or cross one, &c. Upon the plan they are generally represented by this ( ) mark. Most surveyors take the exact range of the first line, and enter it in their field-book ; and from it the range of any other may be easily determined. This method I shall adopt in the following work. The expression, R. off B, or L. off B, &c. denotes that you are to turn to the right or left-hand, and measure from B, &c. Note 1. — Many surveyors not only begin at the bottom of the field-book, but also at its right-hand side, and write toward the left, which method I always follow myself. 2. — It is useful for a beginner to draw a rough sketch of the field, or estate which he is about to measure ; and upon it, to note the stations in the same manner as they are put down in taking the survey. This will materially assist his memory in planning. 3, — The field-book, for practical use, should be made convenient for the pocket, and interleaved with blotting-paper. 4. — The field-notes should always be set down with ink, which may be carried in a bottle suspended from a button of your waistcoat. Double foun- tain-bottles, such as are used by excise officers, are the best. DIRECTIONS and CAUTIONS to YOUNG SUR- VEYORS WHEN IN THE FIELD, #C. In addition to the instruments already described, you must provide ten arroAvs, each about a foot in length, made of strong wire, and pointed at the bottom. These should be bent in a circular form at the top, for the convenience of holding thenu and a piece of red cloth should be attached to each, that they may be more conspicuous among long grass, &c. d3 38 LAND-SURVEYING. (Part II. Poles, likewise, generally called Ranging-poles, or Station- staves, will be wanted as marks, or objects of direction, each about ten feet in length, piked with iron at the bottom ; and haying a red or white flag at the top, that they may be better seen at a distance. Thus equipped, and having entered the field, or estate which you are about to survey, first, make your- self acquainted with its form ; and then consider in what manner you must run your lines, according to the directions hereafter given in Parts Third, Fourth, and Fifth : after which you must proceed in the following manner. Let your assistant or chain-leader take nine arrows in his left- hand, and one end of the chain with one arrow in his right ; then, advancing toward the place directed, at the end of the chain, let him put down the arrow which he holds in his right- hand. This the follower must take up with his chain-hand, when he comes to it ; the leader, at the same time, putting down another at the other end of the chain. In this manner he must proceed until he has put down his tenth arrow ; then, advancing a chain farther, he must set his foot upon the end of the chain, and call out, " change." The surveyor, or chain- follower, must then come up to him, if he have no offsets to take, and carefully count to him the arrows; and one being put down at the end of the chain, proceed as before, until the whole line be measured. Each change ought to be entered in the field-book, or a mistake of 10 chains may happen, when the line is very long. The chain-follower ought to be careful that the leader always puts down his arrow perpendicularly, and in a right-line with the object of direction ; otherwise the line will be made longer than it is in reality. The follower may direct the leader by the motion of his left -hand ; moving it to the right or left, as cir- cumstances require, and always placing his eye and chain-hand directly over the arrow which is stuck in the ground. The leader likewise, as soon as he has put down his arrow, ought to fix his eye upon the object of direction, and go directly toward it. This he may easily effect by finding a tree or a bush beyond the station to which he is going, and in a straight line with it and himself. Part II.) LAND-SURVEYING. 39 In hilly ground, if the follower lose sight of the mark toward which he is going, he must stand over his arrow ; and the leader must move to the right or left, till he sees the follower in a direct line between himself and the mark from which they last departed. The surveyor ought to put down at each station a small stake, called a station-stake, with the number of the station upon it ; so that any of the stations may be readily found, if there be occasion to measure the distance between two of them, as a tie or proof-line, &c. In large surveys, there must be a cross cut in the ground, at each station, making right-angles with the chain-line ; so that, if the stake should be pulled up, the cross may still re- main, and serve as a director. When a survey is taken with an intent to draw a finished plan, all remarkable objects should be noted down in the field- book ; as roads, stiles, gates, trees, &c. If the surveyor can conveniently procure two assistants, the one to lead the chain and the other to follow it, it will be much to his advantage ; as he will thus be left at liberty to take offsets, note down dimensions, &c. without loss of time. He ought always to observe to whom the boundaries belong. If the ditch be in the field which he is about to measure, both it and the hedge usually belong to the adjoining field. This, however, is not always the case ; as it sometimes happens that the hedge is on the reverse side of the ditch. It is advisable, therefore, to inquire of some person resident on the spot, con- cerning the hedges, &c. In some places, 3 feet from the roots of the quickwood are allowed for the breadth of the ditches ; in some 4, in some 5, and in some 6 ; but 4 feet, or 6 links, are commonly allowed for ditches between neighbouring estates, and 7 links for ditches adjoining roads, commons, waste lands, &c. The ditches and fences must always be measured with the fields to which they belong, when the whole quantity of land is required ; but in measuring crops of corn, turnips, &c. only so much must be measured as is, or has been occupied by the corn, &c. n 4 40 LAND-SURVEYING. (Part II. Upon the surveyor depends all the care of measuring, re- marking, noting down, &c. It absolutely behoves him, there- fore, to be, not only particularly careful in his entries, and correct in his dimensions ; but also extremely accurate in his constructions and calculations. Note. — The line in which you have the misfortune to lose an arrow, must be remeasured. DIRECTIONS CONCERNING SCALES, LAYING DOWN FIGURES, ftc. Any scale of equal parts may be used in planning, or laying down figures ; but that, which is most convenient for use, is the ivory plotting-scale, so divided on its edges, that you may prick off distances by laying it upon the line. In la}dng down an offset by the plotting-scale, it is best, first, to prick off the base-line ; and then upon it make a small pencil dot at every place where a perpendicular must be erected. This being done, lay the scale across the base, so that the line which goes across the scale, marked with oo, may coincide with it, the edge of the scale at the same time touching one of the dots. From the dot, by the edge of the scale, draw a line, (which will be perpendicular to the base,) and upon it prick off the offset ; or it may be pricked off without drawing a line. Proceed thus, till all the perpendiculars are erected ; and then draw the fence through each of their extremities. If the fence be curved, it must be drawn by a steady hand, in the same manner as the circumference of an ellipse. (See page \§.) In planning, or laying down figures relating to surveying, the upper part of the paper or book used should always, if possible, represent the north. All the fences and chain-lines should first be pencilled : the first should then be drawn, and the latter dotted with ink. Great accuracy is required in the construction of figures, when the perpendiculars, &c. are to be measured by the scale. The lines should be very fine ; the dots at the stations very small ; and the points of the compasses very sharp, in order that distances may be taken from the scale with the utmost correctness. The scale should never be smaller than Part III.) LAND-SURVEYING. 41 two chains to an inch ; for when its divisions are large, figures may be constructed with much more accuracy, and their per- pendiculars, &c. measured with much greater exactness. After having found the area of any field or estate, you may, however, lay it down by any scale that will reduce it to a more convenient size. Or you may divide the dimensions by 2, 3, 4, &c. in order to make them of a proper size to be laid down by a scale of 2, 3, or 4 chains to an inch. Note 1. — A plotting-scale divided into two chains to an inch on one of its edges, and four on the other, is perhaps most useful for a school-boy ; but practical surveyors prefer those which have both their edges divided in the same manner, because they are more convenient in planning ; and a mistake cannot be made by using one edge instead of the other. 2. — An instrument called a Pricker, which may be made by putting a fine needle into a wooden haft, is used by some persons, in pricking off distances from the plotting-scale ; but a hard black-lead pencil, finely pointed, is pre- ferable, because it does not injure the paper. LAND-SURVEYING. Part t$t 8$trfc To Surrey witk the Chain and Cross; also, to Measure Meres, Woods, and Lines upon which there are Impediments. \^ o>tor jiablt to a statute of 34 Henry VIII. an acre is equal to 10 square chains ; that is, 10 chains in length and 1 in breadth; or 820 X 22 = 4840 spare yards; or 40 x 4 = 160 square rods, poles, or perches, A statute-pole or perch is 16^ feet long; but in different parts of the kingdom there are, by custom, poles of different lengths; as 15, IS, 21 feet, 6cc. The various dimensions of a piece of land are taken in lineal measure, from which its area or content is calculated. Nate. — The method of reducing statute -measure to customary, and the contrary, may be seen in Part the 5 Part III.) LAND-SURVEYING, 43 A TABLE OF LINEAL MEASURES. Inches. 7.92= Link. 1 12 1.5151 = Foot. 1 Yard. 1 36 4.5454 3= Stat. 198 25 16.5 5.5= Perch. 1 Chain. 1 792 100 66 22 4= 7920 1000 660 220 40 10= Furl. 1 63360 8000 5280 1760 320 80 8 = Mile. 1 Note. — Seven yards make one rood of fencing or ditching. 44 LAND-SUKVEY1NG (Part III. A TABLE OF SQUARE MEASURES. .a 5 T— 1 X IT « SO r- 1 o CD CO HIS *^ S (H ■"f *o 00 t= s *> CO «5 CM ^ CO ""I CD —J CD © Part III.) LAND-SURVEYING. 45 PROBLEM I. SQUARE FIELDS. TVhen you enter a field which has the appearance of a square, (for few are accurately such,) fix your cross-staff in a corner of it, and if the two sides be at right-angles, measure one of them, and enter its dimensions in your field-book. Pro- ceed in like manner with each angle and side ; and if you find all the angles right-angles, and all the sides equal, the figure is a square. TO COMPUTE THE CONTENT. Rule. — Multiply the side into itself, and the product will be the area, in square links. Cut off five places as decimals, toward the right-hand of the product, and those on the left will express the number of acres. Reduce these decimals into roods and perches, by multiplying them successively by 4 and 40, and cutting off five figures on the right as before, in each product. If the dimensions be in yards, divide the square of the side by 4840, and the quotient will be acres. Reduce the remainder, if any, into roods and perches, by multiplying it successively by 4 and by 40, as before. Note 1. — Any person who is not in possession of a chain, may take the dimensions in yards, Avhere accuracy is not required. 2. — In measuring with the chain, it is best to set down the number of links, as 956 : where, instead of reading 956 links, read 9 chains and 56 links. 3. — The dimensions of small parcels of land, sold by the square yard, for building, &c. should be taken in feet and inches, with a measuring-tape. Paving, digging, &c. should be measured in the same manner. 4. — In computing the contents of fields, it is customary, among practical surveyors, to call the remainder a perch, if it exceeds half a one ; but if it be less than half a perch, it is considered as nothing. 5. — The learner should carefully work over, and put down all the solutions given in this book, in order that he may better understand the different methods of calculation. 46 LAND-SURVEYING. (Part III. EXAMPLES. 1. What is the area in acres of the square ABCD, whose side is 956 links ? D C 5736 4780 8604 9.13936 4 .55744 40 22.29760 Area 9a. Or. 22p. 2. Required the area in acres of the square, whose side 264 yards. 264 264 1056 1584 528 4840)69696(14 4840 21296 19360 7T936 4 4840)7744(1 4840 2904 40 484,0)11616,0(24 968 1936 1936 Area 14a. 1r. 24p. Part 111.) LAND-SURVEYING. 47 3. If the side of a square be 1567 links; what is its area in acres f Ans. 24a. 2r. 9p. 4. If the side of a square be 263 yards ; what is its area in acres? Ans. 14a. 1r. 6p. PROBLEM II. RECTANGULAR FIELDS. When you enter a field which has the appearance of a rec- tangle, try each angle, and measure each side, as before ; and if you find all the angles right-angles, and the opposite sides equal, the figure is a rectangle. TO COMPUTE THE CONTENT. Rule. — Multiply the length by the breadth, and the product will be the area. EXAMPLES. 1 . What is the area of the rectangle A B C D, whose length A B is 1235 links, and breadth A D, 557 links ? D C B 1235 557 8645 6175 6175 6.87895 4 3.51580 40 20.63200 Area 6a. 3r. 21p. 48 land-surveying. (Part III. 2. Required the area of a rectangle, whose length is 235, and breadth 162 yards. 235 162 470 1410 235 484,0)3807,0(7 3388 .419 4 484)1676(3 1452 . 224 40 484)8960(18 484 4120 3872 . 248 Ans. 7a. 3r. J8p. 3. The length of a rectangular field Is 1225 links, and its breadth 613 links ; required the plan and area. Area 7a. 2jr. 1p. 4. If the length of a rectangle be 135, and breadth 50 yards ; what is its area ? Ans. 1a. 1r. 23p. Note. — As squares and rectangles seldom occur in surveying, it is much more expeditious to treat every field of four sides as a trapezium. (See Problem 4.) PROBLEM III. TRIANGULAR FIELDS. When you have to survey a field in the form of a triangle, set up a pole at each comer, when there are no natural marks. Then measure along the base till you come to the point, where you think a perpendicular will fall from the opposite angle. There plant your cross, and turn its index till the mark at each Part III.) LAND-SURVEYING. 49 end of the base can be seen through one of the grooves. Then apply your eye to the other groove, and if you see the mark at the opposite angle, you are in the right place to measure the perpendicular ; if not, move the instrument backward or for- ward, along the line, till you can see the three marks as above directed. Enter in your field-book the distance from the end of the base to the cross, and the length of the perpendicular. Then measure the remainder of the base. Note 1 . — Be especially careful, that in measuring the two parts of the base and the perpendicular, no confusion of arrows take place. 2. — In finding perpendiculars by the cross, you must always proceed as above directed. CONSTRUCTION. Having the place of the perpendicular, the figure may be easily constructed, as follows. From any scale of equal parts, lay off the base ; erect the perpendicular at its proper point ; draw a line from each end of the base to the end of the perpen- dicular, and the figure will be completed. Note. — Having the diagonal, the two perpendiculars, and the place of each perpendicular given, you may construct any trapezium in the same manner. TO COMPUTE THE CONTENT. Rule. — Multiply the base and perpendicular together, divide the product by 2, and the quotient will be the area. Or, multiply half the base by the whole perpendicular, or the whole base by half the perpendicular, and the product will be the area, examples. 1. It is required to survey the triangular field ABC, and to find its area. 50 LAND-SURVEYING. (Part III. B Measure from A toward C, and when you come to m, for instance, at 935 links : try with your cross; and if this be the point for the perpendicular, measure m B = 62.5 links. Return and measure m C = 628 links, making the whole base = 156'3 links ; then construct the figure, and find its area. 1563 base. 625 per. 4.88437 4 3..53N- 40 21.49920 Area 4a. 3r. 21 p. 2. The distance between the beginning of the base, and the place of the perpendicular is 125. the perpendicular 82, and the whole base 318 vards ; what is the area of the triangle Part III.) LAND-SURVEYING. 51 318 base. 82 per. 636 254*4, 2) 26076 4840)13038(2 9680 3358 4 4840)13432(2 9680 3752 40 484,0)15008,0(31 1452 ..488 484 77i Ans. 2a. 2r. 31 p. 3. Measuring along the base of a triangle 862 links, I found the true place of the perpendicular, and the perpendicular itself = 995 links ; the remainder of the base measured 1110 links; what is the area of the triangle ? Ans. 9a. 3r. 10p. 4. Measuring along the base of a triangular field, I found the perpendicular to rise at 865, and its length 645 links ; the re- mainder of the base measured 569 links; required the plan and area. Area 4a. 2r. 2 Op. Note. — If the examples in this Problem, or any of the following Problems, be thought too few, more may easily be supplied by the Teacher sketching fields, at pleasure, with his pen, which the Learner may measure by a scale. This method will be found very advantageous ; as it will give the Learner a good idea in what manner he must run his lines, take his dimensions, and enter his notes, when he commences field-practice. PROBLEM IV. FIELDS IN THE FORM OF A TRAPEZIUM. A quadrilateral field, having unequal sides, may be surveyed by measuring a diagonal. This divides it into two triangles, to each of which it serves as a base. e 2 52 LAND-SUIIVEYIXG. (Part III. TO COMPUTE THE CONTENT. Rule. — Multiply the sum of the two perpendiculars by the diagonal, divide the product by 2, and the quotient will be the area. Note 1. — Always make choice of the longer diagonal, because the longer the base line of a triangle, the more obtuse is its subtending angle ; and, conse- quently, there is the less chance to mistake, as the perpendicular will be shorter, and its place more easily and more accurately determined. After finishing the surveying, if you choose, measure the other diagonal, which will enable you to prove your work. (See Problems I. and II. Part I V.J 2. — If a field be very long, or elevated in the middle, so that you cannot see from one end to the other, it may be divided into two, or more trapeziums. Or you may range your lines over the hill, as directed in Part the Fifth. 3. — When two perpendiculars cannot be taken upon either of the diago- nals, such fields must be divided into two triangles by measuring a diagonal for the base of one triangle, and one side of the field for the base of the other. (See Example VI.) 4. — Unskilful surveyors affect to reduce trapeziums into squares, or rect- angles, by measuring all the sides, adding each two opposite sides together, and taking half their sum respectively for a mean length and breadth ; but this method leads to very erroneous results. (See Part IV. Prob. 2.) EXAMPLES. 1. It is required to survey the trapezium A B C D, and find its area. Part III.) LAND-SURVEYING. 53 Measure from A toward C. Finding the perpendicular* a B to rise at 473, and its length 437 links ; return, and continue toward C, till you come to the place where the second perpen- dicular b D rises. There note down its distance from A, 1128 links ; measure b D = 508 links ; then complete the measuring of the diagonal to C, and let the whole be 1490 links. After this, measure the diagonal B D, for a proof-line, which you will find 1152 links. 437) 508JP ei - .945 sum. 1490 diag. 85050 3780 945 2) 1408050 7.04025 4 0.16100 40 6.44000 Area 7a. Or. 6p. 2. In taking the dimensions of a trapezium, I found the first perpendicular to rise at 539, and to measure 725 links ; the second at 1890, and to measure 832 links; the whole diagonal measured 2456 links; required the area of the trapezium? Ans. 19a. Or. 19p. 3. The first perpendicular of a trapezium rises at 467, and measures 545 links; the second at 1418, and measures 467 links; required its area, the whole diagonal being 1840 links ? Ans. 9a. 1r. 9p. 4. Lay down a field, and find its area, from the following notes. A D 1625 1252 523 CL B 639 636 Begin at A. Range W. . on the left. Base Line or Per. on the right. Diag. • Area 9a. 1r. 30 £ p. E 3 54 LAND-SURVEYING (Part III. 5. Required the plan and area of a field, from the following dimensions. A D Diag. 1744 545 1365 546 6.52 B. egin at A. Range E. Area 10a. 1r. 30p. >. Lay down a field, and find its area from the following notes. D B 1095 488 L. off D. AD 1358 B .532 410 Be^in at A. Diag. 298 C. Side. Ranee E, Answer. Double areas. 7224.56 Triangle A B D. 326310 Triangle BCD. Whole area ,5a. Or. 39p. ANOTHER METHOD. A field of four sides may sometimes be surveyed by dividing it into two right-angled triangles, and a trapezoid. TO COMPUTE THE CONTENT. Rule. — Multiply the sum of the two perpendiculars by their distance upon the base-line, and the product will be double the area of the trapezoid. The area of each triangle must be found as before . Part 111.) LAND-SURVEYING. 55 EXAMPLES. 1. It is required to survey the annexed figure, and find its area. C Measure the base A D, and enter in your field-book where the two perpendiculars rise, &c. as in the following notes. Triangle ABE. 422 per. 265 base. j 1 ADr: 1326 G C = 645 AG= 952 IE B = 422 AE= 265 i Per. Base. 2110 2532 844 111830 Triangle GCD. 645 per. 374 base. 2580 4515 1935_ 241230 Trapezoid E B C G. 422 \ 645|P er - 1067 sum. 687 base. 7469 8536 6402__ 733029 E 4 56 LAND-SURVEYING. (Part III. 733029 ' Double areas 111- collected. 2)108( 8 5.43044 i L72i76 2^" i. lR. 29p. 2. Required the plan and area of a field, from the foil notes. AB 1 z - 1 E 1015 • 1 D. G 132 705 C. Begin at A. Range W. Frr. on the left. Base. Per. on the right. Area 7a. Or. 1'" : p. 3. Lay down a field, and find its area, from the following dimensions. AB E. C SS3 G. Begin at A. Rang- E Area Sa PROBLEM V. FIELD* COMPREHENDED UXDER MORE THAN FOUR STRAIGHT SIDES. Avy piece of land, consisting of more than four sides, may he surveyed by reducing it into triangles and trapeziums. Thus, a field of fire sides mav he reduced into a triangle and a trapezium : of six. into two trapeziums ; of seven, into two trapeziums and a triangle : of eight, into three trapeziums. &c 57 Part III.) LAND-SURVEYING. The propriety of dividing fields in this manner, depends entirely on the relation which the angles have to one another : it is, therefore, sometimes more accurate to divide them into triangles. TO COMPUTE THE CONTENT. Rule. — By the rules given in the last two problems, find the double area of each triangle and trapezium contained in the figure, Collect all the double areas into one sum, which divide by 2, and the quotient will be the whole area. EXAMPLES. 1. Lay down a field, and find its area from the following notes. CE 1666 Diag. 1326 496 A. 1000 D 376 573 KoffC ~KW ' «* 1433 Diag. 1000 B 273 643 Begin at A. Range W. Per. on the left. Diag. Per. on the right. 1> \ 58 land-surveying. (Part III. CONSTRUCTION. From the notes, the figure obviously consists of five sides, and is divided into a triangle and a trapezium. Draw the base A C, which make = 1433 links ; at 643 links, let fall the per- pendicular a B, upon which lay off 273 links ; join A B and C B, and the triangle is completed. Then, with A as a centre, and 496 links in your compasses as a radius, describe an arc ; and with C as a centre, and 1326 as a radius, describe another arc, intersecting the former in b. — Through b draw the diagonal C E = 1666 links; upon which, at 573 links, erect the per- pendicular c D = 376 links. Join C D, D E, and E A, and the figure will be completed. Note. — If the learner fully comprehend-the above construction, he will not find it difficult to lay down the figures belonging to -the following examples ; as the same process will succeed in all similar cases. Triangle ABC. 1433 base. 273 per. 4299 10031 2866 391209 Trapezium A C D E 376 ) 496 /^ 872 sum. 1666 diag. 5232 5232 5232 872 391209 ) 1452752 j 1452752 Double areas collected. 2)1843961 9.21980 4 .87920 40 35.16800 Area 9a. Or. 35p. Part III.) LAND-SURVEYING. 59 2. Lay down a field, and find its area, from the following dimensions. F 400 D 465 D 235 B263 Begin EG 1150 Diag. 1000 717 R.offE "HE~ 1474 Diag. 1000 975 465 575 G. Lk)ffH ~cW 1635 Diag. v * 1000 910 390 1. 575 R.offC . \ AC 1165 Diag. 1000 530 400 630 I. at A. Range E. SE 60 LAND-SURVJ£Y1NG. Part HI. ^E T:-rZ:-^i A B C I, ill ""' 893 sum. 1165 diag. 5358 • - rrarr£-in C D H I - 1 ' - 'in I 35 diag. 3 : - : 1875 : n :■ f-25 i':4-:-545 ['21-^ Part III.) LAND-SURVEYING. 61 rapezium DEGH. Triangle E F G. 575 j P er - 1150 base. 465 400 per. 1040 sum. 460000 , .„, drag. 14/4 4160 7280 4160 1040 1532960 1 040345 ^ 1021875 ( Double areas 1532960 ( collected. 460000 J 2)4055180 20.27590 4 1.10360 40 4.14400 Area 20a. 1j El. 4p. 3. Required the plan and area of a field, from the following dimensions. Diag. B A 1008 E 195 466 Return to B. AD 1345 C 415 944 855 Begin at A. Diag. 536 B. Range W. Answer. Double areas. 1279095 Trapezium ABDC. 196560 Triangle A EB. Whole area 7a. 1b. 20ip. 62 land-surveying. (Part III 4. Lay down a field, and find its area, from the following notes. D F Diag. 1940 1040 362 B. E 581 825 R.offD. TF Diag. 1488 C 322 772 606 665 B. Begin at A, Range W Answer. Donble areas. 1468656 Trapezium ABDC. 1829420 Trapezium D E F B. Whole area 16a. 1r 38p. 5. Draw a plan of a field, and find its area, from the following dimensions. I 382 E 661 HK m& 740 600 IkoffH. ~YW 1223 803 666 L.offF. E409 C 603 Begin D F 1716 1080 761 R^ftD IF 1547 1023 525 at A. Diag. 162 G. Diag. 276 G. Diag. 246 B. Diag. 488 B. Range W, Part III.) LAND-SURVEYING. Answer. Double areas. 1687777 Trapezium A B D C. 1123980 Trapezium DEFB. 11459.51 Trapezium F G H E. 699040 Trapezium HGKI. "Whole area 23a. 1r. 5p. 63 ANOTHER METHOD. A field consisting of five, six, seven, or more sides, may sometimes be surveyed by measuring one diagonal, and upon it erecting perpendiculars to all the opposite angles, on each side. This process will divide the whole field into right-angled triangles, and trapezoids, the areas of which must be found as before. EXAMPLES. Lay down a field, and find its area, from the following notes. Diag. AF 1896 E 259 1342 1132 1000 C367 763 B756 522 »egin at A. Range E. 325 D. 64 LAND-SURVEYING. (Part III. Triangle A B a. 756 per. 522 base. 1512 1512 3780 394632 Trapezoid a B C m. »«• 1123 sum. 241 base. 1123 4492 2246 270643 Trapezoid m C E r. 367) 259 j^ 626 sum. 579 base. 5634 4382 3130 362454 Triangle A D F. 1896 base. 325 per. 9480 3792 5688 616200 Triangle r E F 554 base. 259 per. 4986 2770 1108 143486 , 394632 VJiT-l IDouWe areas 616200 2)1 7874 15 "8.93707 4 3.74828 40 29.93120 Area 8a. 3r. 30p. 2. Lay down a field, and find its area, from the following dimensions. Part III.) LAND-SURVEYING. 65 AK. 1700 I 290 1465 w 1368 r 1055 F 144 986 m 794 e 515 C 250 444 a 150 000 Begin at A. Diag. d 365 H 381 G n 218 E 350 D c 275 B Range W. Answer. Triangles and Trapezoids on the Right. Double areas. 41250 Triangle A B a. 228125 Trapezoid a B D e. 158472 Trapezoid e D E ra. 156339 Trapezoid m E G r. 233498 Trapezoid r G H w. 121180 Triangle w H K. 938864 sum. Triangles and Trapezoids on the Left. Double areas. 111000 Triangle A C c. 213548 Trapezoid c C F n. 207886 Trapezoid n F I d. _68150 Triangle d I K. 600584 sum. 938864 sum brought down. 1539448 sum total. Whole area 7a. 2r. 31 |p. 3. It is required to lay down a field, and find its area, from the following notes. 66 LAND-SURVEYING. (Part III A L. Diag. 2150 1670 295 K 1530 w 134.5 160 H 1275 n 880 m 780 270 E 465 150 D 305 a 000 300 B at A, Range 31 460 d I 395 r G 670 F 400 e c C 405 Begin Answer. Triangles and Trapezoids on the Right. Double areas, 209250 Trapezoid ABDc. 132300 Trapezoid c D E e. 242950 Trapezoid e E H r. 147875 Trapezoid r H K d. 141600 Triangle d K L. 873975 sum. Triangles and Trapezoids on the Left, Double areas. 123525 Triangle A a C. 462875 Trapezoid aCFm, 422650 Trapezoid m F G n. 271575 Trapezoid n G I w. 53(H00 Trapezoid wIML. 1810725 sum. 873975 sum brought down. 2684700 sum total. TThole area 13a. 1r. 27f p. PROBLEM VI. FIELDS COMPREHENDED UNDER ANT NUMBER OF CROOKED OR CURVED SIDES. When a field is bounded by crooked fences, you must mea- sure a line as near to each as the angles or curves will permit : Part III.) LAND-SURVEYING. 6'7 in doing which, you must take an offset to each corner or angle in the fence. Where the fences are curved, those offsets must be so taken, that a right line drawn from the end of any one perpendicular to the end of the next, on each side, would neither exclude any part of the land to be measured, nor include any of that which is adjacent. Perpendiculars thus erected, will divide the Avhole offset into right-angled triangles and trapezoids, the areas of which must be found as before. Note 1. — If the curves be so large, that many of the offsets would be 2, 3, 4, or 5 chain long ; it will be more expeditious and accurate, to measure the base without taking any offsets, except such as are short, leaving stations in proper places along the base, to which, when you have obtained its length, you may return, and from them run fresh station-lines, to some convenient point, or points, in the curved fence. Upon these lines, take offsets as before. (See Example III.) 2. — If any of the fences be curved inward, it is frequently most convenient to measure a line. on the outside of the field, and upon it erect perpendiculars to the curved fence, which, in this case, are called insets ; and the area thus included must be subtracted from the area of the whole figure. (See Exam- ple IV.) 3. — When the fences and ditches are to be measured with the field to which they belong, it is generally most practicable to fix the stations within the fences, at a little distance from the corners, and then to measure to the roots of the quick-wood ; adding or subtracting 5 or 6 links, according to the custom of the place, for the breadth of the ditch. (See Example V.) 4. — When the offsets are small, their places on the base-line may be deter- mined by laying the offset-staff at right angles upon the chain ; but when large, and accuracy is required, they must be found by the cross, and mea- sured by the chain. 5. — The base of each triangle and trapezoid, forming an offset, may be found by subtracting the distances on the chain-line, from each other. 6. — The methods frequently used, by unskilful surveyors, to find the area of offsets, are very erroneous. Some divide the sum of the offsets by their number, for a mean breadth ; others divide that sum by one more than their number, for a mean breadth ; and both multiply the whole base by the mean breadth, thus supposed to be found, for the area of the whole offset. The first of these methods generally gives the area too much ; and the second sometimes too much and sometimes too little. A third method, which is usually more accurate than either of the preceding ones, is to set down each F 2 68 LAND-SURVEYING. (Part III. offset twice (accounting that one, where the boundary meets the station-line) except the first and last, which are only entered once. The sum of these offsets is then multiplied by the base, the product divided by the number of offsets set down, and the quotient given is the area required. 7. — Directions for laying down offsets by a plotting-scale, may be seen ia Part the Second. EXAMPLES. 1. Lay down the figure of a right-line offset, and find its area, from the following notes. AB n 200 1569 m 210 1249 1000 i TO 952 e.50 745 c 159 450 a 120 265 000 egin at A . Range E BY THE TRUE METHOD. Triangle A r a. 265 base. 120 per. 5300 265 Trapezoid r a c s 279 sum. 185 base. 31800 ■ 1395 2232 279 51615 Part III.) LAND-SURVEYINGL Trapezoid sceu, Trapezoid ueiw. 69 per. 1*9) 50 j 209 sum. 295 base. 1045 1881 418 6^655 Trapezoid wimx, 70) 210 }per. Trapezoid x m n B 210) 200/P er - 280 sum. 297 base. 410 sum. 320 base. 1960 2520 560 83160 8200 123 131200 31800 51615 61655 1 24840 83160 131200 2)384270 1.92135 4 3.68540 40 27.41600 Double areas collected. Hence the true area is 1a. 3r. 27e, f3 70 land-suhveyixg. (Part HI. BY THE FIRST FALSE METHOD. 120 159 50 70 210 200 6)809 1569 length. 134.8 breadth. 12552 6276 4707 1569 2.11.5012 134.8 mean breadth. 4 .460048 40 IS. 40 1.9 20 Here the area appears to be 2a. Or. 18p., which is too much by 31 p. BY THE SECOND FALSE METHOD. 120 1569 length. 159 115.5 breadth. ™ 7845 210 1569 200 1569 ~ 7)809 1.812195 115.5 mean breadth. 4 3.248780 40 9.951200 Here the area appears to be 1a. 3r. 10p., which is too little by 17p. BY THE THIRD FALSE METHOD. o 120 1569 length. 1418 sum. 120 159 159 50 12552 1569 6276 1569 50 70 7" 210 21" 200 12)22.24842 1.85403 4 3.41612 4" 1418 sum 16.64480 Part III.) LAND-SURVEYING. 71 Here the area appears to be 1a. 3r. 16p., which is too little by Up. 2. Lay down a curve-line offset, and find its area, from the following notes. Begin at AB 1012 892 53 786 80 £45 95 500 45 350 63 200 84 100 52 000 A. Range W. 52 100 5200 No. 1. 52 84 136 100 13600 No. 2. 84 63 147 150 7350 147 63 45 108 150 5400 1 08 16200 No. 4. 45 95 140 145 700 56 14 22050 No. 3, 20300 No. 5, 95 80 175 141 175 700 175 24675 No. 6, 80 53 133 106 798 13 14098 No. 7. F 4 72 LAND-SURVEYING. (Part III. 53 120 1060 53 6360 No. 5. Double areas collected. 5200 13600 22050 16200 20300 24675 14098 6360 2) 122483 .61241 4 2.44964 40 17.98560 Area 2r. 18p. 3. Lay down the figure of a piece of land adjoining a riyer, and find its area, from the following notes. Left off F, EB 1350 1265 140 a 1200 170 1100 244 1000 250 900 190 i 800 100 > 700 « 600 500 94 400 142 300 153 200 70 000 and go S W. to Part III.) XAND-SURVEYING. 73 Return H 50 110 g 154 cc 173 142 O o 1— 1 u 82 m P3 N W. to E. Triangle B C E. 1950 base. 698 per. 15600 1755 1170 1361100 74 LAND-SURVEYING. (Part 111. 60 100 6000 No. 1, 60 165 225 150 11250 225 33750 No. 2. Offsets taken on the line A D. 110 70 180 100 18000 No. 3. 163 70 11410 No. 4. 6000 No. 33750 18000 — 11410 69160 sum. Offsets taken on the line C E. 82 200 16400 No. 1. 154 110 264 100 142 200 26400 No. 5 28400 No. 2. 110 50 142 173 315 100 160 100 16000 No. 6, 31500 No. 3. 60 50 173 154 327 100 32700 No. 4. 3000 No. 7. 16400 No. 28400 31500 32700 26400 16000 3000 154400 sum. Part III.) LAND-SURVEYING. 75 Offsets taken on the line E B. 70 190 200 250 14000 No. 1. 440 100 70 44000 No. 8. 153 - 223 250 100 244 22300 No 2. 494 100 153 49400 No. 9. 142 295 244 100 170 29500 No. 3. 414 100 41400 No. 142 10. 94 236 170 100 140 23600 No. 4. 310 65 1550 94 100 186 9400 No. 5. 20150 No. 11 100 85 100 140 10000 No. 6. 3400 85 100 11900 No. 12 190 290 100 29000 No. 7. 14000 No. 22300 29500 23600 9400 10000 29000 44000 49400 41400 20150 11900 304650 sum. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 1361100} Whole 69160 ( double 154400 ( areas 304650 ) collected. 2) 1889310 9.44655 4 1.78620 40 31.44800 Area 9a. lit. 31 p. 76 land-surveying. (Part 111. 4. Lay down a field, and find its area, from the following notes. Begin at C A 525 Perpen. R.tDffC. BC 846 600 64 400 85 200 50 000 R. off B. AB 1253 1000 586 a, the place of the perpen A. Range W. Triangle A B C. 1253 base. 525 per. 6265 2506 6265 657825 Part 111.) LAND-SURVEYING. 77 Insets taken on the line B C. 50 85 10000 200 64 27000 10000 149 200 29800 29800 15744 50 82544 85 135 246 200 64 27000 984 1476 15744 657825 Triangle ABC. 82544 Insets. 2)57528 J Difference 2.87640 4 3.50560 40 20.22400 Area 2a. 3r. 20p. Double areas collected. 5. Draw a plan of a field, and find its area, from the follow- ing notes. Diag. 520 N. West. Fence, to A. A C 1155 1000 495 915 360 From A >g° To the 48 660 53 630 40 500 25 380 50 200 62 000 From D, g o South. 78 LAND-SURVEYING. (Part III Fence. To! the 25 615 35 550 30 400 10 240 22 150 45 000 From B,go To the 33 1090 45 1045 56 800 40 500 48 300 30 000 »gin at A, and . . to C. North. Fence. toB. go West. Answer. Double areas. 1172325") Trapezium A B C D. 98055 I A B ( 32980 >B C 1 Offsets taken on the 812541 CD '\ different lines . 812541 C D') 58820 IDA! "Whole area 7 a. Or. 34|p. Part III.) LAND-SURVEYING. 79 C. La) T down a field, and find its area, from the following dimensions. EB 442 345 74 25G 25 115 56 000 L. off E. CE 387 296 43 200 59 100 36 000 L. off C. AC 1294 Diag. 1050 B 530 1000 290 485 D R. off A. DA 567 32 458 67 364 24 235 43 123 000 R. off D. CD 1116 1000 129 465 80 + 30 310 65 200 42 100 000 R. off C. BC 584 Diag. E 293 328 R. off B. 80 LAND-SURVEYING. (Part III AB 1173 37 1000 44 -900 78 750 46 600 85 400 42 200 o 000 in at A Range w. I — I X B Answer. Double areas. 1313410 Trapezium A B C D. 171112 Triangle B E C. 111401") A B i 62395 / C D \ Offsets taken 37326 >DA<; on the 26805 ICEJ different lines. 33850JEB t Whole area 8a. 3r. 5p. 7. It is required to lay down a field, and find its area, from the following notes. III. B : r. - m 130 SHI 196 596 IM as 50 200 40 3 - : 2 -, . >: :• m . :,...-. ■» C A I hoi ■ 1 9 ! 1 m pjpjpj 69 Br A. : 82 land-surveying. (Part III 8. Required the area and plan of a field, from the following dimensions. AD 1080 1000 40 950 60 890 5* 820 3S 740 12 650 10 580 35 535 60 480 75 420 65^ 300 35 220 3a 100 60 50 70 000 50 L. off A, C A 1170 Diag, 920 540 B 525 225 r, off a BC 1065 25 1005 35 946 50 870 40 830 90 780 115 715 110 650 80 625 75 510 55 440 70 330 65 250 35 215 48 150 40 100 60 50 55 000 R. off B. Part III.) LAND-SURVEYING To the 700 40 645 55 570 72 500 68 450 49 375 42 300 37 225 53 170 40 130 50 50 52 000 From the Fence, Fence, to B. to A. go North. S3 Answer. Double areas. 1246050 Trapezium A B C D. 67710 Offsets taken on the line A B. 129820 Ditto on the line B C. 91210 Ditto on the line A D. Whole area 7a. 2r. 27f p. 9. Lay down a field, and find its area, from the following notes. E A 500 18 450 40 400 74 350 08 300 04 250 80 200 35 100 20 50 000 R. off E. 62 84 LAND-SURVEYING. Parr III DE 20 550 50 110 94 110 .' ac m 150 50 2S 50 °l 000 Serum ; :: ;_: B 550 915 * R. off A. D A ; ": £ ?:: R. offD. '"CD n 34 V 55 654 n 34 r : : " 95 450 M 75 350 320 44 : ' 40 i 30 50 1 . : = D Diag, Diag. Part III.) LAND-SURVEYING. 85 BC 640 18 600 25 550 30 500 25 450 35 430 €5 350 60 320 40 250 10 140 20 100 40 000 R. off B. To the €5 1115 70 1075 60 1000 55 920 60 868 40 800 20 750 28 700 65 600 80 550 73 400 70 300 34 200 40 134 23 100 000 Begin at A. Fence. toB. Range W. Answer. Double areas. 1310280 Trapezium A B C D. 281750 Triangle AED. 116056^ A B Offsets taken on the different lines. 41020 /B C 83180 >C D 92400 iDE 53650J E A Whole area 9a. 3r. 22£p. g3 86 land-suhveying. (Part 111. PROBLEM VIL NARROW PIECES OF LAND. The method frequently adopted, is to take breadths in dif- ferent places, add all these breadths together, and divide their sum by their number, for a mean breadth ; and this supposed mean breadth is multiplied by the length, for the area ; but this process generally leads to very erroneous results, as the method •of finding the mean breadth is void of truth. If a piece of land taper regularly from one end to the other, you may take its breadth at each end ; half the sum of these breadths, will be its mean breadth ; and multiply this mean breadth by the length, for the area. But if- it be irregular, you must take breadths in the widest and narrowest places, or at every particular curve, noting the place of each breadth, upon the chain-line. These breadths will divide it into trapezoids, which you must compute as before. Note 1. — The breadths must he taken directly across the laud to be mea- sured, and therefore, if considerable, will require the use of the cross. 2. — If a piece of land be curved, or longer on one side than on the other, by measuring along the middle, you will obtain the true, or mean length. 3. — When several piecesof land, of various lengths, are contiguous to each other, it will generally be most expeditious to measure only one base-line, noting the point, where each piece begins and ends, perpendicularly to the line. In this case, be especially careful that no confusion take place in noting down the breadths of the respective pieces. A. — Paring, reaping, &c. both in this and the foregoing problems, should be surveyed with a slack chain, in order to obtain the measurement of the surface. 5. — It is best 'to take the first and last breadths of lands or ridges, about half a chain from each end, and account them as the end-breadths ; because, Part III.) LAND-SURVEYING. 87 in turning, the plough usually makes some of them appear either broader or narrower than they are in reality. It may also be observed that it is fre- quently necessary to take the breadths to half a link ; for when the length is great, half a link in the breadth is too considerable to be neglected. 6, — If a narrow piece of land be very irregular, you may obtain its area most accurately, by measuring a base-line, in a convenient position ; and, upon it, erecting perpendiculars to the boundaries, on each side. 7. — In surveying with the chain and cross, when the area only of any field or piece of ground is required, it is unnecessary to lay down the figure. EXAMPLES, I. Find the area of a tapering piece of land, whose length is 2562 links, and breadth at one end 126, and at the other 232 links. 232 f breadths. 2)358 sum. 179 mean, 2562 length. ~358 1074 895 358 4.58598 = 4 2.34392 40 13.75680 Area 4a. 2b. 14p. 2. Find the area of a piece of land, which is broadest towards the middle, from the following dimensions. g4 88 LAND-SURVEYING. (Pari III. BY THE TRUE METHOD. j 2322 169 2000 1056 215 1000 1 000 1 Base. 125 Per. 125 1 215 / P er - 340 sum. 1056 base. 170 34 359040 215 i 384 sum. 1266 base. 2304 2304 768 384 359C 4S6144 | 2)8451 S4 4.22592 4 .90368 40 36^14720 Double areas collected. Area 4a. Or. 36p. BY THE FALSE METHOD. 125 i 215 > breadths. 169 I 3)509 169.6 mean. 2322 length. 169.6 breadth. 13932 20898 13932 2322 3.93S112 4 a 752448 40 To. 097 920 Here the area appears to be 3a. 3r. 30p., which is too little by 1r. 6p. Again, the dimensions remaining as before, suppose the piece to be narrowest towards the middle ; the area by the false method will be the same as already found. Part III.) LAND-SUIIVEYING. 89 BY THE TRUE METHOD. 2322 2000 1056 1000 000 Base. "l69~j 125 i 215 Per. 215 ) 125/I Jer - 340 sum. 1056 base. ~2040 170 - 34 359040 125 169/P er 294 sum. 1266 base. 1? T 64 1764 588 294 372204 359040 ) Double areas 372204 J collected. 2)731244 3.65622 4 2.62488 40 24.99520 The true area is 3a. 2r. 25p. ; hence the false area is too much by 1r. 5p. Lastly, the dimensions still continuing, suppose the breadth towards the middle to be greater than that at one end, and less than at the other ; the false area will still be the same. BY THE TRUE METHOD. 2322 2000 1056 II 10C 000 Base. 125 169 215 Per. 215 ) 169/ per. 384 sum. 1056 base. 2304 1920 384 405504 169 125 per. 294 sum. 1266 base. 1764 1764 588 294 372204 90 laxd-slrveyixg. (Part III. 40.5504 372204 2)7777^ 3.SS654 4 Double areas collected. 3.5541 1 40 22.16640 The true area is 3a. 3r. 2 2 p. ; hence the false area is too much by Sp. Thus we see the absurdity of a method which, however, has been long practised, and is not yet abolished. 3. Draw a plan of an irregular piece of land, and find its area, from the following dimensions. A B 1325 246 1015 987 790 31S 71S 560 223 465 345 346 266 372 000 From A, go 136 58 134 162 125 246 East. A $■.» Part III.) LAND-SURVEYING. 91 Answer. Double areas. 361176 Offsets on the right. 684860 Ditto on the left. 2)1046036 sura. T.23018 = 5a. Or. 36|p. the area required. 4. Find the area of five lands, from the following dimensions. 2378 185 2000 190 1700 194 1400 198 1000 200 700 195 400 189 000 185 Area 4a. 2r. 13^ p. 5. Required the area of six lands, from the following notes. 3422 189 3000 2500 204 2000 1800 226 1000 800 191 000 165 Area 6a. 3r. 12p. 6. Find the area of seven lands, from the following dimensions. Note. — In calculating the area, the half -links must be treated as decimals. 2900 99£ 2600 98J 2300 101 2000 97A 1900 100^ 1600 102 1300 99h 1000 10H 900 100 600 98i 300 100* 000 100 t Area 2a. 3r. 23|p. 92 LAND-SURVEYING. (Part III. 7. It is required to lay down a narrow piece of land, and find its area, from the following dimensions. AB ■:-" 1230 460 250 60 918 300 25 800 690 235 500 440 108 •300 100 216 150 130 From A. go N. Answer. Double area 5. 552-:" C ffsets on the right. 14■::> 50 ' " re , : : :■ 61 I R. oBD Part III.) LAND-SURVEYING. 95 Begin at CD 1450 1200 70 1000 80 820 GOO 400 95 110 150 000 R. off C. BC 1100 950 110 700' 70 550 142 300 100 000 R. off B. AB 1450 1200 55 1000 900 15 550 32 250 65 000 A. Range W. Answer. 1595000 Area of the rectangle A B C D. 135550^ AB r 183800 (B C J Double areas of the insets taken on the 168450 ( C D) different lines. 95500 ) D A( 2) 5833 00 291650 Area of the whole insets. 13.03350 Ditto of the mere. 4 .13400 40 5.36000 Area 13a. Or. 5p. 9*> LAND-SURVEYING. (Part III. 2. Let the following figure represent a wood ; its area is required. B Set up your cross at A, and let your assistant fix the marks B and D, so that the angle at A may be a right angle ; and mea- sure the line A B, taking insets as before. Then fix the mark C, as most convenient ; measure the, other three lines, and you will find in your field-book the following notes. DA 1550 160 1440 50 1200 1000 900 L. off D. CD 950 120 '500 000 L. off C. Part III.) LAND-SURVEYING. 97 BC 1340 1050 1000 50 700 60 400 000 L. off B. Tb" 1150 1000 50 900 550 100 300 110 160 000 Begin at A. Range 1 N. Answer. Having constructed the figure, you will find the diagonal B D to measure 1930, the perpendicular A a 923, and C a 605 links, Double areas. 2949040 Trapezium A B C D. "102000^ AB/ 114000 / C T)\ * nsets ta ^ en on tne different lines, 83000 ) Di( 373 500 Whole Insets, Area 12a. 3r. 20p. 2575540 Wood. PROBLEM IX. To find the Area of a Segment of a Circle, or any other Cur- vilineal Figure, by means of Equidistant Ordinates, RULE. If a right line A N be divided into any even number of equal parts A C, C E, E G, &c. ; and at the points of division be erected perpendicular ordinates A B, C D, R E F, &c. terminated by any curve B D F, / &c. ; and if A be put for the sum of the ex- J treme or first and last ordinates, A B, N O ; H KMO A C EG I L N OS i... YiNvr. Pet 111. B for the sum of the even ordinate? C D, G. H. L M. \ the second, four sum of all the rest E F. I K. &c fix. : rliird, filth, &e.. or the odd ordinates, wanting the first and las: the common distan: A. '. h C E. & : of the ordinates, being multiplied by the sum arising from the addition of A, four times B. and two times C ; one- third of the product will be the area A B O X. very nearly ; that A — -» B — ° C is. - — — xDr the area, putting D = A t •3 common distance of the ordinates. Note. — The foregoing rule being expressed in an algebraic form, is seldom properly understood by learners ; but the following one may be easily com- prehended and committed to memory. KULK. T :he sum of the first and last ordinates, add four tin: sum of all -rdinates, and twice the sum of all the odd ordinates, not including the first and last^ multiply th: r commoi of the ordinates, divide the product by 3, and the quotient will be the area required. Note. — The length of the base must be ascertained before yon begin to take the ordinates, in order that yon may divide it into an even number of equal parts ; or you may take the dimensions without doing this, and find :'.1t ire;-.= ::' : r jir: — :: :he e:.i. ":; ...i rulr: ::r :r:i: j.t- „:.£ rr-^Tri:::~. which being added to that part of the figure computed by equidistant ordi- nates, will give the whole area. See the following example. 1 . Required the plan and area of a piece of land, measured by equidistant ordinate?, from the following notes. Part III.) LAND-SURVEYING, 99 Besfin AB 1167 1100 44 EF 1000 97 CD 900 139 800 175 700 206 600 230 500 248 400 260 300 264 200 268 100 262 000 252 at A, and go West E C The first and last ordinates. 252 The first ordinate A G. 97 The last ordinate C D. 349 Sum. The even ordinates. 262 Second. 264 Fourth. 248 Sixth. 206 Eighth. 139 Tenth. TTl9 Sum. 4 4476 Four times the sum. h 2 100 land-surveying. (Part III. The odd ordinates, 268 Third. 260 Fifth. 230 Seventh. 175 Ninth. 933 Sum. 1866 Twice the sum. 349 The first and last ordinatef> 4476 Four times the sum, &c. 1866 Twice the sum, &c. 6691 Sum total. 100 The common distance. 3)669 100 223033 The area of the figure A C D G. frapezo id C E F D. Triangle EBF 97 67 44 44 141 268 100 268 14100 2948 Double areas. 14100 Trapezoid CE F D 2948 Triangle EBF. 2)17048 Sum. 8524 The area of the figure CBD. 223033 Ditto of the figure ACDG. 2.31557 Sum. 4 1.26228 40 10 49120 Hence the area of the ^hole figure A C E B F D G A, i* 2a. Ir. IO^p. nearly. Part III.) LAND-SURVEYING. 101 2. Lay down a piece of ground, and find its area from the following equidistant ordinates. AB 1000 85 900 150 800 200 700 230 600 247 500 250 400 240 300 216 200 180 100 130 000 egin at A, and 75 125 160 180 185 177 157 125 73 102 land-surveying. (Part III. The first and last ordinates. 130 The first ordinate. 000 The last ditto. 130 Sum. The even ordinates. 180 + 73 — 253 Second. 240 + 157 = 397 Fourth. 247 + 185 = 432 Sixth. 200 + 160 = 360 Eighth. 85 -f 75 = 160 Tenth. 1602 Sum. 4 6408 Four times the sum. The odd ordinates. 216 + 125 = 341 Third. 250 + 177 = 427 Fifth. 230 + 180 = 410 Seventh. 150 + 125 = 275 Ninth. 1453 Sum. 2 2906 Twice the sum. 130 The first and last ordinates. 6408 Four times the sum, &e. 2906 Twice the sum, &c. 9444 Sum total. 100 The common distance. 3)944400 3.14800 Area in square links. .59200 40 23.68000 Area 3a. Or. 23 |p. 3. Required the plan and area of a piece of ground, from the following equidistant ordinates. N Part III.) LAND-SURVEYING, 103 AB 220 1200 234 1100 245 1000 250 900 246 800 235 700 221 600 200 500 176 400 140 30® 100 200 55 100 000 -gin at A, and range E. Answer. 220 The first and last ordinates. 4456 Four times the sum, &c. 1976 Twice the sum, &c. 6652 Sum total. 100 the common distance. 3)665200 2.21733 Area in square links. 4 .86932 40 34.77280 Area 2a. Or. 34|p. 4. Find the area of 4 lands, measured by equidistant ordi- nates, from the following notes. 182 1290 183 1200 178 1100 189 1000 190 900 187 800 179 700 150 600 182 500 185 400 180 300 160 200 170 100 188 000 ... .. 70 101 115 112 96 98 95 100 120 110 131 133 137 130 H 4 104 Land- ; vzyixg. Part 111, 602 The first and last ordin i . Four times the sum, &c. : 5am total. 100 The common distance. — -— I rapeaoid at the end. 3." : . Area in square li: c :■:: — *o c.-i :■ Area 3a. 3b. Of p. 5. Find the area oi *■: Hiving iizifzsiiz.;. 5, by equidistant ordinates, from the 14? c r 153 ?■:■:■■• - :-•:■■:■ : : : •:,: :< 14-9 •: : : ■- 14*3 is-: o 144 i t : :• 142 -.::• t-00 I4fl fOfl 141 GOO 145 • : :■ A:- ":: 298 The first and last ordinates. 2936 Four times the sum. & : 1171 T^ice the sum. ft : 4408 Sam total. S :?.-4 " 4 " x : DO Trapexoid at the end. 1 r Area in square 0. 4 2.172 6.88000 Area. 4a. 2k. 6f p. Part III.) LAND-SURVEYING. 105 6. Required the plan and area of a piece of ground from the following equidistant ordinates. 180 220 246 265 270 269 260 243 215 180 134 65 goW. Answer. 743 The first and last ordinates. 7900 Four times the sum, &c. 3264 Twice the sum, &c. Tl907 Sum total. 100 The common distance. AB 236 1200 170 1100 126 1000 90 900 67 800 55 700 57 600 66 500 87 400 120 300 170 200 232 100 327 000 Begin at A, and 3)1190700 3.96900 Area in square links. 4 3.87600 40 35.04000 Area 3a. 3r. 35p. 7. Required the plan and area of a field from the following equidistant ordinates. AB 217 1096 187 1000 150 900 125 800 107 700 98 600 95 500 100 400 114 300 130 200 167 100 190 000 Begin «.t A, and 202 150 112 84 66 58 57 65 80 110 148 200 go X. 106 land-surveying. (Part III, Answer. 727 The first and last ordinates. 4384 Four times the sum, &c. 1540 Twice the sum, &c. 6651 Sum total. 100 The common distance. 3)665100 221700 36288 Trapezoid at the end. 2.57988 Area in square links. 4 2^31952 40 12.78080 Area 2a. 2r. 12|p. Note. — Whenever the rule given in this Problem can be applied, it will be found more easy, expeditious, and accurate, in finding the areas of offsets, and of narrow pieces of land, than the rules for triangles and trapezoids. (See my Mensuration, page 274.) Part IILj LAND-SURVEYING. 107 PROBLEM X. TO FIND THE BREADTH OF A RIVER. EXAMPLE. Let the following figure represent a river, the breadth of which is required. B Fix upon any object B, close by the edge of the river, on the side opposite to which you stand. By the help of your cross, make A D perpendicular to A B ; also make A C = C D, and erect the perpendicular D E ; and when you have arrived at the point E, in a direct line with C B, the distance D E will be = A B, the breadth of the river ; for by Theo. 1, Part I, the angle A C B = D C E, and as A C = C D, and the angles A and D right angles, it is evident that the triangles A B C, C D E are not only similar but equal. Note 1. — The distance between A and the edge of the river, must be de- duced from D E, when it is not convenient to fix A close by the river's edge. 2. — This Problem may also be well applied in measuring the distance of any inaccessible object ; for let A C equal 8, C D equal 2, and D E equal 10 chains ; then, by similar triangles, as CD :DE : : A C : A B ; that is, as 2 : 10 :: 8 : 40 chains = A B. (Sec Thco. 11, Part I.) 108 LAND-SURVEYING. (Part III. PROBLEM XI. LINES UPON WHICH THERE ARE IMPEDIMENTS NOT OBSTRUCTING THE SIGHT. EXAMPLE. Suppose m n, to represent a deep pit or water, and A and B two objects, the direct distance of which is required. At the verge of the impediment, having fixed the mark m, in a right line with A and B ; measure from A to m ; and at m, by the help of your cross, erect the per- pendicular m a, which measure to the out- side of the interposed obstruction, as at c. Then on the other side, as at n, in a line with A and B, erect the perpendicu- lar n e ; and make n b equal to m c. Measure b c, which will be equal to m n ; and from n, measure the distance n B ; then b c, added to A m and n B, will give the whole distance A B, 9B 4A Part III.) LAND-SURVEYING. 109 PROBLEM XII. LINES UPON WHICH THERE ARE IMPEDIMENTS OBSTRUCTING THE SIGHT EXAMPLE. Suppose C D E F to represent the base of a building, which obstructs the sight, and through which it is necessary that a straight line should pass from an object at A, Measure from A to m ; at m, erect the perpendicular m a, which measure until you are clear of the impediment, as at c, Erect the perpen- dicular c e, which measure until you are beyond the building, as at b. Erect the perpendicular b d ; and make b n, equal to m c, at which point you will be in a direct line with m A. Erect the perpendi- cular n B, which mea- sure ; then b c, added to A m and n B, will give the whole dis- tance A B. Note. — The last two pro- blems are very useful when you meet with impediments upon a base-line> LAND-SURVEYING. ^art tijt tfouvfy. The Method of Surveying with the Chain only ; and of measuring Meres. Woods, Distances, Lines upon which there are Impediments, and Hilly Ground. MISCKLLANEO US INSTE UCTIQN& JL he method of surveying with the chain only, is adopted by most Practical Surveyors, and is certainly preferable to that by the chain and cross ; because it is not only always as accurate, but generally more expeditious. TThatever be the form of the field or ground to be surveyed, you must measure as many lines as will enable you to plot it with accuracy. The plan being drawn, you may then divide the figure into trapeziums, triangles, kc; and measure the diagonals, perpendiculars. &e. with your plotting-scale. It is better, however, to divide small pieces, and single fields, into trapeziums and triangles, by measuring the diagonals and daring the survey ; so that to find the area, you will have only the perpendiculars to measure with the scale. You must also measure, in some convenient direction, a proof-line to each trapezium and triangle. Ni :-: 1 . — The offsets must be treated according to the directions in Part III. Prob. 6. Or, you may reduce the crooked sides to straight ones, by including as much of what does not belong to the field under your survey, as you ex- clude of what does, in the following manner. Apply to the crooked line in Part IF.) LAND-SURVEYING. Ill question, the straight edge of a clear piece of lantern horn, so that the small parts cut off by it, from the crooked figure, may be equal to those which are taken in ; (of this equality you will presently be able to judge very cor- rectly, by a little practice ;) then, with a pencil, draw a line by the edge of the horn. The sides being thus successively straightened, the content may be easily found. 2. — A slender bow of cane or whale-bone, strung with a silk thread, may- be substituted for the horn. The thread must be applied to the crooked fence, and two marks made, by which a straight line must be drawn. 3. — The sides may also be straightened by a parallel ruler ; but the operation is generally tedious, and must be performed with the greatest care, or it will not be more correct than the foregoing method. 4. — When the three sides of a triangle are given, the area may be found as follows. From half the sum of the three sides subtract each side seve- rally ; multiply the half sum and the three remainders continually together, and the square root of the last product will be the area required. This method is too prolix, except in particular cases ; the operation may, how- ever, be considerably simplified, by performing the multiplication and evo- lution by Logarithms. PROBLEM I. TRIANGULAR FIELDS. When you have a triangular field to survey, begin at the most convenient corner, and measure each side ; and, while measuring any one of the sides, leave a mark in some situation on the chain-line, that the distance between it and the opposite angle being measured, may be a proof line. Or, leave marks upon any two of the chain-lines, and the distance between them will prove your work. EXAMPLES. 1. It is required to construct a figure, and find its area, from the following notes. 112 LAXD-SLRVEY1XG, (Part IK. DC 913 proof-line. Return to D. Begin at D, station for a proof-line. Having constructed the figure, you will find the line D C to measure 913 links, as in the field-book ; hence, you may con- clude there is no error committed in taking, or setting down the dimensions. Note 1 . — If your proof-line upon the plan does not agree, or nearly so, with that taken in the field, you may be assured that some error has been committed ; you must, therefore, repeat the survey in order to discover it. 2. — When land is level, and the lines are well driven, and not very long, you will generally find them to meet correctly, Part IV.) LAND-SURVEYING. 113 TO FIND THE PERPENDICULAR. Vide Part I. Prob. 6. Or, if you make use of a plotting-scale, lay it across the base in such a manner, that the line which goes across the scale may coincide with it, the edge of the scale at the same time touching the opposite angle ; by that edge draw a line from the base to the opposite angle ; this line, or perpendicular C a, in the present case, you will find to be 878 links. 1462 base. 878 per. 11696 10234 11696 2) 1283 636 6.41818 4 1.67272 40 26.90880 Area 6a. 1r. 27p. COMPUTATION OF THE AREA FROM THE THREE SIDES. TT 1462 + 1275-1-1029 3766 n _ „,._ Here — = — — = 1 883, half the sum of the 2 2 three sides. Then 1883 - 1462 = 421, the first remainder; 1883 - 1275 = 608, the second remainder; and 1883 - 1029 = 854, the third remainder ; whence -v/1883 X 421 X 608 X 854 = ^41161 7533376 = 641574 square links, the area, equal to 6 acres, 1 rood, and 26^ perches, nearly the same as before. THE SAME BY LOGARITHMS. The log. of 1883 = 3.2748503 421 = 2.6242821 608 = 2.7839036 854 = 2.931 4579 Divide by the index of the root 2 )1~1. 6144939 The quotient is the log. of 641 574, the area ~~ 5.8072469 Ill land-surveying. rPart IV. 2. It is required to construct a figure, and find its area, from '.lowing n C A o - U - yg 15 55 212 ) R. [ B C 4 M 354 22S : >ffB. AB Q a proof-line, which goes to n, and measures 352 links. 48 V 56 2 5 745 :ion for a proof -line. Begin at A. Range N. E. computation or the aw fpsbts, &c B Part IF.) LAND-SURVEYING. 115 Having constructed the figure, you will find the line m n to measure 352 links, as in the field-book. You will also find the perpendicular B a, to be 528 links. Triangle ABC. 1252 base. 528 per. 10016 2504 6260 661056 256 25 1280 512 6400 25 56 81 239 729 243 162 19359 Offsets taken on the line A B. 56 76 132 105 660 132 13860 76 48 124 145 620 496 124 17980 228 48 1824 912 10944 ~64(Xn ! 19359 | 1 Double 13860 > areas 17980 | collected, 10944 i 68543 i mm. 12 ]16 LAND-SURVEYING. (Part IV. 229 49 49 64 113 125 505 226 113 14125 Offsets taken on the line B C. 64 4U 104 182 208 S32 104 I S 9 2 > 147 _ *° Double areas collected. 50154 sum. Offsets taken on the line C A, 232 72 252 55 45 37 1060 117 1764 LC 106 756 11660 7 "2 9324 55 11, 12402 11660" 15 14840 45 69 16182 Double ,0 12402 \- areas 212 12312 collected 14840 114 18656 108 9324 v 15 912 95376 sum. 72 114 87 186 522 12312 69 696 37 87 106 16182 176 636 742 106 18656 Part IV,) LAND-SURVEYING. 661056^ 68543 ( Whole 50154 ^ double areas 05376 j collected - 2)875129 4.37564 4 1750256 40 20.10240 Area 4a. 1r. 20e. 117 COMPUTATION OF THE AREA BY REDUCING THE CROOKED SIDES TO STRAIGHT ONES : GENERALLY CALLED " CASTING." JB Having constructed the figure as before, and taken out the chain-lines ; draw the three dotted lines A B, B C, and C A, in such a manner, that the parts included may be equal to those excluded, as nearly as your eye can judge. Then the base A O being measured, will be found = 1390 links; and the perpen- dicular B a = 630 links. 1390 base. 630 per. 41700 8340 E 2)875700 4.37850 4 1.51400 40 20.56 000 Area 4a. Ir. 20p. i 3 118 LAND-SURVEYING. (Part IV. Note. — Although the method of finding the area by Casting (which de- pends entirely upon the accuracy of the eye) is adopted by most Practical Surveyors ; it is certainly less correct than that by Offsets, &c. A learner, therefore, ought to practice both, until he can habitually come very near to the truth by the former. 3. Lay dov\Ti a field, and find its area, from the following notes. BD 760 Return to DA 1035 R. offD. CD 61 1145 55 1100 12 1000 72 950 119 900 80 850 61 800 59 750 110 700 179 600 210 550 215 500 212 450 180 400 159 350 142 300 165 250 173 200 161 150 126 100 65 50 000 R. offC. A~C 1590 B 890 Begin at A, and proof-line. B. Range AV Part IV.) LAND-SURVEYING. 119 Answer. Having constructed the figure, you will find the perpendicular D a, upon the base A C, to measure 740 links. Double areas. 1176600 Triangle A C D. 275770 Offsets taken on the line C D. Area 7a. 1r. If p. 4. Lay down a field, and find its area, from the following dimensions. D B 575 proof-line. Return to D. C A 1320 D 600 R. off C. BC 880 31 800 73 750 95 700 58 600 60 550 95 500 60 380 63 250 60 200 45 100 55 000 R. off B. To the fence. 30 930 17 875 to B. 48 800 65 700 74 600 65 500 58 400 55 300 30 200 17 100 000 Begin at A, and Range N. 1 I 4 120 LAND-SURVEYING. (Part IV. Answer. Having constructed the figure, you will find the perpen- dicular B a, upon the base A C, to measure 573 links. Double areas. 756360 Triangle ABC. 85060 Offsets taken on the line A B. 106270 Ditto on the line B C. Area 4a. 2r. 38p. 5. Lay down a field, and find its area, from the following notes. DC 596 Return to C A 1080 6 1000 50 900 110 800 130 700 145 620 106 550- 65 500 30 450 16 410 36 350 54 300 70 250 74 200 86 150 70 100 46 50 O 000 K, off C. proof-line. D. D, station for a proof-line. Part IV.) LAND-SURVEYING. 121 "8 J C GO M P © M o o A BC 848 30 800 60 750 80 700 70 650 48 600 20 520 46 450 90 380 100 330 110 270 70 200 40 150 50 100 45 000 R. off B. To the fence. 50 800 45 755 30 700 40 650 # 75 600 130 550 170 500 156 450 135 400 50 350 24 300 66 250 80 200 40 150 20 100 23 50 000 From A, Range toB. N. E. Answer. Having laid down the figure, you will find the perpendicular B a, upon the base A C, to measure 587 links. Double areas. 633960 Triangle ABC. 110800 Offsets taken on the line A B. 100120 Ditto on the line B C. 149310 Ditto on the line C A. Area 4a. 3r. 35|p. 122 land-surveying. (Part IV. PROBLEM II. FIELDS IN THE FORM OF A TRAPEZIUM. When you have a trapezium to survey, measure each side, and both the diagonals, one of which will enable you to con- struct the figure, and the other will serve as a proof-line : or, you may measure the longer diagonal, and a proof-line in any other direction most convenient. Note I. — From various obstructions it is sometimes impossible to take either of the diagonals ; in such cases, you must measure tie-lines across the angles of the field, at any convenient distance (not less than two chains) from the corners. These you will find sufficient for constructing the figure, and for proofs. Or, you may take an external angle, or angles, as directed in Problem IV. 2. — When the lines, including the angle you intend to take with the chain, are of a considerable length, it vail be necessary to measure more than two chains from the angular point, before you take the chord-line ; because a small inaccuracy in constructing the figure, when the angular distance is short, will throw the lines, when far produced, considerably out of their true position. It sometimes happens, however, in consequence of obstructions, that it is im- possible to measure the chord-line at a greater distance from the angular point, than one or two chains. In such cases, multiply both the chord-line and angular distance by 2, 3, 4, or any larger number, as circumstances may require ; and use the products resulting, in laying down the figure. 3. — When the measurement of the surface is required,for reaping, &c. you must let the chain touch the sides of the lands, in all places where you measure across them. If you do not measure across the lands, but along the headland ; then you must add as many links to the length of the chain-line, as will make it equal to one measured across the lands, parallel to and near the headland. You may easily ascertain what number of links you oUght to add, by stretch- ing the chain across the lands, and putting down an arrow at each end ; after which, leave hold of one of the ends, and you will observe it recede from the arrow. The number of links, by which it falls short of its former position, you must add to each chain. Some lands you will find so low, that nothing need be added to the chain-line ; and some will require a link to four, three, two, or even (where the lands are very high) a link or more to one chain. To this method some may object ; but, when the lands are high, if the lines measured along the headlands be not lengthened, the perpendiculars will obviously measure less than they ought to do ; consequently, the horizontal measure will be returned, instead of the measure of the surface. Part IV.) LAND-SURVEYING. 123 In the opinion of others, the diagonal, measured with a slack chain, will give the measure of the surface ; but, in this case, the perpendiculars will evidently he shorter than they would have been, if the diagonal had been measured with a tense chain ; consequently, the measurement will be the same, or very nearly the same, whether the diagonal be measured with a tense or slack chain, unless the headland lines be lengthened. 4. — If two or three persons measure the same piece of land separately, or even if one person measure the same piece twice over, there will generally be a difference between the measurements ; this difference, however, in small pieces, should scarcely ever exceed four or five perches. 5. — When land, crops of corn, &c. are bought and sold, the buyer and seller commonly choose each a surveyor ; and in their measurements it oc- casionally happens that there exists a considerable difference. In this case, the best method, perhaps, of adjusting the dispute is, that the two surveyors meet, and jointly remeasure the land. If this fail, it only remains that the buyer and seller jointly choose an experienced surveyor, as an umpire, by whose decision the law will compel the parties to abide. EXAMPLES. 1 . It is required to construct a figure, and find its area, from the following notes. Begin at BD 1400 1000 Diag. Return toB. AC 1916 1000 Diag. R. off A. D A 558 R. offD. C~D 1626 1000 R. off C. BC" 689 R. off B. AB 1492 1000 A. Range W. 124 LAND-SURVEYING. (Part IF. _ x> Having constructed the figure, lay your scale from B to D; and if you find it exactly 1 400 links, as in the field-hook ; you may then measure the perpendicular B a = 468 links ; and the perpendicular D a = 432 links ; from which you will readily compute the area required. 468 432 per. 900 sum. 1916 diag. 2)l724400 8.62200 4 2.48800 40 19.52000 . Area 8a. 2r. 19p. BY THE FALSE METHOD. Remarked in Part III. Prob. 4. Note 4. 1492 =AB 1626 = C D 1559 623 2)3118 1559 mean length. 4677 3118 9354 689 = B C 558 = D A 2)1247 623 mean breadth. 9.71257 4 2.85028 40 34.01120 Here the area is found to he 9a. 2r. 34p., which is too much by 1a. Or. 15p. ; but the more nearly a trapezium approaches to a square, or rectangle, the less will be the error. Part IV.) LAND-SURVEYING. 125 2. Required the area of a field, from the following notes. Begin at DB 1365 Diag. 1000 Return toD. AC 1288 Diag. 1000 L. off A. DA 750 L. off D. CD 765 L. offC. BC 720 L. off B. AB 1600 1000 A. Range E. Having constructed the figure, you will find that in conse- quence of the length of the side A B, a perpendicular from the angle A to the diagonal D B, cannot be taken; you must, 126 LAND-SURVEYING. (Part IV. therefore, let fall the perpendicular D a, from the angle D to the side A B, which you will rind = 638 links. The perpen- dicular C a will be found = 294 links. > Triangle A B D. 1600 base. 638 per. 12800 48 96 Triangle B C D 1365 base. 294 per. 5460 12285 2720 1020800 401310 1020800 | 401310 J Double areas, collected. 2)1422110 7.11055 4 .44220 40 17.68800 Area 7a. 0itri8p. 3. It is required to find the area of a field, from the following notes. B D 1236 1000 Return to B. ; AC 1326 1000 R. off A. D A 515 28 400 50 300 65 200 33 100 000 R. offD. Diag. Diag. Part IV.) LAND-SURVEYING. 127 CD 1375 50 1300 7a 1200 84 1000 52 800 652 356 44 200 50 100 000 R. off C. BC 664 25 570 483 378 32 300 72 150 85 100 60 50 000 R. off. B. AB 946 784 50 725 93 650 106 600 75 500 32 400 335 242 50 40 000 Begin at A. Range E 128 LAND-SURVEYING. Part IV.) BY OFFSETS, &C. Having constructed the figure, you wffl find the perpen- dicular D a = 512, and the perpendicular B a = 446 links. Trapezoid A B C D. is}** 958 sum. 1326 diag. 5748 1916 2874 958 1270308 Part IV.) LAND-SURVEYING. 129 Offsets taken on the line A B. 242 75 59 50 106 50 12100 181 100 2950 65 18100 32 =— 12100' 130 106 2080 195 93 • 10700 Double 2080 199 18100 )■ areas 50 9950 collected 32 75 9950 10725 2950^ 107 100 93 66605 Sum. 50 10700 143 75 715 1001 10725 ■ 50 60 3000 60 85 145 50 7250 85 72 157 __50 7850 Offsets taken on the line B C. 72 32 104 150 5200 104 15600 78 __32 156 234 2496 181 25 905 362 4525 3000 7250. 7850 f Double 15600 r ™ e ™ a 2496 V collected. 4525 40721 S um . 130 LAND-SURVEYING. (Part IV. 100 50 5000 50 44 94 100 9400 156 44 624 624_ 6864 148 52 296 740 7696 Offsets taken on the line C I>, 52 84 136 200 27200 84 75 159 200 31800 75 50 125 100 12500 75 _50 3750 5000] 9400 6864 Double 7695 ] [■ areas 27200 collected 31800 12500 3750 J 104210 Sura, Offsets taken on the line D A. 33 50 100 28 3300 78 ZZZ.ZZZ 100 33 65 7800 98 115 ioa 28 9800 £20 230 65 3220 50 : — : — 115 100 11500 3300^ 9800 / Double 11500 > areas 7800 I collected. 3220.) 35620 Sum. Part IV.) LAND-SURVEYING. 131 Whole -double area* collected. 1270308 66605 40721 104210 35620 2) 1517464 7.58732 4 2.34928 40 13.97120 Area 7a. 2r. 14p. BY CASTING. Having constructed the figure, draw the four dotted lines A B, B C, C D, and D A, in such a manner, that the parts in- cluded may be equal to those excluded ; then the diagonal A C, will be found = 1364, and the perpendiculars Da = 636, and Ba = 476 links. k2 182 LAND-SURVEYING, (Part IF. 636 476 per. 1112 sum. 1364 diag, 4448 6672 3336 1112 2) 1516768 7.58384 4 2.33536 40 13.41440 Area 7a. 2r. 13p. 4. It is required to find the area of a field, from the following notes, BD 1460 Dif 1000 Return to B. AC 1480 Dh 1000 R. off A. DA 672 R. off D. CD 1244 1000 47 800 70 600 85 400 68 200 30 000 r. off c. Part IV.) LAND-SURVEYING, 133 BC 720 85 650 112 550 88 450 360 Cross the fence. 300 83 200 130 100 100 000 R, off B, AB 1350 1000 n at A. Range W, c *> Having constructed the figure, you will find the perpen- dicular C a = 613, and the perpendicular A a = 618 links. Trapezium A B C D. 613) _618|P er - 1231 sum. 1460 diag. 73860 4924 1231 1797260 k3 134 LAND-SURVEYING^. (Part IV. Insets taken on the line B C. 100 130 230 100 23000 130 83 213 100 21300 83 60 4980 10000) 23000 (Double areas 21300 ( collected. 4980J 59280 Sum. Offsets taken on the line B C. 88 90 7920 112 85 197 100 19700 85 70 5950 Insets taken 85 70 155 200 31000 70 47 117 200 23400 7920^) 20000 (Double areas 19700 ( collected. 5950 J 88 53570 Sum. 112 200 100 20000 200 30 6000 30 68 ~~98 on the line C D. 6000 \ 19600/ 30600 { Double areas 31000 ( collected. 23400 \ 11468 J 122068 Sum. 200 19600 68 85 153 200 244 47 30600 3708 976 11468 Part IV.) LAND-SURVEYING. Double areas. 1797260 Trapezium ABCD. 53570 Offsets. 1850830 Sum. ~ 59280 122068 135 Insets. 181348 Sum to be deducted from the above sum. 2)1669482 Whole field. 8.34741 4 1.38964 4t) 15.58560 Area 8a. 1r. 16p. 5. It is required to find the area of a field, from the^following notes; neither of the diagonals having been measured, in con- sequence of obstructions. Begin at DA 476 L. offD. CD 618 200 r, proof-line, 417 to B. L. offC. BC 443 L. offB. AB 723 192 from m to n. 200 from A to m, on the line A D< 200 from A to n, on the line A B. the angle A range E. K4 136 LAND-SURVEYING. D (Part IV. fr..-": Having constructed the figure, you will find the diagonal AC = 963, and the perpendiculars Da = 257, and B a = 316 links. 573 sum. 963 diag. 1719 3438 5157 2)551799 2.75899 4 3.03596 40 1.43840 Area 2a. 3r. Ip. Part IF.) LAND-SURVEYING. 137 6. Required the plan and area of a field, from the following notes. BD 1437 1000 Return to B. AC 939 L. off A. D A 567 L. offD. CD 712 L. offC. BC 765 L. offB. Begin at AB 1457 1000 A. Range Diag. ! Diag. E. Answer. Having constructed the figure, you will find one of the per- pendiculars = 560, and the other = 166 links; hence the area is = 5a. Or. 34p. 7. It is required to lay clown a field, and find its area, from the following notes. Pari IV* B D _ t 7 _;_ DA l - d : 1 :z '. L. :f I A B 2 ^ •: :■ ; ; A. Range ---"- = E. Answer. ii-il-irs = Li: = -IS '__ £i : i.-_.t :lr m Li = - " required to lay down a field, and find its area, from tike following notes; neither of the diagonals haying been B -.'-':'. :.:•■: L - Part IV.) LAND-SURVEYING. 139 Begin at AC 1094 L. off A. E A 1800 1000 L. offE. DE 837 L. off D. BD 1528 1000 860 L. off B. A B 621 A. Range N. Answer. Having constructed the figure, you will find the diagonal BE = 1927, and the perpendiculars = 580 and 637 links re- spectively ; hence the area is = 11 a. 2r. 36p. 9. The plan and area of a field are required from the fol- lowing dimensions. Return DB 1730 toD. AC 1660 R. off A. Diag. Diag. 140 LAND-SURVEYING. (Part IV. To the Fence 99 1580 110 1500 to A. 100 1450 116 1400 132 1300 115 1200 65 1100 33 1000 25 950 40 900 150 850 210 800 250 700 255 630 240 550 218 500 117 400 41 300 18 250 15 200 100 150 140 100 157 50 165 000 R. offD. To the Fence. 60 1085 82 920 toD. 80 850 42 750 40 700 121 600 140 550 136 500 70 400 25 1 350 17 j 300 14 250 30 ! 200 70 150 92 1 100 100 000 R. offC. Part IV.) LAND-SURVEYING, 141 To the Fence 52 1440 70 1340 toC. 60 1250 37 1200 33 1150 45 1100 83 1000 70 900 25 800 12 750 20 700 40 650 48 600 54 500 59 450 60 400 72 350 84 300 70 200 86 150 80 100 75 000 R. off B. To the Fenc< 67 1005 78 930 toB. 86 850 90 750 75 700 40 650 27 600 36 550 57 500 85 450 78 400 58 300 62 200 79 100 83 50 80 000 legin at A, and goN Answer. Having constructed the figure, you will find the pern diculars A a = 810, and Car 708 links. 142 LAND-SURVEYING. Double ar 2626140 Trapezium A B C D. 13794.5 Offsets taken on the line 167800 Ditto on the line B C. 1.57520 Ditto on the line C D. 39.5420 Ditto on the line D A. (Part IV. A B. 3484825 Sara. Area 17a 1r. 27^ p. PROBLEM III. FIELDS OF MORE THAX FOUR SIDE>. TVhen a field consists of more than four sides, you rnusr divide it into triangles and trapeziums, agreeably to the direc- tions given in Part III. Prob. 5. Then take the dimensions of each, as directed in the last two problems. Note. — Notwithstanding what has already been advanced with regard to taking proof- lines, you are again requested never_to omit measuring such distances as will enable you to confirm every part of your survey. Some may perhaps deem this tedious and superfluous ; but the satisfaction which a Sur- veyor finds, when his lines meet correctly, fully compensates him for his ad- ditional labour. Beside, he had certainly much better be at the pains of de- tecting his own errors, than expose himself to ridicule, by suffering them to be detected by some other Surveyor. EXAMPLES. 1. It is required to find the area of a field, from the following notes. Diag. Diag. m, proof-line, goes to D, and measures 285. Part IV.) LAND-SURVEYING 143 Begin at AC 1200 1000 R. off A. E A 393 R. off E. DE 692 R, off D. CD 620 R. off C. BC 535 R, off B. AB 1334 1000 A. Range Diag. W. Having constructed the figure, you will find the perpen- diculars C a = 410, Aa = 330, and D a = 215 links. 144 Trapezium A B C E. 410) 330}P er - 740 sum. 1510 diag. LAND-SURVEYING. (Part IV. Triangle C D E. 1238 base. 215 per. 6190 1238 7400 2476 370 74 1117400 266170 1117400 ) Double areas 266 170 J collected. 2)1383570 6.91785 4 3.67140 40 26.85600 Area 6a. 3r. 27p. 2. It is required to find the area of a field from the follow- ing notes, DA 1042 Return to D. CE 420 R. off C. A C 768 Roff A. E A 585 R. off E. DE 518 R. offD. CD 365 L. off C. Diag, Diag. Diag. Part IV.) LAND-SURVEYING. 145 Begin at m, proof-line, goes to C, and measures 260. Having constructed the figure, you will find the perpen- diculars C a = 223, Cn = 200, and E a = 176 links. Triangle ABC. 1054 base. 223 per. 3162 2108 2108, 235042 Trapezium A C D E. 200) 176JP er - 376 sum. 1042 diag. "752 » 1504 376 391792 146 LAND-SURVEYING. f Part IV. 235042 \ Double areas 391792 / collected. 2)626834 303417 4 .5366$ 40 21.46720 Area 3a. Or. 21p. 3. It is required to find the area of a field, from the follow- ing notes. Diag FB 660 Return to F. BE 970 L. off B. D B 268 L. off D. AD 832 R. off A. FA 285 L. off F. EF 384 40 300 53 200 32 100 000 R. offE. D E L. offD. Diag. Diag. Diag Part IV.) LAND-SURVEYING 147 CD 383 52 200 000 R. offC. BC 475 300 R. off B. AB 850 Begin at A. Range m, proof-line, goes to D, and measures 255. W. Haying constructed the figure, you will find the perpendi- culars Fa= 185, F m = 185, D n = 190, and D a = 216 links. Triangle A B F. Trapezium B D E F 850 base. 185 ) 190/P er ' 185 per. 4250 375 sum. 6800 970 diag. 850 26250 157250 3375 363750 L 2 148 LAND-SURVEYING (Part IV. Triangle BCD, 475 base. 216 per. 2850 475 950 102600 Offset taken on the line C D. 383 52 766 1915 19916 Offsets taken on the line E F- 32 100 3200 32 53 85 100 8500 53 40 93 100 9300 84 40 3360 3200 8500 9300 3360 Double areas collected. 24360 sum. 157250^ 363750 f Whole 102600 > double area* 19916 k collected. 24360 ) 2)667876 3.33938 4 E35752 m 40 14^30080 Area 3a. 1r. 14p. 4. It is required to lay down a field, and find its area, from the following notes. Part IV.) LAND-SURVEYING, 149 DB 1440 1000 Return to D* AC 107S L. off A. E A~~ 1324 1000 Return to E. DF 712 L. offD. AD 818 L. off A. FA 755 L. off F. EF 692 L. offE. DE 754 R. off D. CD 540 L. off C. BC 1048 L. off B. Begin at ~AB 1360 1000 A. Range Diag. Diag. Diag. Diag. Diag, L 3 150 LAND-SURVEYING. (Part IV. Answer. Having constructed the figure, and divided it into two tra- peziums, ABC D, and AD E F : you -will find the perpen- dicular -which falls from the angle C upon the diagonal DB = 31. 5 links; and that which falls from the angle A upon the same diagonal = 7-5S links. The perpendicular which falls from the angle D upon the diagonal E A. you will find = 42.5 links ; and that which falls from the angle F upon the same diagonal z=. 28? links. Hence the area is = 12a. 1r. 30p. 5. Required the plan and area of a field, from the following notes. E B 424 R. offE. Proof-line. F E 750 L. ,-r F. Diag. 31 F 400 R. offM. - H M R. off H. 227 to K. L H R. DffL. D L 43'.' Return to D. F L R. off F. H F 730 400 R. off EL Diag. Diag. ~~dTT~ 926 R. offD. Diag. GD 950 Return to G. Diag. Part IV.) LAND-SURVEYING. 151 Begin at GE 580 R. off G. FG 630 R. off F. DF 540 R. off D. AD 1050 R. off A. E A 450 R. off E. DE 670 R, off D. CD 500 R. off C. AC 780 500 A. Range Diag. Diag. Diag. B. L4 152 LAND-SURVEYING. (Part IV, Answer. Having constructed the figure, you will find the perpendi- culars of the trapezium A C D E = 354 and 195 ; of D F G E = 404 and 340 ; ofDLHF = 426 and 316 ; and the per- pendicular of the triangle F H M =. 227 links. Hence the area of the field is = 10a. 2r. 25p. 6. Required the plan and area of a field, from the following dimensions. leturn BD 1480 toB, Diag. Line 14 L. off GE 1725 Diag. Line 13 L. off CG 1295 c, Diag. Line 3 2 L. off FC 935 Diag. Line 11 R. off DF 793 D, Diag. Line 10 Part IV.) LAND-SURVEYING. 153 GD 358 37 300 49 250 CO 200 GG 150 62 100 30 50 000 R. off G, FG 783 78 700 3 34 650 154 600 170 550 172 500 150 450 185 400 208 350 205 300 180 250 149 200 107 150 62 100 24 50 000 R. off F, 1 EF 1043 36 1000 67 900 85 800 100 700 140 600 152 550 143 500 135 450 110 400 €5 350 50 300 40 200 25 100 000 R. off E, Line 9. Line 8. Line 7. 154 LAND-SURVEYING. (Part IV. CE 743 70 600 135 500 160 450 185 400 190 350 170 300 150 250 95 200 60 100 000 R. off o, DC 1000 L. off D, AD 700 600 500 450 400 350 300 250 200 100 000 L. off A, C A 1578 R. off c, BC 865 60 750 104 650 72 600 88 500 100 400 86 350 75 300 95 200 80 100 70 000 R. off B, Line 6. Diag. Line 5. 50 130 160 173 184 190 150 107 60 Line 4. Diag. Line 3. Line 2. Part IV.) LAND-SUItVEYING. 155 To the 80 1820 73 1750 60 1600 56 1500 70 1400 95 1300 120 1200 105 1100 110 1000 140 900 186 800 184 700 125 600 114 500 93 400 86 300 75 200 70 100 000 ;gin at A, Fence. toB. Range "W. Line 1. (See the Figure, Page 39 2. J Answer. Having constructed the figure, you will find the perpen- diculars of the trapezium A B C D, falling upon the diagonal C A, to measure 862 and 314 links ; the perpendicular of the triangle D G C, falling upon the diagonal C G, to measure 184 links ; and the perpendiculars of the trapezium CEFG, falling upon the diagonal G E, to measure 513 and 300 links. Double areas. 1855728 238280 1402425 362460 133750 143250 149010 157548 200374 30696 467352? Trapezium A B C D. Triangle D G C. Trapezium CEFG. Offsets taken on the line Ditto on the line B C. > Ditto on the line A D. Ditto on the line C E. Ditto on the line E F. Ditto on the line F G. Ditto on the line G D. Sum. AB, Area 23a. Ir. 18|p. LAND-SURVEYING. (Pc i-i £^i :i-r rr-jT-riTi-f -i- ::' :lr 1 = 7:7:-- ii:'.^-^. it.: :lr ::---: ::' :if -zi.l-r. ~:~ :1: rill:— Izj Lr_ri^:=5 —Tie fidd-aotes in tkis example arc entered fin the left to war* : :•:-::.- -. Part IF.) LAND-SURVEYING. 157 1 ToC 685 54 600 92 500 105 400 100 300 78 200 44 100 000 Go from D, Line 5. ToD 632 600 24 500 55 400 78 300 82 250 Gate. 200 76 100 58 000 Go from A, Line 4. To A 995 Diag. Go from c, Line 3. ToC 615 46 500 .53 400 62 300 60 200 50 100 000 Go from B, Line 2. ""ToT" 662 53 600 88 500 96 400 92 300 70 200 35 100 000 Begin at A, and go N. Line 1 158 LAND-SURVEYING. (Part IV. To the 668 ToG 638 600 500 400 300 200 100 000 Go from E, ToE 965 Go from D, ToD 735 32 700 75 600 55 500 20 430 Gate 380 28 300 42 200 40 100 000 Go from F, ToF 593 500 400 300 200 100 000 Go from E, ToE 712 600 500 400 340 274 200 100 000 Go from c, Fence. 22 24 26 42 48 45 30 18 Line 10= Diag. Line 9. Line 8. 30 52 57 48 32 Line 7. 43 52 45 Gate. 28 + 52. 76 42 Line 6. Part IV.) LAND-SURVEYING. 159 Finis. ToH. 895 Diag. }o from B, "ToB~ Line 16. 720 600 40 500 48 460 Gate. 400 32 350 18 300 28 200 68 100 55 000 34 Go from K, Line 15. To the Fence. 580 28 ToK 546 30 500 32 400 46 300 45 200 40 100 34 000 Go from H, Line 14. ToG 908 Diag. Go from c, Line 1 3. ToC 624 54 500 65 400 63 300 52 200 30 100 000 Go from H, Line 12. ToH 750 700 18 600 38 490 60 +35 350 104 220 15 +80 100 25 000 30 Go from o, Line 11. 160 land-surveying. (Part IV. Answer. Having drawn the plan, you will find the perpendiculars of the different trapeziums to measure as follow : viz. D m = 426, and B n = 400, in No. 1 ; C m = 503, and F n — 44S, in No. 2 ; H n = 515, and E m = 498, in No. 3 ; and Cd = 428, and K m = 439. in No. 4. ABBA OF NO. 1. Double areas. 821870 Trapezium A B C D. 84786 Offsets on A B. 64890 Ditto on B C. 72968 Ditto on A D, 1034514 Sum. 93790 Insets on C D. 2)940724 Difference. 4.70362 Area in square links. 4 2.S1448 40 32.57920 Area 4a. 2r. 32^p. AREA OF NO. 2. Double areas. 917715 Trapezium D C E F. 93790 Offsets on C D. 55510 Ditto on D F. 1067015 Sum. 60758 Insets on C E. 43590 Ditto on E F. 10434S Sum. 962667 Difference. Area 4a. 3r. 10p. Part IV.) I.AND-SUKVEYING. l()l AREA OF NO. 3. Double areas. 919804 Trapezium C E G H. 60758 Offsets on C E. 42480 Ditto on E G. 81310 Ditto onG H. 1104352 Sum. 54096 Insets on C H. 1050256 Difference. Area 5a. Ir. Op. AREA OF NO. 4. Double areas. 775965 Trapezium B C H K. 54096 Offsets on C H. 41024 Ditto on H K. 57200 Ditto on K B. 928285 Sum. 54890 Insets on B C. 873395 Difference. Area 4a. Ir. 18|p. No. 1. CONTENT. A. . 4 . 4 . 5 . 4 . 19 R. P. 2 32£ 3 10 2 3 1 4 1 18J 21 Sum Note 1. — In the last example, every field is measured separately ; but they are so connected by the chain-lines, that no difficulty can arise to the learner, in planning them. It may also be observed that no proof-lines were mea- sured ; but they should never be omitted in practice. If they be, the Sur- veyor cannot depend upon the accuracy of his work. M 162 land-surveying. (Part IV. 2. — If the foregoing Estate be laid down upon a sheet of drawing paper, by a scale of one chain, or of two chains to an inch, a finished Plan may then be made, and ornamented with Indian ink, in a similar manner to Plates IX. and XL Or the quick-wood hedges may be made by a pen and Indian ink ; or they may be represented by running narrow shades of colouring along the lines which form the boundaries of the fields ; and each field may then be washed over with a different colour, mixed up thinly with water, and laid on with a small brush, or camel's hair pencil. (See Part V. for the method of transferring a rough Plan to a clean sheet of paper, in order to make a finished Plan, with proper embellishments.) 3. — In drawing the finished Plan, all the out-boundaries may be con- sidered as belonging to the fields which they respectively adjoin ; that fence from B to C. may be made as belonging to No. 1 ; that from C to D, as belonging to No. 2 ; that from C to E, as belonging to No. 3 ; and that from C to H, as belonging to No. 4. (See a remark on the 39th page, re- lating to fences.) 4. — The title of the finished Plan of the foregoing Estate, may run thus : Plan of an Estate lying in the Parish of Bradford, in the West-Riding of the Countv of York, PROBLEM IV. MEREs AND WOODS'. The method of measuring Meres and "Woods by the Chain and Cross, has already been shewn in Part III. It is here pro- posed to survey them by the Chain only. In this case, you must not only measure on the outside of the mere, or wood, and take insets as before directed ; but also take such external angles, or tie-lines, as will enable you to lay down the figure. EXAMPLE. Let the following figure represent a mere, the area of which is required. Part IF.) LAND-SURVEYING. 163 AS 1 ,'••• Begin at -f- 1, and measure eastward as far as -f 2, taking insets as you proceed ; then produce the line to -j- 3. Return to -j- 2, and measure northward as far as -j- 4 ; thence run a line backward to -f- 3, which will tie the first and second lines. Return to -f- 4, continue the line to -f- 5, and produce it to + 6. — Return to -f 5, and proceed westward to -J- 7> * ne di s ~ M 2 16-4 LAND-SURVEYING. (Part IV. tance between which and 4- 6. being measured, will tie the second and third lines. Return to + ?, and continue the line to 4- 8. From -|- 8 proceed to -f- 1, and you will have ob- tained the following dimensions. Note. — Here it may be observed, that after the first three lines are laid down, the fourth line will exactly reach from + 8 to + 1 ; if the operations have been performed with correctness. 1625 to 4- I. 60 1100 iooo 23 800 30 600 60 96 ooo From + 8, go S. 1150 to 4- 8. 100 1100 1000 900 700 - 40 400 4- 7. which is 550 000 from 4- 6. Return to -4- 5. and goVT. 2000 to 4- 6. 1650 + 5. 56 1300 1000 550 400 4- 4. which is 490 40 300 from + 3. 103 48 000 Return to + 2. and cro N. 1500 to 4- 3. 1200 + 2. 50 1100 iooo 850 600 100 400 80 250 000 Begin at + i, Range E. Part IV.) LAND-SURVEYING. 165 Answer. Having constructed the figure, you will find the diagonal, drawn from -+- 1 to -f- 5 = 2085, the perpendicular from -f- 2 upon the diagonal = 950, and that from + 8 = 890 links. Double areas. 3836400 Trapezium made by stations 1, 2, 5, and 8. 84500 ) 1 line ( 87380 (2 J Insets taken on the 53000 (3 ) different lines. 118120 j 4 ( ~343000 Whole Insets. 3493400 Mere, Area 17a. 1r. 35p. PROBLEM V. TO MEASURE AND PLAN ROADS, RIVERS, CANALS, S?c, In measuring Roads, Rivers, or Canals, angles or tie-lines must be taken at the different turns, in order to lay down the chain-lines ; and offsets must be taken to the boundaries, as you proceed, to enable you to draw the plan. Note 1. — The length of a road is generally returned either in miles, fur- longs, and poles, or else in miles and yards. (See the Table, page 43.) 2. — A machine called a " Perambulator" is sometimes used to ascertain the lengths of roads. It has a wheel of 8 feet 3 inches, or half a pole, in circumference, which being made to pass over the ground, puts in motion the clock-work within, and the distance measured is pointed out by an index on the outside. This instrument is much more expeditious for measuring the length of a road, than the chain ; but it is certainly less correct ; for by the wheel passing over stones, sinking into holes, &c the distance is made to appear more than it is in reality. EXAMPLES. 1. Let the following figure represent a serpentine road, a plan of which is required. M -J 166 LAND-SURVEYING. (Part IV. 3 ( Be°in at + 1. and measure to + 3, taking offsets on both sides, as you proceed. Return to + 2, and measure to + 4, from which run a line to + §•> """hich iwD tie the first and second lines. Return to -f- 4, and continue the line to + 6. From -r 6, proceed as before, until you arrive at -f 14 ; and you will have obtained the following dimensions, from which a plan may be drawn, Part IV.) LAND-SURVEYING.. 167 To + 14. 58 350 60 68 200 44 150 + 13 is 184 from + U 50 100 80 Go from + 12, Line 5. To + 12. 30 720 ,70 6.50 600 + 11. 86 550 33 70 300 50 8 is 200 from -f 10 200 120 135 Cross-fence. Go from + 9, Line 4. To + 9. 700 600 Cross-iience. 500 + 8. 38 480 84 40 300 60 52 180 65 150 + 7 is 160 from + 5. 50 100 Go from + 6, Line 3. To + 6. 20 512 50 450 52 380 70 350 + 5. 20 300 80 200 + 4 is 232 from + 3. 18 100 93 Go from + 2, Line 2. To + 3. 600 480 Cross-fence. 400 4-2 38 350 95 15 300 28 200 80 55 000 70 Begin at -|- 1, Line 1. M 4 168 land-surveying. (Part IV. 2. Let the foregoing figure represent a river, a plan of which is required. Begin at a, and measure to c ; taking offsets to the river's edge, as you proceed. From c measure to d ; and there take the tie or chord-line d b, which will enable you to lay down the first and second lines. Continue the second line to n ; and from m, measure to r, at which place take the tie-line r n ; and thus proceed until you come to the end of your survey at x. If the breadth of the river be every where nearly the same, its breadth taken in different places, by the next Problem, or by Problem 10, Part III. will suffice ; but if it be very irregu- lar, dimensions must be taken on both sides, as above. "When the area is required, it must be found from the plan, I by dividing the river into several parts ; and taking the neces- sary dimensions by the scale. Note. — Any Bog, Marsh, Mere, or Wood, whatever may be its number of sides, may be measured by this Problem. Part IV.) 1 AND-SURVEYING. 169 PROBLEM VI. TAKING DISTANCES B Y THE CHAIN AND SCALE. EXAMPLE. Required the distance of an object at A, from B. First, make a station at B ; then, in a direct line with B A, set up a pole, suppose at C ; measure the distance B C. Return to B, and measure in any direction, making an angle with B C, suppose to D ; then set up a pole in a direct line with D A, as at E. Measure the lines D E and E C, and also the diagonal C D ; these will enable you to construct the trapezium B CED. The lines B C and D E, pro- duced, will evidently meet at A. Measure the line B A with the same scale, by which you have con- structed the trapezium, and it will be the distance required. Note. — This method may be well applied to measuring the breadth of a river, or the distance of any inaccessible object ; and any person, acquainted with trigonometry, may easily find the correct distance, after mea- suring the lines before mentioned. 170 LAND-SURVEYING. (Part IF. PROBLEM VII. TO ERECT A PERPENDICULAR BY THE CHAIN, OR TO MEASURE LINES UPON WHICH THERE ARE IMPEDIMENTS. EXAMPLE. Suppose C D E F to represent the base of a building, through which it is necessary a line should pass to an object at B, seen from A. Measure from A to m ; and from m, measure back to a, 40 links. Let one end of the chain be kept fast at a, and the eightieth link at m; take hold of the fiftieth link, and stretch the chain so that the two parts a n. and m n, may be equally tight : then will m n be perpendicular toam, For m n will be 30, a m 40, and a n 50 links; or the sides of the right-angled triangle a m n will be in proportion to each other as 3, 4, and 5. (See Prob. 18. Part L) Measure from m, upon the line m n continued, until you are clear of the impediment, as at c ; then con- tinue the line 40 links farther, to b. *A Find by the above process the perpendicular c d j and proceed in that direction till you are beyond the building, as at h. Again erect the perpendicular h e, upon which measure till you have made h p, equal tome; Part IV.) LAND SURVEYING. 171 and you will then be in a direct line with m A. Erect the per- pendicular p x, which (if you have conducted the work with correctness,) will be in a right line with B. Measure the dis- tance p B ; then A m, added to c h (= m p), and p B, will give the whole length of the line A B. PROBLEM VIII. HA VING THE PLAN OF A FIELD, AND ITS TRUE AREA, TO FIND THE SCALE BY WHICH IT HAS BEEN CONSTRUCTED. Rule. — By any scale whatever, measure such lines as will give you the area of the figure ; then say, as this area is to the square of the scale by which it was found, so is the true area, to the square of the scale required. EXAMPLE. Suppose the true area of a field, the plan of which is given, to be 9a. 1r. 32p. ; and that by a scale of 2 chains to an inch, I find the area to be 4a. Or. 32p. ; required the scale by which the plan was constructed. First, 9a. 1r. 32p. — 945000 square links; and 4a. Or. 32p. = 420000 square links ; then, as 420000 : 4 : : 945000 : 9. Hence, it appears, the plan was constructed by a scale of 3 chains to an inch. N t e . — The principle of this process is, that the areas of similar figures are to each other as the square of their homologous sides. (Theo. 16, Part I.) 172 LAND-SURVEYING. (Part IV. THE METHOD MEASURING HILLY GROUND. A line measured upon the acclivity or declivity of a hill, -will evidently exceed one measured upon the horizontal base ; con- sequently, if a plan be laid down by the hypothenusal lines, every part will be thrown out of its true situation ; so that the boundaries of a mountainous lordship would appear distorted and unnatural ; and the estate would scarcely be recognised by its own inhabitants. Surveyors, therefore, agree in their opinions concerning the necessity of reducing hypothenusal to horizontal lines, for the purpose of planning ; but they differ with regard to the modes of finding the area ; some contending that it should be com- puted according to the hypothenusal, and others according to the horizontal lines. The advocates for the horizontal measure assert, that no more corn, trees, &c. can grow upon the surface of a hill, than upon a space equal in area to its base, admitting both to be of the same quality ; and that hilly ground, in general, is less productive than plains, and its cultivation attended with more expense. The advocates on the other hand state, that the surveyor has nothing to do with the quality of the land ; and that it is his duty to return the measurement of the surface, and leave the value to those whom it more nearly concerns. The horizontal measure, however, is now generally adopted, except for paring, reaping, &c. in which cases the hypothenusal measure is very justly preferred. (See Deut, xxiv. 14, 15 ; and Prov, xxii, 16.) Part IV.) LAND-SUllVEYING. 173 Methods used by Practical Surveyors to reduce hypothenusal to horizontal Lines. METHOD I. When the hill is of a regular slope, take its altitude with a Theodolite, or with a Quadrant ; then, by a trigonometrical canon, in which the hypothenuse may be counted 100 links, determine the number of links in the base. These deducted from 100, will shew the number of links by which each chain must be shortened, for the purpose of planning. Note. — For the principles of Trigonometry, the reader is referred to the works of Simpson, Emerson, Vince, Horsley, Keith, Bonnycastle, and the Rev. W. Wright, on that subject ; and for the history, construction, and use of Logarithms, to Dr. Hutton's Mathematical Tables. EXAMPLE. Suppose the altitude of a hill to be 16° 15', and the length of a line measured upon its surface, to be 2550 links ; required the length of the line, that must be used in planning. In the right-angled triangle ABO, are given the hypothenuse A C =. 2550, and the angle B A C = 16° 15', to determine the base A B. Or A D = 100, and the angle EAD = 16° 15' to find A E. As Radius 1 0.00000 Is to the hypoth. A D — 100 links 2.00000 So is the co-sine of the angle E AD = 16° 15' ... 9.98229 To A E = 96 links 1798229 in I. AND SURVEYING. (Part IV. Hence it appears, that 4 links must be subtracted from each chain; consequently, (25 X 4 -f- 2 =) 102 links must be taken from A C ; hence AB = 2448 links, the line required. Proof. — As 1 : 2550 :: .96005 (the nat. co-sine of 16° 15') : 2448.1275 links — A B. A Table for reducing hypothenusal to horizontal Lines. Different Altitudes of Hills Links to be subtracted from each Chain measured upon the Surface. Deg. Min. Links. 5 44 h 8 6 1 11 28 2 14 4 3 16 16 4 18 12 5 19 57 6 21 34 7 23 4 8 24 30 9 Deg. Min. j Links. 25 51 10 27 8 11 28 21 12 29 32 13 30 42 14 31 47 15 32 52 16 33 54 17 34 55 18 35~ 54 19 36 52 20 37 49 21 38 44 22 39 39 23 40 32 24 Note. — To construct the above Table, suppose the base A B, in the pre- ceding triangle, to be = 99.5, and the hypothenuse A C = 100 ; then, by Trig, as 100 : 1 :: 99.5 : .995, the nat. co-sine of the angle B A C= 5° 44'. — In the same manner, the rest of the angles are obtained, by different opera- third, &c, Part IV.) LAND-SURVEYING, 175 A Quadrant for taking the altitude of Hills , Steeples ■> fyc. By those who do not wish to incur the expense of a Theo- dolite, a Quadrant may be made of about twelve inches radius, by which the altitude of a hill, steeple, &c. may be taken to a tolerable degree of accuracy. The arc A B must be correctly divided into 90 equal parts or degrees ; and numbered from right to left. Upon the radius A C, must be fixed two brass sights, a and b, through each of which must be made a very fine hole ; and from the centre C must be suspended a plummet, by a thread of fine silk. 176 land-surveying. (Part IV. Note. — In taking the altitude of an object, the quadrant is commonly held in the hand ; but it is much better to fix it to a staff, which may be done by means of a nail, passing through the quadrant and staff, upon the end of which must be screwed a small nut. To take the Altitude of a Hill with the Quadrant. Upon the top of the hill fix an object, exactly as high as yonr eye 'will be from the ground, in taking the observation. At the bottom of the hill, fix the quadrant-staff perpendicularly to the horizon ; which may be easily done by means of the plummet. Then with one eye at A, the other being closed, look through the sights, turning the quadrant until you per- ceive the object at D; so will the arc B G, cut off by the plumb-line C G, be the measure of the angle D C E, or the altitude of the hill, in degrees, &c. Note. — When you take the altitude of a hill by a Theodolite, the obser- vation must be referred to an object fixed upon the top of the hill, exactly as high as the telescope. To take the Altitude of a Steeple, §c. with the Quadrant. Screw the quadrant fast to its staff, so that the plummet may hang exactly at 45°, when the staff is perpendicular to the hori- zon. Then, move the staff backward or forward (always keep- ing it perpendicular) until you can see the top of the object through both the sights. Measure the distance between the bottom of the staff and that of the object, which being added to the height of your eye, will give the altitude required, METHOD II. As the foregoing method of reducing hypothenusal to hori- zontal lines, can only be applied, with accuracy, when hills are of a regular slope ; surveyors, in general, elevate the chain, as they ascend or descend a hill, in order to preserve the horizontal line. Part IV ) LAND-SURVEYING. 177 EX \ MPLE8. i L— ]n a>- V. ^ r c w- \ g D c Suppose the lines A I> and B C, to represent the acclivity and declivity of an irregular liill ; it is required to raeasue them, and to preserve the horizontal line A ('. i A. stretch the chain toward B, and suppose it to reach to a ; th stent, upon the hase, will evidently reach from A to g ; and a perpendicular erected from g will intersect the line A B in d ; hence the distance A d, upon the hypothenuse, will make one chain upon the hase At A, stick your offset- staff into the ground, perpendicularly to the horizon, and let your assistant hold the chain, suppose at the twenty-fifth link, close to the surface of the hill, as at b ; at the same time you must elevate tie- end of the chain to c, forming the horizontal line c b ; then move forward to b, at which place fix your staff Let your assistant hold the fiftieth link at p, whi! the twenty-fifth to n, forming the horizontal line n p. Again, fixing your staff at p, elevate the fiftieth link to m, while your assistant holds the Beventy-fifth at e. Lastly, put down the staff at e. and elevate the seventy-fifth link to r, while the hundredth is held by your assistant at d. There he • put down an arrow ; and thus you must proceed until you arrive at I>, where you will have ohtained the horizontal line A D. In descending from B to C, let your assistant hold one end of the chain at B, whilp you elevate, suppose, the fiftieth link to n. N 178 LAND-SUBVEYING. P< rt IV. forming the horizontal line B n ; then fix the staff at a. perpen- dicularly to the horizon, and touching the chain at n. Xext. at hold the fiftieth link at a. while you elevate the hundredth to m, and put down the staff at r, as before. In this manner, having arrived at C. you will r ained the ntal line D C, which I ~e the ratal line A C. as requL 1. — If you wish to obtain the hypothenusal, as well as the horizontal line, divide your field-book into four columns, in one of which you mu- the number of links between a and d, «Jcc. which being added to the horizon- tal, will give the hypothenusal line. 2. — When ^eent of a hill is great, you will not be able to more than 10 or 15 links of the chain at one time ; for, in such cases? rtempt to r I : U find that the perpendiculars A c, b n, &c will exceed your own height, before you can form the fa talline-: . . ire.) -METHOD in. Hypothenusal lines may likewise he expeditiously and cor- rectly reduced to horizontal by an instrument invented by Mr. Robert King, of Scarborough,. Land-Surveyor, and caD i nt." THEDESCRHTIONAND USE OF KING's SURVEYING QUADRAXT. by TT'. Jonas, M I: DESCRTPT s: Tkf. quadrant is fitted to a wooden square, which - upon a -staff, and may be fixed at any height by rat a screw, which draws in the diag : staff; thus em- bracing the four sides . the limb of the square per- pendicular to with iron, I, on the Part IV.) land-survuyixg. 179 station -line, the square answers the purpose of a cross-staff, and may, if desired, have sights fitted to it. The quadrant is three inches radius, of brass, is furnished with a spirit-level, and is fastened to a limb of the square, by means of a screw. When the several lines on the limb of the quadrant have their first division coincident with their respective index-divisions, the axis of the level is parallel to the staff. The first line next the edge of the quadrant, is numbered from right to left, and is divided into 100 parts, showing the number of links in the horizontal line, which are completed in 100 links on the hypothenusal line, and in proportion for any smaller number. The second, or middlemost line, shows the number of links the chain is to be drawn forward, to render the hypothenusal measure the same as the horizontal. The third or uppermost line, gives the perpendicular height, when the horizontal line is equal to 100." USE. " Lay the staff along the chain-line on the ground, so that the plane of the quadrant may be upright ; then move the quadrant, till the bubble stands in the middle, and on the several lines you will have, — 1. The horizontal length gone forward in that chain. 2. The links to be drawn forward to complete the horizontal chain. 3. The perpendicular height or descent made in going forward one horizontal chain. The first two lines are of the utmost importance in surveying land, which cannot possibly be planned with any degree of accuracy without having the horizontal line ; and this is not to be obtained by any instrument in use, without much loss of time to the surveyor. Whilst with this, he has only to lay his staff along the ground, and set the quadrant till the bubble is in the middle of the space, which is very soon performed. And he saves by it more time in plotting his survey, that he can lose in the field ; for as he completes the horizontal chain as he N 2 180 land-surveying. (Part IV. goes forward, the offsets are always in their right places, and the field-book being kept by horizontal measure, his lines are sure to close. If the superficial content, by the hypothenusal measure, be required for any particular purpose, he has that likewise, by entering in the margin of his field-book the links drawn forward in each chain, having thus the hypothenusal and hori- zontal length of every line. The third line, which is the perpendicular height, may be used with success in finding the height of timber. Thus, measure with a tape of 100 feet, the surface of the ground from the root of the tree ; and find, by the second line, how much the tape is to be drawn forward to complete the distance of 100 horizontal feet ; and the line of perpendiculars shows how many feet the foot of the tree is above or below the place where the 100 feet distance is completed. — Then, inverting the quadrant by means of sights fixed on the staff, place the staff in such a position, as to point to that part of the tree whose height you want ; and sliding the quadrant till the bubble stands level, you will have on the line of perpendiculars on the qua- drant, the height of that part of the tree above the level of the place where you are ; to which add or subtract the perpen- dicular height of the place from the foot of the tree, and you obtain the height required." Note i. — If the real utility of Mr. King's Surveying Quadrant was better known among Land-Surveyors, it would be in more estimation ; and would save them a great deal of trouble in measuring hilly ground. It may be had of Mr. W. Jones, price If. 18s. 2. — For the sake of those who may think Mr. King's Quadrant too expen- sive, I have invented one of a cheaper kind, which answers the same purpose in surveying, as Mr. King's, and may be used with equal facility. Any com- mon mechanic will be able to make the wood-work ; and after the lines are drawn upon the plate, an engraver will cut them for about five shillings. The whole expense of one which the Author had made for his own use, five inches radius, together with the offset-staff belonging to it, amounted to about twelve shillings. Hiiro II. "/> J3 I /// E G- Q--fe Part IV.) LAND-SURVEYING. 181 The following Table, by which the Quadrant may be constructed, shows the Number of Links to be drawn fonoard upon the Sur- faces of Hills of different Altitudes, to complete the horizontal Chains. Deg.Min 5 43 Lks. i Deg 41 Min. ~44~ Lks. Deg .Mm Lks. 34 53 ~~ 28" ~68~ 8 4 1 42 12 35 58 43 69 11 22 2 42 40 36 53 58 70 13 52 3 43 7 37 54 13 71 15 51 4 43 34 38 54 27 72 17 45 5 43 59 39 54 41 73 19 22 6 44 25 i 40 54 55 74 20 50 7 44 50 1 41 55 9 75 22 12 8 45 14 42 55 23 76 23 27 9 45 38 1 43 55 36 77 24 37 10 46 1 44 55 49 78 25 43 11 46 24 ' 45 56 2 79 26 46 12 46 46 46 56 15 80 27 45 13 47 8 47 56 28 81 28 42 14 47 30 48 56 40 82 i 29 35 15 47 51 49 56 53 83 30 27 16 48 11 50 57 5 84 31 16 37 48 32 51 57 17 85 32 4 18 48 52 52 57 29 86 32 49 19 49 11 53 57 40 87 33 33 20 49 30 54 57 52 88 34 16 21 49 49 55 58 3 89 34 57 22 50 8 56 58 15 90 35 37 23 50 26 57 58 26 91 36 15 24 50 44 58 58 37 92 36 52 25 51 2 59 58 48 93 37 28 26 51 19 60 58 58 94 38 3 27 51 36 61 59 9 95 38 38 28 51 53 62 59 19 96 39 11 29 52 9 63 59 30 97 39 43 30 52 26 64 59 40 98 40 14 31 52 42 65 59 50 99 40 45 32 52 58 66 60 100 'J 41 15 33 J 53 13 67 N 3 182 LAND-SURVEYING, (Part IV. The Construction of the preceding Table. C In the right-angled triangle A B C, suppose the base A B to be 100, and the hvpothenuse A C 100.5 ; then by Trig. as 100. 5 : 1 :r 100 : .99502, the nat. co-sine of the angle BAG — 5° 43'. — In the same maimer, the rest of the angles are obtained, by different operations, accounting the hypothenuse 101 in finding the second angle, 102 in finding the third, &c. — Now, from the preceding Table, it evidently appears, that if an instrument be constructed to take the altitude of a hill at every chain, if necessary, and a line traced upon the instrument, be so divided as to exhibit the number of links which the chain must be drawn forward, upon the surface of the hill, to com- plete the horizontal chain, according to the Table ; it may be used with great advantage in surveying h ill v ground. The method of constructing the Quadrant, Sfc. Procure a piece of soft sheet-brass, and upon it draw the lines A B and A C perpendicular to each other ■ and with a radius of five inches describe the quadrant B C. Next, draw the lines D E and D F perpendicular to each other ; and with four inches in your compasses for the first sweep, describe the double arc E F, which divide correctly into 90 equal parts or degrees. At a proper distance, likewise, from the arc E F describe the double arc G H, and the double arc m n. Of these, the latter must be cut through the brass by a file. You must also procure a small glass tube, nearly filled with spirit, (generally called 4 a spirit-level,') and a piece of sheet- Part IV.) LAND-SURVEYING. 183 brass K L, in length equal to A B, and in breadth rather exceeding the diameter of the tube ; which call " the Index." Then procure another piece of sheet-brass in the form of a semi-cylinder N P, large enough to admit the tube ; and in it make the aperture b c d, in order to see the bubble. Its edges solder to the index K L, so that the centre c may be exactly in the middle point between r and a ; r a rather exceed- ing D E ; and a u being exactly equal to D m. The end N must also be closed up, by soldering a piece of brass upon it ; and the end P left open, in order to admit the tube. Next make a wooden quadrant, exactly the size of A B C, and in it a grooye corresponding with the aperture m n, and large enough to admit a small screw-nail, with a square head and neck, so as to run, but not to turn round in the grooye m n. Then fix the plate A B C to the wooden quadrant, by the countersunk screws, 1, 2, 3, 4, 5 ; taking care first to insert the screw-nail aboye-mentioned, into the aperture m n, at a small hole made for that purpose at n. Next, let the index K L be fixed upon the face of the qua- drant, by a screw-nail passing through it at a, which must enter the quadrant exactly at the centre D. The nail in the aperture m n must likewise pass through the hole at u, and upon the end of this nail must be screwed a small nut, by which the end K of the index may be made fast at any altitude. Now, to diyide the arc G H, moye the end K of the index toward C, until the line or edge r e, which must be exactly in the centre of the index, cuts the arc E F at 8° 4', as per Table ; and upon the arc G H, mark the first division. In the same manner, moye the index until it cuts off 11° 22', and there mark the second ; continuing these operations, until you haye made as many divisions as are necessary. — The divisions marked upon the arcs E F and G H, must then be properly cut and figured by an engraver. Next procure a wooden cross, R T S W, the three limbs of which must each be in length equal to A B or A C ; and must form with each other three right angles, R S T, T S W, and WSR. N 4 184 land-surveying. (Part IV. This cross must be made to slide upon an offset-staff by means of a square or rectangular aperture through the limb R S ; and if a screw be fixed in the side of the limb at n, the cross may be fastened to the staff at any convenient height, by turning the screw against the side of the staff. As it will be somewhat difficult, however, on account of the limb R S being hollow, to make a joint at S sufficiently strong to keep the limbs at right angles with each other, they may be supported by means of the brackets, a b, c d, and e f. The quadrant ABC must then be fixed upon the square R S T, by means of two screws pass- ing through the bracket a b, and one through the bracket m, so that the outside of the limb S R may coincide with A B, and the outside of the limb S T with A C. To fix the tube or spirit-level correctly in the semi-cylinder N P screw the index fast at no altitude, and place the edge A B of the quadrant upon a level table, which you may do by laying the tube upon it, and varying the position of the table until the bubble stands in the centre of the tube ; then put the tube into the semi-cylinder N P, and fix it in such a manner that the bubble may be seen at c ; after which, close up the end P with brass or putty. Note. — If the quadrant be made the same size as that in Plate II., instead of five inches radius, as before directed, it will save much trouble in di- viding ; as the engraver may then follow the divisions given in the Plate ; and the construction of this useful instrument will thus become very simple. The Method of proving the Quadrant, C B Part IV.) LAND-SURVEYING. 185 Let AC b strong plank, placed with one end against the perpendicular wall B C, and the other npon the horizontal plane A B. Lay an offset-staff, suppose of 12 links, upon A C, with one end at A ami the other at m ; then elevate the lower i that the stall' a n may he parallel to A \\. Measure the i d, which suppose to be 10.5 inches \ then say, as 12 link* is to 10.5 i is l"<) links to 87.5 inches, or 11 links. A B of the quadrant upon the plank A ( . the end Iv of the index, until the bubble stands at I if the index cut off 11 links, or nearly BO, upon the are OH, the quadrant us The Method ofuting the Quadrant. the stafi 1 ', with the quadrant fixed to it, along the chain- that the edge A B of the quadrant may come in contact with the pound; then elevate the end K of the index, until the bubble stands at C ; and you will have the altitude of the hill upon the are 1] J\ and the number of links to be drawn forward to complete the horizontal chain, upon the arc G H. If you lix the bottom of the staff into the ground, upon the chain-line, the limbs S T and S W will serve as a cross, by which perpendiculars may be erected. I . — In using the quadrant, care should be taken to place it upon the even part of the surface of the hill. . measuring and reducing a line upon a hill, if it happen that the end of the chain reach' .at the end of the line, you n deduct from the chain instead of drawing it forward. i\, r ex- : if yon fmd that tlu- chain oughl to be drawn forward 6 links, you instead <»f 100 links. Or, if tin- fiftieth link reach to the station, istead of 50 links, \c. [nine, by < I chain, and aKo 1 iv the Quadrant. thr number of link iwn forward upon the surface of i hill, in order ri/.ontal chain, you will seldom find them precisely the 183 land-surveying. (Part IV. same ; because it is almost impossible to prevent the chain from forming a curve line, or to keep the staff perpendicular to the horizon. In every case however, the conclusions of an instrument, constructed upon mathematical principles, are to be preferred. Methods for finding the kypotkenusal Measure of Hilly Ground. This is by far the most difficult part of surrevinp; ; and though we may approach ' toward, we can seldom obtain the true area of hills ; because their surfaces are generally so irre- gular, that it is almost impossible to divide them into proper figures. — If the land to be surveyed, lie in the form of a square, rect- angle, trapezoid, trapezium, or triangle, against the side of a hill of a regular slope, take the dimensions and find the area in the same manner as if the figure lay upon a plane. But should it be required to find the area of a field (suppose in the form of a trapezium) in which there is a hill so situated as to affect the diagonal only ; if the sides and diagonal be measured, and the figure laid down according to those dimensions, the perpendi- culars will obviously measure less than they would have done, had the diagonal been reduced to a-horizontal line ; consequently, we cannot obtain the hypothenusal measure of such a field, by the common method of measuring trapeziums, or triangles. In such cases, it is perhaps best, first, to measure the hill only. For this purpose, surround its base by station-staves, dividing it into an irregular polygon, each side of which must be mea- sured. Then fix upon a convenient place, near the top of the hill, for a station ; and between it and each station at the bot- tom, measure a line. Thus will the whole surface be divided into triangles, the areas of which, must be found by laying down each triangle separately. Or, from the three sides, you may find the area of each triangle, as already directed. Next, measure the remainder of the field, by dividing it into proper figures. Collect all the areas together, and their sum will be the area required. "When the land to be surveyed, ascends a hill on one side, occupies a plane upon the top, and descends on the other side ; Part IF.) LAND-SURVEYING. 187 you must divide it into such figures as will enable you to ap- proach as nearly as possible to the true area. — The foregoing directions may, perhaps, be found useful to a learner ; but, in practice, much will always depend upon the Surveyor ; he ought, therefore, to be very careful, whatever be the shape or size of the hill, to divide it into such squares, rect- angles, trapezoids, trapeziums, or triangles, as are most likely to give him the hypothenusal measure. Note 1 . — In surveying a triangular field, of which one side passes over a hill, the other two being upon the horizontal plane of the base ; it will be necessary to divide it into two triangles, by measuring a line from some part of the fence passing over the hill, to the opposite angle. Thus will two sides of each triangle be affected by the hill, the areas of which, found separately, will give the hypothenusal measure of the field. 2. — After making some experiments, and considering the subject very maturely, the Author is of opinion that the most correct method of finding the surfaces of hills, in general, is to take the dimensions in such a manner that the areas of the different figures into which the hills are divided, may be found from the lines measured in the field, without having recourse either to the scale or plan. Hence, if the figures be rectangles, their lengths and breadths must be measured in the field ; and if they be triangles, trapeziums, or trapezoids, their bases and perpendiculars must be measured in the field. Several very experienced Laud-Surveyors with whom the Author is ac- quainted, perfectly agree with him on this subject. EXAMPLES. 1. The length (or hypothenusal line) of a rectangular field, lying upon the side of a hill of regular ascent, is found to be 900 links, its breadth, 800 links, and the altitude of the hill 28° 21'; required the hypothenusal measure, and the length of the line that must be used in planning : 900 800 7720000 4 .80000 40 32.00000 Area 7a. Or. 32p. 188 land-surveying. (Part IV. Now, by the Table, page 174, we find that 12 links must be deducted from each chain ; hence 9 X 12 = 108, which being taken from 900, leaves 792 links, the length of the line required. Note.— If we multiply 792 by 800, we find the product 633600 square links, equal to 6a. 1r. 14p. the horizontal measure, which is less than the hypothenusal by 3r. 18p. 2. Let A B C D represent a field in the form of a trapezium, lying upon the side of a hill of an irregular ascent, the sides A B and B C being upon the horizontal plane of the base ; re- quired the horizontal and hypothenusal measures, from the following notes. I Part IV.) LAND-SURVEYING. 189 no BD 1154 6 12 1100 11 1000 12 900 10 i 800 11 700 10 600 8 500 9 400 7 300 8 200 6 100 From B, goN. A C 1300 R. off A. 78 DA 990 6 7 800 9 700 8 600 7 500 9 400 10 300 . 11 200 11 100 R. offD. 96 CD 1044 5 10 1000 11 900 12 800 11 700 9 600 10 500 8 400 7 300 6 200 7 100 R. offC. BC 800 R. off B. AB 700 Begin at A. - Diag. Diag. reduced for a proof-line. Range S. TV. 190 land-surveying. (Part IV. The Operation of finding the horizontal Measure. First, 700 -f 1154 -f 990 = 2844, the sum of the three sides, which being divided by 2, gives 1422. — From this num- ber, deduct severally each side, and we obtain 722, 268, and 432, for the three remainders. Then, by multiplying the half sum and the three remainders continually together, and ex- tracting the square root of the product, we obtain 344768 square links, the horizontal measure of the triangle A B D. In a similar manner, we find the horizontal measure of the triangle B C D = 405559 square links ; which, added to 344768, gives 750327 square links, equal to 7a. 2r. the hori- zontal measure of the trapezium ABC D. — The Operation of finding the hypothenusal Measure. First, 1154 -f- 110 =: 1264, the hypothenusal line BD; and 990 + 78 — 1068, the hypothenusal line D A. Then, 700 + 1264 -f 1068 — 3032, the sum of the three sides, which being divided by 2, gives 1516. From this number, deduct severally each side, and we obtain 816, 252, and 448, for the three remainders. Then, proceeding as before, we ob- tain 373709 square links, the hypothenusal measure of the triangle A B D. — In a similar manner we find the hypothenusal measure of the triangle BCD = 437917 square links, making jointly 821626 square links, equal to 8a. Or. 34p. the hypothenusal measure of the trapezium ABCD, which exceeds the hori- zontal measure by 2r. 34p. Note 1. — If you lay down the trapezium by the horizontal and hypothe- nusal lines respectively,and measure the perpendiculars by the scale, you will find the areas the same as those resulting from the foregoing operations. Part IV.) LAND-SURVEYING. 191 2.— From these examples, it appears that the difference between the hori- zontal and hypothenusal measures of hilly fields, is often very considerable, and is deserving of particular notice. For instance ; suppose the field, in the last example, to have been sown with wheat, and the owner to have sold the crop at the rate of 12/. per acre ; the reapers have a claim upon the buyer for the hypothenusal measure ; but if he makes his payment to the seller, by the same admeasurement, he will receive 8/. lis. more than his clue. Practical Surveyors, however, in general, (as before observed,) return the horizontal measure, in surveying estates ; whence few farmers, comparatively speaking, are charged for more ; and ought not, therefore, when they sell a crop of corn, &c. to expect pay for the hypothenusal measure. REMARK. Since the publication of the first edition of this Work, the Author has consulted several eminent Land- Surveyors, and also Commissioners for Inclosures, in very extensive practice, in the West-Riding of Yorkshire, and in Cumberland, and Westmore- land, places noted for their hills ; and they, without one ex- ception, inform him that the horizontal measure of hilly ground is always returned, both by them, and by every practical Sur- veyor with whom they are acquainted. Some late writers on Surveying contend very strenuously for the hypothenusal measure of hills ; but the Author and his friends have no hesitation in saying, that those writers are very deficient in practical knowledge. If we consider the earth as a perfect sphere whose diameter is 7957 miles, it is not necessary to take its curveture into con- sideration in surveying single Fields, Farms, or Lordships ; for it is evident that the quantity of land even in the County of York, would form such a small spherical segment, that its con- vex surface would exceed the area of its base extremely little. But we know that the hills upon the earth's surface are pro- tuberances, and the valleys are cavities, both of which tend very materially to destroy the globosity of the earth ; consequently it is evident that if the surfaces of all the mountains, hills, val- leys, plains, oceans, seas, rivers, lakes, Sec. &c. were measured 192 land-surveying. (Part IV. separately, and then added together, the aggregate sum would greatly exceed the convex surface of the earth, measured as a perfect sphere ; hence the absurdity of the arguments of those writers who contend that all hills, however irregular, should be considered as bearing some similitude to a spherical segment^ or to a hemisphere of the earth. Now, as all hills are more or less irregular, the Author must confess that he is completely at a loss how to consider any hill as resembling the segment of a sphere ; much less Snowdon and Plinlimmon, in Wales ; the Peak, in Derbyshire ; Whernside and Ingleborough, in Yorkshire ; Helvellyn and Skiddaw, in Cumberland ; the Cheviot Hills, in Northumberland ; and the Grampian Hills, and Ben Nevis, in Scotland ; to say nothing of the Pyrenees, the Alps, the Apennines, the Carpathian, the Koelen, and the Uralian Mountains, in Europe ; and the still higher mountains of Asia, Africa, and America. But let us consider the subject on a less extensive scale ; and we shall still find that the advocates for the horizontal measure have the advantage, both with regard to practicability, expe- dition, accuracy, and justice. It may be seen by inspecting the figure on page 177, that it requires no more posts, fixed at a certain horizontal distance from each other, to extend over the surface of a hill, than would be required for the horizontal plane of its base, if the hill were actually removed. It is also well known that no more trees, corn, &c. will grow upon the surface of a hill, than upon a plane equal in area to its base ; because the natural direction of all vegetation is perpendicular to the horizon ; hence the in- justice done to the occupier, by returning the hypothenusal measure of hills. Again, if the area of a field containing hills and valleys, either natural or artificial, be found from lines measured on the surface, and the field be sold by this measurement, and it be afterwards levelled by filling up the valleys with the hills ; it is evident that the buyer will not have the quantity of land for which he paid, if the field be re-measured ; hence the injustice of selling ground by the hypothenusal measure. Lastly, it is evident that no more houses can be built upon Part IF.) LAND-SURVEYING. 193 a hill, than what could be built upon its base, if the hill itself ■were removed ; because the walls of all houses are perpendicular to the horizon, and their eaves parallel to it ; hence the buyer of building ground situated on a hill, forming an inclined plane, will be completely defrauded, if the ground be sold by the hypothenusal measure. The same observations are equally just in all cases, relating to the measurement of hills, except for labour performed by the acre, which should always be calculated from lines measured upon its surface ; because the spade, plough, si the, or sickle, must inevitably pass over the whole hypothenusal area. It may fairly be presumed that those writers who contend for the hypothenusal measure of hills universally, have never taken an actual survey of a mountainous district, where almost every line is affected by a hill, or they would have discovered the im- practicability of the method which they recommend. It is allowed by every one that the horizontal lines must be used, in order to produce a correct plan of a mountainous estate ; but when a plan by the horizontal lines, and the area by the hypothenusal lines are wanted, it is evident the Surveyor must not only have two sets of lines, but also two different plans laid down from those lines. One of those plans being laid down from the horizontal lines will exhibit the buildings, fields, rivers, &c. &c. in their natural situations ; and the other being laid down by the hypothenusal lines, will shew the surfaces of the hills extended on a plane : hence their hypothenusal areas may be found. Either this method must be followed, or the Surveyor must first take the horizontal lines for planning; and afterwards measure such lines on the surface of the ground, as will give him the hypothenusal area of the hills. Every professional Surveyor will readily perceive, that both these methods must be very liable to errors, without any pos- sibility of detecting them ; for neither in planning from hypothe- nusal lines, nor in finding the area from dimensions taken in the field, can we have the least proof of the accuracy of the work. And, if to these objections, we add the difficulties which will present themselves in taking the angle of elevation or depression o 194 land-surveying. Pari IV. of erery hill with a theodolite ; the impossibility of doing this correctly, when a hill varies frequently in its inclination time that must necessarily be consumed in measuring rwo sets of lines : drawing two plans. together with the inac- curacies which must arise from such a multiplicity of operations, devoid of proofs ; it will manifestly appear that surveying, on these principles, is a theoretical dream, a labyrinth of perplexi- > aid a system of absurd: - LAND-SURVEYING. $art m dfiffi> THE METHOD OF SURVEYING AND PLANNING LARGE ESTATES, OR LORDSHIPS. V arious methods are adopted by different Surveyors, in taking the dimensions of large estates, or lordships ; I shall, however, describe only four, which I conceive to be more accurate and practical than any other with which I am acquainted. METHOD I. Having made yourself acquainted with the form of the estate, either by actual examination, or by the assistance of a previous plan, select two suitable places, at the greatest convenient distance from each other, as grand stations ; and measure a prin- cipal base, or what is generally called a " main-line," from one to the other, noting every hedge, brook, or other remarkable object, as you cross or pass it ; taking offsets likewise to the bends or corners of the hedges that are near you. Next, fix upon some other suitable place, towards the outside of the estate, as a third grand station ; to which, from each extremity of the diagonal or main-line, or from two convenient points in it, lines must also be run. These three lines being laid down, will form one large trian- gle ; and in a similar manner, if necessary, on the other side of the diagonal or main line, a second triangle may be formed. The survey must then be completed by forming smaller trian- gles, on the sides of the former ; and measuring such lines as o 2 196 LAND-SURVEYING. (Part V. will enable you to obtain the fences of each enclosure, the boundaries of rivers, roads, lakes, &c. &c. ; and prove the whole work. Note 1. — If the estate be of a triangular form, three lines must be run, in the most convenient manner, so as to form the largest triangle possible ; after which, other lines must be measured, offsets taken, &c. &c. ; so that ail the fences may be obtained, and the survey completed, as in Plate VIII. 2. — When an estate is divided into two triangles, it is generally best to finish one of them before you measure any of the internal lines of the other, as in Plate III. Sometimes, however, it is more convenient and expeditious to run some lines in the second triangle before you have finished the first, as in Plate X. 3. — Estates similar to those ha Plates III. and VIII., are very easy to sur- vey, as they contain no impediments ; but it is otherwise with estates like that in Plate X., where the windings of rivers, roads, and fences, make it necessary to run a great number of lines in order to obtain a correct plan of the whole estate, and the true area of every part. 4. — In extensive surveys, where two measurers^are employed, it is best to consider the estate as divided into two distinct parts by the diagonal or main- line. Each Surveyor may then take a part, and make use of the diagonal as his base-line ; and measure such other lines as are necessary to complete that part of the survey which he undertakes. By this means the lines of one Sur- veyor do not become entangled with those of the other ; and the work is more expeditiously and more correctly performed, than if both the Surveyors were employed on the same side of the main-line. 5. — It is sometimes advisable to divide a very large estate in the following manner : Measure a line across the estate as near to the middle as convenient ; and at right-angles to this line, or nearly at right angles, measure another line, through the middle of the estate. These two lines being tied together by a connecting line measured from one to the other, will divide the estate into four parts, all of which may be measured separately by dividing them into triangles as before directed ; and taking such dimensions as are necessary to complete the survey. This method is a very good one where three or four Surveyors are employed in measuring a large lordship, or even where one Surveyor only is employed ; for the first two lines being considered as out-boundaries, the estate may be measured in four separate parts ; and yet the whole will be so well connected by those lines, that it will be as easy to plan as a small survey. Plate m. Part V.) LAND-SURVEYING. 197 6. — The method of surveying estates by dividing them into triangles, is exemplified and illustrated by Plates III. VIII. and X., the last two of which are actual surveys. The field-notes belonging to them are given in an en- graven Field-Book ; and Plates IX. and XI. are the finished plans. 7. — No notes are given to Plate III. as they would have occupied too many pages of copperplate ; but the directions of all the lines may be easily ascer- tained by the following particulars : The first, or main-line, leads from -I- 1 to 4 8 ; the second line from -I- 8 to 4 10 ; and the third from 4 10 to 4- 1 ; which three lines form the first large triangle. The fourth line extends from 4- 2 to 4- 15 ; and the fifth from 4 15 to 4 8 ; which two lines and part of the main-line form the second large triangle. The sixth line leads from 4 9 to 4 1 1 ; the seventh from 4 20 to 4 6 ; the eighth from 4 7 to 4 22 ; the ninth from 4 21 to 4 4 ; the tenth from 4 24 to 4- 13 ; and the eleventh from 4 12 to 4 23 ; which complete the survey of the first triangle. The twelfth line extends from 4 5 to 4 17 ; the thirteenth from 4 25 to the main-line, southward of 4 3 ; the fourteenth from 4 1 to 4 14 ; the fifteenth from 4 14 to 4 26 ; the sixteenth from 4 27 to 4 16 ; the seventeenth from 4 18 to 4 28 ; and" the eighteenth from 4 28 to 4- 19 ; which finish the whole survey. 8. — The content of the estate may be found in the following manner : Measure the Hues upon the plan, and take the necessary offsets, by a scale of 8 chains to an inch ; and enter the dimensions in a Field-Book. From the dimensions thus obtained, draw a plan by a scale of 2 chains to an inch ; then straighten the fences as directed in Part IV. or Part V. ; and measure diagonals, perpendiculars, &c. from which compute the content of each field. The diagonals, perpendiculars, and contents may be entered in a Book of Castings, similar to those belonging to Plates VIII. and X. ; and if you should not have a scale of 8 chains to an inch, any other scale will do just the same for practice. 9. — Taking the dimensions, &c. as directed in the last note, will be found of infinite service to the learner ; as it will tend to make him very expert in entering the field-notes, laying down the lines, and casting the contents, which are no small acquisitions towards becoming a complete Land-Sur- veyor. 10. — At the particular request of several eminent Land-Surveyors, who very much approve of this Work, I have altered the method of entering the notes in the engraven Field-Book. In the first edition, the notes were en- tered from the right towards the left ; in this edition they are entered from the left towards the right. Both methods are practised by different Sur- veyors ; but it appears that the latter method is gaining ground. o 3 198 land-surveying. (Part V. 11. — Some Surveyors represent the crossings of fences by lines drawn across the right and left-hand columns of the Field-Book ; and others by lines crossing the middle column. The Author prefers the latter method ; but every Surveyor will, of course, follow that of which he most approves. 12. — Many Surveyors enter their notes in a book about four inches and a half in breadth, and fourteen or fifteen in length, when open ; and others prefer a book about eight or nine inches long, and seven or eight inches broad when open. (See the description of the Field-Book, Part II. ; and also the engraven Field-Book belonging to Plates VIII. X. and XII.) METHOD II. Measure a main-line as nearly to one of the out-boun- daries of the estate, as the curves in the hedges will permit ; noting the crossings of fences, and taking offsets as before directed. At a convenient distance, measure another main-line parallel or nearly parallel to the first line, so that a number of fences running in that direction may be obtained ; and from any two stations in the first line, measure lines to some station in the second main-line, thus forming a triangle ; so will a station in the second main-line become determined or fixed. From the first main-line to the second, or from the second to the first, measure lines in order to obtain all the fences which run in that direction. The remainder of the fences of the en- closures contained between the first and second main-lines being obtained by running lines in the most convenient man- ner, you will have completed the dimensions of a portion of the estate, which may then be laid down. Parallel or nearly parallel to the second main-line, and at a proper distance from it, measure a third ; and proceed with the internal lines as before, and you will obtain the dimensions of another portion of the estate, which may also be laid down. Carry on the survey in a similar manner, until you finish it. Plate l\ Part V.) LAND-SURVEYING, i99 y 0(e i._This method is illustrated by Plate IV. which displays the chain- lines and stations used in taking the survey. The field-notes are not given ; but the following particulars exhibit the directions of all the lines: The first main-line leads from + 1 to 4- 6 ; the second from 4- 6 to 4- 7 ; and the third line or second main-line, from 4- 7 to 4- 16. The fourth line extends from + 16 to 4- 1 ; the fifth or tie-line from + 16 to + 2 ; the sixth from 4- 2 to 4- 14 ; the seventh from 4- 17 to + 18 ; the eighth from 4- 12, through 4- 18, to 4- 3 ; the ninth from 4- 4 to 4- 10 ; and the tenth line leads from 4- 8 to 4- 5 ; thu3 all the fences between the first and second main-lines are obtained. The eleventh line, or third main-line lead=. from 4- 1 9 to 4- 29 ; the twelfth from 4- 29 to 4- 16 ; the thirteenth from 4- 29 to 4- 15 ; the fourteenth from 4- 15 to 4- 28 ; the fifteenth from 4- 26 to 4- 13 ; the sixteenth from 4- 12 to 4- 25 ; the seventeenth from 4- 23 to 4- 11 ; the ■ + 30 to 4- 31 ; the nineteenth from 4- 9, through + 31, to 4- 22 ; and the twentieth from 4- 7 to 4- 19, which complete the survey between the second and third main-lines. The twenty-first line, or fourth main-line, extends from 4- 32 to 4- 40 ; the twentv-second from 4- 40 to 4- 29 ; the twenty-third from 4- 40 to 4- 28 ; the twenty-fourth from 4- 28 to 4- 38 ; the twenty-fifth from 4- 37 to 4- 27 ; the twenty-sixth from + 34 to 4- -36 ; the r .th from 4- 35 to 4- 23 ; the twentv-eighth from 4- 34 to 4- 21 ; the twenty-ninth from 4- 20 to 4- 23 ; the thirtieth from 4- 32 to + 19, which finish the whole estate. 2. — In order to practise the learner, a Field-Book may be formed, and the content of the estate found in the same manner as directed in Note 8, Mothod I. 3. — Some writers on Surveying instruct their pupils to measure main, lines through the estate to be surveyed ; and upon these, by the help of a cross, to erect perpendiculars to the opposite angles, and curved fences ; and upon these perpendiculars, again, if necessary, to erect other perpendicu- 1 ars ; thus dividing the whole estate into right-angled triaDgles and trapezoids. The method here described is extremely tedious, as many of the perpen- diculars will be 12 or 15 chains in length, when the fields are large ; and where the fences are much curved, it becomes almost impracticable, ir. sequence of the great number of offsets or perpendiculars that must be taken, in order to obtain a correct plan of the estate- Besides, when the fence to which perpendiculars must be erected, is at a considerable distance from the base-line, it will be necessary for an ass:- alk along, by the fence, in order to point out to the Surveyor, the ar _ and curves to which offsets ought to be taken: and if there be a crooked fence on each side of the base-line, two extra helpers will be necessary, if the Surveyor intends to perform his work with expedition. Hence we see that this process of measuring, not only subjects the Surveyor to a great deal of extra trouble, but also to a very considerable, unnecessary expense. 4 200 land-surveying. (Part V. This method I have never followed in measuring estates ; neither have I ever seen it followed by any experienced Surveyor. On the contrary, all with whom I am acquainted, consider it quite preposterous. METHOD III. An estate of four sides may frequently be conveniently sur- veyed as follows : Measure four lines in such a manner that offsets or insets may be taken to the four out-boundaries of the estate ; and tie the first and fourth lines together by a diagonal or tie-line measured from one to the other, at the distance of five, six, or more chains from the angular point, according to extent of the survey ; thus you will be enabled to lay down the first four lines, and also the out-boundaries of the estate. Next proceed to obtain the internal fences, by measuring lines in the most convenient manner ; some of which must be run from the first to the third, or from the second to the fourth line, or in some other proper direction, so that they may become proofs and fast-lines, into which other lines may be run with propriety. In thus proceeding, it is evident that a great deal will always depend upon the dexterity and ingenuity of the Surveyor, as no directions can be given that will suit every particular case to be met with in practice. Note. — This method of surveying an estate, is exemplified by Plate XII. the field-notes of which are contained in the engraven Field-Book, given with this Work. It is also illustrated in my Mensuration, by Plate III. which is the plan of an estate lying in the Township of Farnley, in the Parish of Leeds. With this plan there is likewise given an engraven Field- Book, and also a book of dimensions, castings, and areas. METHOD IV. The method which I here intend to describe, is a compound of all the foregoing methods of surveying with the chain ; for as there are never two estates to be met with which are exactly alike, sometimes one method claims the preference, and some- times another; but a skilful Surveyor will always adopt that by which he can take his dimensions and proofs with the greatest accuracy, by the fewest lines. Part V.) LAND-SURVEYING. 201 If an estate be in the form of an irregular .polygon of five, six, or more sides, and*" the fences very crooked, such an estate may generally be most easily surveyed by dividing it into tri- angles, as in Method I. ; but if many of the fences of the dif- ferent enclosures run a considerable way in the same direction, and the fields in general pretty neat trapeziums, it is commonly more eligible to proceed as directed in Method II. Sometimes an estate varies so much in its shape, that all the methods before described may be used with propriety and ad- vantage ; and it frequently happens that an ingenious Sur- veyor adopts methods, in particular cases, entirely new to him- self; care, however, must always be taken to make one line depend upon another, throughout the whole survey, so that when you come to lay it down, you may find no lines whose positions are undetermined. Note 1. — Whatever method of surveying is adopted, the field-notes must be entered in a similar manner to those given in the engraven Field-Book. Some Surveyors place the letter S, against straight fences, in the Field- Book, to distinguish them from those that are crooked ; but they may be very well denoted by drawing straight, or crooked lines, as the case requires. 2. — The estates given in this Work, as examples, are not very extensive, in consequence of the serious expense that attends large plates, and the great inconvenience of folding them in books ; but it may be remarked, that the foregoing methods of surveying are applicable to estates of all sizes ; even to those of many thousand acres. MISCELLANEOUS INSTRUCTIONS. 1. When you have *an estate to survey, never begin your work too hastily. Walk over the estate ; examine it minutely ; and observe by which of the foregoing methods it can be most easily measured. Next determine upon that point at which it will be most convenient to begin ; and never omit to take the range of the first line with a compass. If you do, it will be impossible for you to lay it down, in its true position, upon the plan. 202 LAND-SURVEYING. (Part V. 2. In measuring your main, or any other chain-line, put down stations at every place to which you apprehend it may be ne- cessary to run lines, in order to complete the surrey. 3. You may sometimes put down a station, whether you see any particular use for it or not ; because it may become ser- viceable in correcting an error, should one be committed ; and, if it be not used, it will be immaterial. 4. In measuring your internal lines, it will give you the least trouble to run them from one station to another, if you can make it convenient ; if not, you must run them from, and continue them to some chain-line, and measure the distance upon that line, to the nearest station, which may be entered in the field- book, thus; run upon 1 line, 30 links S. of -f- 1, &c. 5. The place where you run upon, or cross a chain-line, may be easily ascertained by setting up poles at two of the nearest stations in that line ; the crossing will be at the place where you are in a direct line with these poles, which may be repre- sented by marks cut in the ground, pointing out the directions of the lines. 6. In ranging the poles, there must be one fixed at the station from which you intend to depart, and another at the place to- ward which you direct your line, if there be no natural mark, as a tree, the corner of a house, &c. Then, in a straight line with these marks, put down poles at the distance of 4, 6, or 10 chains from each other, accordingly as impediments may render them necessary. 7. When you are measuring a line across a valley, you must proceed forward until you are likely to lose sight of the station to which you are going ; then, let your assistant take a pole to the other side of the valley, and direct him to place it exactly in the line which you are measuring, s^o as to be seen from the bottom of the valley ; to this you may continue your line, and thence to the end. 8. "When the stations between which you wish to run a line, are so far distant that you cannot see from one of them to the other, or when your view is obstructed by an elevation between them, you must then, accompanied by your assistant, go to the place whence you can distinctly see both ; and turning face to Part V.) LAND-SUllVEYING. 203 face, at a little distance, direct each other to the right or left, until you are both in a right line with the stations ; then, one of you putting down a pole, the line will be correctly found. If the line, however, be so long, that you cannot possibly find it by the above methods, it must be ranged at random ; but, in this case, you should be extremely careful that your pole ranger keeps one pole in a direct line with another, which he may accurately effect by always having, at least, two behind him. 9. In measuring a line which passes over a hill, you must attend to the directions given in Part IV. in the Method of measuring Hilly Ground; but' you will not always find your lines to meet correctly, in surveying mountainous estates. 10. When a river runs through the estate, it will be necessary to continue some of your lines across the river, in order to tie the whole survey together. 1 1 . Rivers, large brooks, public roads, and common sewers, shall not be included in the area, but only delineated upon the plan. If however, their areas be required, they should be given separately. 12. Marshes, bogs, heaths, rocks, &c. belonging to the estate, should be distinctly represented upon the plan ; and their mea- surements separately returned. 13. You will generally have an opportunity of representing some part of each hedge in your field-book ; and you may de- note on which side of the ditch the fence stands, by drawing a small bush, or by specifying it in writing. 14. In surveying estates, the crossings of fences must be taken at the outer extremities of the ditches, and not at the roots of the quickwood ; because the ditch, and not the fence, is the division line between* adjoining fields; but in measuring enclo- sures which are separated by walls, the case is generally dif- ferent, as the walls most commonly form the lines of division. It may also be observed, that the ground upon which a wall stands must be measured with the field to which the fence be- longs, and as walls are generally broader at the bottom than at the top, it is necessary to attend to this circumstance in taking the dimensions. 204 LAND-SUHVEYIXG. (Part V. 15. When the Surveyor finds it convenient, lie may put down stations at the outer extremities of the ditches ; and in planning, these stations will, of course, fall upon the black lines, because they always represent the boundaries between adjoining fields. This accounts for several of the stations appearing on the black lines, of the rough plans, in Plate VIIL X. and XII. 16. In taking a survey, you must enter in your field-book the name of each field, or of its proprietor or occupier ; or you may make such remarks, as will enable you to distinguish the fields from each other, &c. and after the plan is drawn, acquire, from persons acquainted with the estate, every necessary addi- tional information. 17. When hedges obstruct your sight, in running the lines, it will be necessary to cut down part of their tops, in order to see the poles. 18. If it should happen that you measure a line for which you have no particular use, it will serve as an additional proof : it is evident that you had better measure too many lines than too few. 19. In taking a survey, you ought to observe to whom the adjoining ground belongs ; and specify the same upon the plam 20. Some of our Practical Surveyors use only nine arrows. When the leader has advanced ten chains, the follower goes up to him, and places his foot or offset-staff at the end of the chain, instead of the tenth arrow ; but in this method I do not per- ceive any particular advantage. GENERAL RULES FOR PL ANNINGLARGE SURVEYS. The method of laying down a large survey, from the field- book, may easily be acquired by practice ; but as the least ap- pearance of difficulty generally discourages a learner, it is pre- sumed that the following directions may be found acceptable. Having provided a sheet of drawing-paper of a proper size, trace with a pencil, a meridian, or north and south line, in such Part V.) LAND-SURVEYING. 205 a manner that your first station may be in some convenient point in this line. Then, from your first station, draw your first or main-line, making its proper angle with the meridian line, which you may then take out with Indian rubber. Next, take separately in your compasses, your second and third lines, or any two more convenient ones, forming a triangle with the main-line ; and placing one foot of your compasses in the proper centres respectively, describe arcs intersecting each other. Thus will you have three points, from which to form a triangle. In the same manner proceed with each triangle formed upon the main-line, (or upon any other line,) proving your work as you advance, until all the triangles are laid down ; and if you find all your lines correctly meet, it will be an infallible proof of the accuracy of the work. The chain-lines being thus laid down, next prick off the crossings of fences, and draw lines in their proper situations, from one crossing to another, to represent the straight fences. The curved fences must be formed by laying down the offsets, as already directed. When the whole survey is planned, all the fences must be drawn with Indian ink, the chain-lines and offsets dotted, and the stations, gates, stiles, &c. marked in their proper places : the sheet will then represent what is called a " Rough Plan." Note 1. — When a fence represents a chain-line, it must not be dotted. 2.— Practical Surveyors never dot their chain-lines or offsets, but only mark their stations upon the plan ; but it is more satisfactory to a learner, to be able to see all his chain-lines at a single view. 3. — In taking a very large survey, it is necessary that the work be laid down, and proved every night ; for if an error be committed, and the survey continued two or three days before it be discovered, the detection, in the field, will probably be attended with a great deal of trouble. 4. — In laying down large surveys, it sometimes happens that one sheet of paper will not contain the whole ; in this case, two or more, must be pasted together. 5. — When you have to lay down a line exceeding the length of your scale, draw a line with your pencil, in some convenient place upon the plan ; and 206 LAND-SURVEYING-. (Part V. upon it, at two or more operations, prick off" the distance in question, which you may then take in your compasses. 6. — " Beam compasses, which are very useful in drawing large circles, taking great extents, &c. consist of a long straight beam or bar, carrying two brass cursors ; one of them fixed at one end, the other sliding alongthe beam, with a screw to fasten it on occasionally. To the cursors may be screwed points of any kind, as of steel, pencils, &c. To the fixed cursor is sometimes applied an adjusting or micrometer screw, by which an extent maybe obtained to a very great nicety." — See Hutton's Mathematical Dictionary, I. 315. DIRECTIONS FOR PLANNING THE ESTATE IN PLATE VIII. FROM THE DIMEN- SIONS IN THE ENGRAVEN FIELD-BOOK. It appears by the first page of the field-book, that the range of the first line is N. N. W. ; and by referring to the compass, Plate I. we find that the angle which this line makes with the meridian line, is 22° 30'. By Prob. 23, Part I. lay down a line making an angle of 22° 30' which the meridian line ; and by a scale of four chains to an inch, prick off 2802 links, from cross or station (-[-) 1, to -J- 3 ; and you will thus have the part of the first line. Now, as the third line could not be run to + 1, in conse- quence of a large quickwood hedge intervening too far to be cut down ; it was necessary to produce the first line 30 links southward, in order that the first three lines might form a trian- gle; consequently, the first line must be continued 30 links southward from -j- 1 , in laying down the plan ; and this con- tinuation completes tbe first line. Take the second line, 3075 links, in your compasses, and with one foot in -\~ 3, describe an arc ; and with 3270 links, the third line in your compasses, and one foot in a point 30 links south of -{- 1, describe another arc, intersecting the former in + 6 ; join these three points hj drawing lines from -j- 3 to + 6, and from -j- 6 to the above-named point ; and you will thus form the triangle 1, 3, 6. Part V.) land-surveying. 207 Next, prick off stations 2, 4, 5, 7, and 8 ; and lay your plotting-scale from -f 2 to -f 8, and if it measure 1046, as in the field-book, line six, you Lave good reason to conclude tliat your dimensions are thus far correctly taken and laid down. Also, mark off -f 10, try its distance from -f- 4 ; likewise examine the distance from -4-5 to + 7 ; and if you find both these lines the same as in the field-book, your survey is evi- dently correct. With the fourth line, 257, in your compasses, and one foot in -4- 1, describe an arc; and with the fifth line, 1004, as a radius, and -j- 2, as a centre, make another arc cutting the former in + 9 ; hence you have three points by which to form the triangle 1, 9, 2. Lastly, complete the rough plan by pricking off, and drawing all the straight fences; laying down the offsets; making the gates ; numbering the fields, &c. &c, as in the Plate. DIRECTIONS FOR PLANNING THE ESTATE IN PLATE X. FROM THE DIMENSIONS IN THE ENGRAVEN FIELD-BOOK. We find from the fourth page of the field-book, that the first line ranges W. b. N. \ W., making an angle with the meridian line, 84° 22£'. By Prob. 23, Part I. draw aline, making an angle of 84° 22^' with the meridian line ; and by a scale of four chains to an inch, prick off 5445 links, from -j- 1 to + 12; and you will thus obtain the first line ; upon which prick off stations 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. With 900, part off the third line, in your compasses, and -f 1, as a centre, describe an arc ; and with 625, the fourth line, as a radius, and one foot in -f 2, intersect the former arc in -f 22. From -f 2, draw a line to -j- 22 ; and from -f 1, through -f 22, draw the third line, equal to 1360, and you will obtain + 23. 208 land-surveying. (Part V. With the second line, 3790, in your compasses, and + 12, as a centre, describe an arc ; and with 925, part off the fifth line, as a radius, and -f- 23, as a centre, describe another arc, cutting the former in + 21. From + 23, through + 21, draw a line equal to 2090, and you will thus obtain the fifth line, and also stations 24, 25, and 20. Draw a line from + 12 to + 21, and you will have the second line; and also stations 13, 14, 15, 16, 17, 18, 19, and 20; and draw another from + 2G, to a point in the first line, 295 "W. of + 10 ; and you will obtain the sixth line ; and like- wise stations 27 and 28. With 2325, the twenty -sixth line, in your compasses, and + 3 as a centre, describe an arc; and with 1210, part of the twenty- seventh line, as a radius, and one foot on the first line, 150, -yy. of + 7, describe another arc, cutting the former in + 33. Draw a line from + 3 to + 33 ; and from + 33, through the intersection of the first line, draw the twenty-seventh line, equal to 2040, and you will obtain + 43. Next, with 446, the seventh line, in your compasses, and + 12, as a centre, describe an arc; and with 2528, the eighth line, as a radius, and + 33, as a centre, describe another arc, cutting the former in + 29. Draw lines from + 12 to + 29, and from + 29 to + 33, and you will obtain stations 30, 31, and 32 ; and also draw the ninth line from + 32, through + 8, and _j_ 1 6, to + 27, and you will have stations 34, 35, 36, and 37. Join stations 11 and 13, and you will obtain the 10th line ; 28 and 30, and you will have the 11th line; 37 and 18, and you will obtain the 12th line; 19 and 25, and you will have the 13th line; 38 and 20, and you will obtain the 14th line; 20 and 39, and you will have the 15th line; 24 and 39, and you will obtain the 16th line; 39 and 19, and you will have the 17th line; 17 and 27, and you will obtain the 18th line. From + 31, through + 9, draw the 20th line, equal to 1175, and you will obtain stations 40 and 41 ; join 36 and 40, and you will have the 19th line; and from + 41, through + 34, draw a line to a point in the 1st line, 72 E. of + 7, and you will obtain the 21st line. Draw a line from + 35 to + 43, and you will have + 42, Part V.) LAND-SURVEYING. 209 and the 23rd line ; and join -f 42 and 36, and you will obtain the 22nd line. Draw a line from + 23 to the first line, 115 E. of + 5, and you will obtain + 45, and the 29th line; from -f 43 to -f 45, and you will have -f 44, and the 24th line ; from -j- 3 to -f 45, and you will obtain the 25th line. Lastly, complete the rough plan, by pricking off, and drawing all the straight fences ; laying down the offsets ; making the gates ; forming the bases of buildings ; shading the river ; numbering the fields ; &c. &c. as in the Plate. Note 1. — Hot-pressed drawing-paper is best for plans, because its surface is very smooth ; consequently, fine lines maybe drawn upon it. Parchment and vellum are more durable than paper ; hence they are generally used for planning estates belonging to gentlemen who are desirous that the plans may be handed down to their posterity. Vellum exceeds parchment in durability ; and it may be necessary to remark, that when either of them is used for plan- ning, it must first be rubbed with clean flannel dipped in the best Paris whiting. This operation clears its surface from grease ; and facilitates the movements of the pen. 2. — In damp weather, paper expands, and in dry weather, it contracts ; consequently, if a plan be drawn when the paper is in a moist state, and the content be not found till after it has become perfectly dry, the diagonals and perpendiculars will measure too little, and will of course give the area too little also ; but if the plan be drawn when the paper is dry, and the area be found after it has expanded by a change in the atmosphere, the diagonals and perpendiculars will measure too much, and will consequently give the area too much likewise. Hence the necessity of having the paper in the same state of temperature when you find the area, that it was in when you laid down the chain-lines, offsets, &c. 3. — The most expeditious method of laying down crooked fences, is by means of an offset-scale, which must be used with the plotting-scale in the following manner : Lay one edge of the plotting-scale close by the base-line, and bring the end of the offset-scale in contact with the edge of the plotting- scale, so that the edges of the scales may form a right-angle ; then by the edge of the offset-scale, prick off, in its proper situation, the first offset, with a pencil finely pointed. Keep the plotting-scale firm, and slide the offset-scale to the place of the next perpendicular, which prick oft' as before ; and thus proceed until all the offsets are finished. 4. — Bi-ooknian and Langdon's prepared lead pencils, of different degrees of hardness, for the iw of Engineers, Architects, Land-Surveyors, and Artists, P 210 LAND-SURVEYING. (Part V. are now in high repute among Draftsmen. The pencils marked H. H. very hard, and H. not quite so hard, are well adapted for the use of Land-Sur- veyors ; as they bear pointing better than any other ; and produce much finer lines. TO COMPUTE THE CONTENTS. After the -whole survey is laid down, Practical Surveyors straighten the crooked fences of each field, as directed in Part IV. ; and then divide the fields into trapeziums and triangles, and take such dimensions, by the scale, as are necessary to find the separate area of each field. They then collect all the areas into one sum ; afterward find the area of the whole survey, as if it were a single field, and if it appears to be equal, or nearly equal, to the sum of the separate areas, previously found, they justly infer that their survey is correct. Note 1 .—Those who do not approve of finding the area by the method of casting, may make use of the offsets taken in the survey, where convenient ; and if more be wanted, they may be measured by the scale ; for in measuring a number of small parts by it, some will probahly be taken a little too large, and others a little too small, so that, in the end, they will nearly counter- balance each other. 2. — Practical Surveyors generally lay down their lines by a scaleof 4 chains to an inch, when their surveys are very large ; and in computing the contents, they measure the bases and diagonals by the same scale, but the perpendi- culars by a scale of 2 chains to an inch ; consequently, the product of the base and perpendicular of a triangle, will be its area. To treat small surveys, in a similar manner, by a scale of 2 chains, and of 1 chain to an inch, must, of course, be very correct. 3. — When the survey is not very large, the content of each field may be set down in some convenient place upon the plan. In other cases, it may be entered within the field itself. Some gentlemen, however, prefer having the areas of their estates given in a book of particulars, containing numbers, or letters of reference, corresponding to those upon the plan. 4. — As some Surveyors prefer a parallel ruler to a lanternhorn, or abowof whale-bone and silk, for reducing crooked fences to straight ones, I have in . the following Problems, given the method of using that instrument, in order that this work may meet the approbation of all classes of scientific readers ; and be rendered as useful and practical as possible. Part V.) LAND-SURVEYING. 211 5. When there are no dimensions given in the following Problems, the figures may be measured by a scale, and then laid down in the learner's book ; after which, the operations by the parallel ruler may be performed. Or, for practice, figures may be made at pleasure ; and the necessary equa- lising lines drawn, according to the subsequent directions. THE USE OF THE PARALLEL RULER IN REDUCING CROOKED FENCES TO STRAIGHT ONES, IN ORDER TO FIND THE AREAS OF FIELDS BY THE METHOD OF CASTING. PROBLEM I. To draw a right Line A D,from the Point A, through the Line B (7, so that the Quantities on each Side of the Line A D, may be equal. E Draw, with your pencil, a temporary line C E, at pleasure ; then your ruler being closed, lay it from C to A ; hold the side, that is next to you, fast ; open the other to B ; make a mark with your pencil upon the temporary line C E, where the edge of the ruler cuts that line, as at D ; draw a line from A to D, and the quantities on each side of this line will be equal ; that is, the triangle A B F will be equal to the triangle CDF. p 2 212 land-surveying. (Part V. DEMONSTRATION. Draw the line A C, and also the line B D, which is evidently parallel toA C; then by Theo. 6, Part I. the triangle ABC is equal to the triangle ACD; take away the triangle A C F, which is common to both, and there remains the triangle A B F equal to the triangle CDF. Note 1 . — The solutions of all the following Problems are founded upon the foregoing demonstration. 2. — If it had been required to draw the equalising line from the angle C, through the line A B, the temporary line must have been made from the angle A. 3. — All the operations must be performed with the utmost care and accu- racy ; and if, at any time, the ruler be suffered to slip, the work must be repeated, or it will not be correct. 4. — When an error has been committed, it may frequently be discovered by the eye, after the equalising line is drawn. PROBLEM II. Let the irregular figure A B C D E A represent an Offset taken in surveying a Field; it is required to draw a right Line from the Angle A, so as to reduce the Figure to a right-angled Triangle. Produce the perpendicular B C, for a temporary line. Lay your ruler from C to E; bring it down in a parallel Part V.) LAND-SURVEYING. 213 position to D ; and make a mark upon the line B C, where the edge of the ruler intersects that line, as at m. Lay jour ruler from m to A ; move it in a parallel direction to E ; and make a mark upon the line B C, close by the edge of the ruler, as at F. Draw a line from Ato F; and the triangle A B F will be equal to the irregular figure A B C D E A ; hence the area may be found by multiplying the base A B, by half the per- pendicular B F. Note 1. — In practical operations, the equalising and temporary lines must be made with a pencil finely pointed ; and effaced with Indian rubber, after the area is found. 2. — If perpendiculars be let fall from the angles E and D, upon the base A B ; the necessary dimensions taken by a scale ; and the area of the irregular figure A B C D E A obtained by the rules for triangles and trapezoids, it will be found equal to the area of the right-angled triangle ABF; great care, however, must be used to make the lines very fine, and to take the dimensions of all the figures with the utmost accuracy. PROBLEM III. It is required to reduce the Offset 1, 2, 3, 4, 5, to a right-angled Triangle, hy drawing an equalising Line from the fifth Angle, through the irregular Fences, 214 land-surveying. (Part V. Perpendicularly to the base, and from the first angle, draw a temporary line. Lay your ruler from the first to the third angle ; move it in a parallel position to the second angle ; and mark the tempo- rary line at number 1. Lay your ruler from number 1, to the fourth angle ; bring it down in a parallel direction to the third angle ; and mark the temporary line at number 2. Lay the ruler from number 2, to the fifth angle ; move it parallel to the fourth angle ; and mark the temporary line at number 3. Draw a line from the fifth angle to number 3 ; and 5, 1, 3, will be the right-angled triangle required ; hence the area of the irregular offset may be found by multiplying the base 1, 5, by half the perpendicular 1, 3. PROBLEM IV. It is required to lay down a right-line Offset* from the following Dimensions ; to reduce it to a Scalene Triangle ly the Parallel Ruler ; and to find its Area loth ly the Method of Offsets and Casting. 300K 100 G 200 E 150 C "West AL 1500 H 1100 F 800 D 500 B 100 000 From A, go Part V.) LAND-SURVEYING. 215 Having laid down the figure ; produce the side A C, at pleasure, for a temporary line. Lay the ruler from the first angle A, to the third angle E ; move it parallel to the second angle C ; and mark the temporary line at 1, which, in this case, is at the second angle, because the said A C, is the temporary line. Lay the ruler from 1, to the fourth angle G ; move it parallel to the third angle E ; and mark the temporary line at 2. Lay the ruler from 2, to the fifth angle K ; move it parallel to the fourth angle, G ; and mark the temporary line at 3. Lay the ruler from 3, to the sixth angle L ; move it parallel to the fifth angle K ; and mark the temporary line at 4. Draw a line from the sixth angle L, to number 4 (M) ; and A L M will be the scalene triangle required. Computation of the Area by Offsets. Here 150 X 100 = 15000, twice the area of the triangle ABC; 150 + 200 x 400 = 350 X 400 = 140000, twice the area of the trapezoid B D E C ; 200 -f 100 X 300 = 300 X 300 = 90000, twice the area of the trapezoid DFGE; 100-1- 300 X 300 = 400 X 300 = 120000, twice the area of the trapezoid FHKG; and 400 X 300 = 120000, twice the area of the triangle HLK; then 15000 -f 140000 + 90000 -f 120000 -f- 120000 = 485000, twice the area of the whole offset ; and 485000 ~ 2 = 242500 square links = 2a. 1r. 28p. the area required. p 4 216 LAXD-SURVEYING. (Part V. Computation of the Area by Casting. From the angle M, let fall the perpendicular M N, which you •11 £ j , «« i. , i 323 X 1500 484500 will find to measure 323 links; then — — 2 2 242250 square links = 2a. 1r. 27.6p. the area required; which differs only four-tenths of a perch from the area found by offsets. PROBLEM V. Lay down a curve-line Offset from the following Dimensions ; re- duce it to a right-angled Triangle by the Parallel Rider ; and find its Area both by equidistant Ordinates and Casting. AN 1200 M 190 1000 K 260 800 G 270 600 E 250 400 C 180 200 ' 000 From A > g° L H F D B East. Having laid down the figure, erect the perpendicular A P, for a temporary line. Part V.) LAND-SURVEYING. c 2l7 Lay the ruler from A to E ; move it parallel to C ; and mark the temporary line at 1. Lay the ruler from 1 to G ; move it parallel to E ; and mark the temporary line at 2. Lay the ruler from 2 to K ; move it parallel to G ; and mark the temporary line at 3. Lay the ruler from 3 to M; move it parallel to K ; and mark the temporary line at 4. Lay the ruler from 4 to N ; move it parallel to M ; and mark the temporary line at 5. Draw a line from N to 5 (P) ; and NAP, will be the right- angled triangle required. Computation of the Area by equidistant Ordinates. See Prob. 9, Part III Here the sum of the first and last ordinates is nothing; (J 80 + 270 -f 190) X 4 = 640 X 4 = 2560, four times the sum of the even ordinates; and (250 -f- 260) X 2 = 510 x 2 = 1020, *^ A « A ~1J JT ' « A 2560 + 1020 + 200 twice the sum ot the odd ordinates ; then 3 3580x200 716000 nn nnn = — = 238666 square links = 2a. 1r. 21. 8p. 3 the area required. Computation of the Area by Casting, Measure the perpendicular A P, which you will find to be ,. , . 398x1200 477600 398 links ; then = -= 238800 square links = 2a. 1r. 22p. the area required; which differs only two-tenths of a perch from that found by equidistant ordinates. Note. — When a curve-line offset is to be reduced to a triangle by the parallel ruler, a competent number of points must be assumed in the curve, to denote angles. These points must be taken at such distances from each other, that a right line drawn between any two adjacent points, would nearly coincide with the curve. Q1Q LAXD-SURVEYIXG. ( p art y PROBLEM VI. It is required to reduce the following curve-line Offset to a right- angled Triangle by the Parallel Ruler. Erect a perpendicular at one end of the base, for a temporary line ; and assume a competent number of points in tbe curve to denote angles. Lay the ruler from 1 to 3 ; move it parallel to 2 ; and mark the temporary line at 1. Lay the ruler from 1 to 4 ; move it parallel to 3 ; and mark the temporary line at 2. Lay the ruler from 2 to 5 ; move it parallel to 4 ; and mark the temporary line at 3. Lay the ruler from 3 to 6 ; move it parallel to 5 ; and mark the temporary line at 4. Lay the ruler from 4 to 7 ; move it parallel to 6 ; and mark the temporary line at 5. Lay the ruler from 5 to 8 ; move it parallel to 7 ; and mark the temporary line at 6. Draw a line from 8 to 6 ; and 8, 1, 6, is the triangle required ; hence the area of the irregular offset may be found by multi- plying the base 1, 8, by half the perpendicular I, 6. Part V.) LAND-SUllVEYING. 219 PROBLEM VII. It is required to reduce the irregular Figure A B C D E F G H K,toa Triangle, by the Parallel Ruler. 1 A 3 2 Produce the base A B, both ways, at pleasure, for a tem- porary line. Lay the ruler from A to H ; move it parallel to K ; and mark the temporary line at 1. Lay the ruler from 1 to G; move it parallel to H ; and mark the temporary line at 2. Lay the ruler from 2 to F ; move it parallel to G ; and mark the temporary line at 3. Draw a line from F to 3 ; and it will be a side of the re- quired triangle. Again, lay the ruler from B to D; move it parallel to C ; and mark the temporary line at 1. Lay the ruler from 1 to E ; move it parallel to D ; and mark the temporary line at 2. 220 land-surveying. (Part V. Lay the ruler from 2 to F ; move it parallel to E ; and mark the temporary line at 3. Draw a line from F to 3 ; and 3 F 3 will be the triangle required ; hence the area of the irregular figure A B C D E F G H K, may be found by multiplying the base 3, 3, by half the perpendicular F m. Note. — The method of reducing fields of four or five sides, to triangles of equal areas, may be seen in Problems 16 and 17, Part L PROBLEM VIIL It is required to reduce the irregular Figure A B C D E F G H K L M JV, to a Triangle, by the Parallel Ruler. V Draw the temporary line 1, 2, to touch the angle A. Part V.) LAND-SURVEYING. 221 Lay the ruler from A to C ; move it parallel to B ; and mark the temporary line at 1. Lay the ruler from 1 to D ; move it parallel to C ; and mark the temporary line at 2. Lay the ruler from 2 to E ; move it parallel to D ; and mark the temporary line at 3. Draw a line from E to 3 ; and produce it at pleasure, for a temporary line. Lay the ruler from 3 to M ; move it parallel to N ; and mark the temporary line at a. Lay the ruler from a to L ; move it parallel to M ; and mark the temporary line at n. Lay the ruler from ntoK; move it parallel to L ; and mark the temporary line at m. Draw a line from mtoK; and produce it at pleasure, for a temporary line. Lay the ruler from KtoG; move it parallel to H ; and mark the temporary line at 1 . Lay the ruler from 1 to F ; move it parallel to G ; and mark the temporary line at 2. Lay the ruler from 2 to E ; move it parallel to F ; and mark the temporary line at 3. Draw a line from E to 3 ; and E 3 m, will be the triangle required ; hence the area of the irregular figure A B C D E F G H K L M N, may be found by multiplying the base E m by half the perpendicular 3 x. 222 LAND-SURVEYING (Part V. PROBLEM IX. It is required to reduce the irregular Figure A B C D E F G H K L M, to a Trapezium, by the Parallel Ruler. Produce the line A B, at pleasure, for a temporary line. Lay the ruler from A to L ; move it parallel to M ; and mark the temporary line at 1 . Lay the ruler from 1 to K ; move it parallel to L ; and mark the temporary line at 2. Draw a line from 2 to K ; and produce it at pleasure, for a temporary line. Lay the ruler from K to G; move it parallel to H ; and mark the temporary line at 3. Lay the ruler from 3 to F ; move it parallel to G ; and mark the temporary line at 4. Lay the ruler from 4 to E ; move it parallel to F ; and mark the temporary line at 5. Draw a line from 5 to E ; and produce it at pleasure, for a temporary line. Part V.) LAND-SURVEYING. 223 Lay the ruler from E to C ; move it parallel to D ; and mark the temporary line at 6. Lay the ruler from 6 to B ; move it parallel to C ; and mark the temporary line at 7. Draw a line from 7 to B ; and B, 7, 5, 2, will be the tra- pezium required ; hence the area of the irregular figure ABC D E F G H K L M, may be found by multiplying the diagonal B ,5, by half the sum of the two perpendiculars 7 m and 2 n. PROBLEM X. It is required to reduce the irregular Figure A B C D E F G H K L M N P R, to a Trapezium, by the Parallel Ruler. Continue A R, for a temporary line. Lay the ruler from A to C ; move it parallel to B ; and mark the temporary line at 1 . Lay the ruler from 1 to D ; move it parallel to C ; and mark the temporary line at 2. 224 land-surveying. (Part V. Draw a line from D to 2 ; and produce 4t at pleasure, for a temporary line. Lay the ruler from 2 to P ; move it parallel to R ; and mark the temporary line at 3. Lay the ruler from 3 to X ; more it parallel to P ; and mark the temporary line at 4. Draw a line from 4 to X ; and produce it at pleasure, for a temporary line. Lay the ruler from X to L; move it parallel to M; and mark the temporary line at .5. Lay the ruler from 5 to K; more it parallel to L ; and mark the temporary line at 6. Lay the ruler from 6 to H ; move it parallel to K ; and mark the temporary line at 7. Draw a line from 7 to H ; and produce it at pleasure, for a temporary line. Lay the ruler from H to F ; move it parallel to G ; and mark the temporary line at 8. Lay the ruler from 8 to E ; move it parallel to F ; and mark the temporary line at 9. Lav the ruler from 9 to D ; more it parallel to E ; and mark the temporary line at T. Draw the line D T ; and D T 7, 4, will be the trapezium required ; hence the area of the irregular figure may be found by multiplying the diagonal D 7, by half the sum of the two perpendiculars T m and 4 n. Part V.) LAND-SURVEYING. 225 PROBLEM XI. It is required to draw an equalising Line, by the Parallel Ruler, through the irregular Fences A B C D E, so that the two Fields which they separate, may be reduced to Trapeziums. Lay the ruler from A to C ; move it parallel to B ; and mark the temporary line K G, at 1. Lay the ruler from 1 to D ; move it parallel to C ; and mark the temporary line at 2. Lay the ruler from 2 to E ; move it parallel to D ; and mark the temporary line at 3. Draw a line from E to 3 (L) ; and the irregular figure A B C D E F G, will he reduced to the trapezium LEF6; and the irregular figure A B C D E H K, to the trapezium L E H K ; hence their respective areas may be obtained by measuring diagonals and perpendiculars. Note 1. — Sometimes the proprietors of adjoining estates agree to straighten crooked fences or brooks, by giving and taking equal quantities of land. 226 LAND-SURVEYING. (Part V. When this is the case, you must first measure and plan the ground ; then draw the equalising line as directed in the last Problem ; and take the dis- tance from A to L, very correctly by the scale. Measure this distance in the field, from the angle A ; range the division line E L, and takes it out ; and the work will be completed. 2. — It will be advisable to measure, both on the plan and in the field, the parts cut off on each side, by the division line, in order to prove the work ; for an error committed in dividing land, is of serious consequence, if it be not discovered and rectified before the new fence is made. If the discovery takes place after the groundhas been fenced off, either the fence must be altered, or the land must be valued ; and the person who has had too much awarded to him, must pay the balance. PROBLEM XII. It is required to draw an equalising Line by the Parallel Ruler, so that the curved Fence which separates the two Fields in the following Figure, may be reduced to a straight Fence. Lay the ruler from 1 to 3 ; move it parallel to 2 ; and mark the temporary line A B, at 1. Lay the ruler from 1 to 4 ; move it parallel to 3 ; and mark the temporary line at 2. Part V.) LAND-SURVEYING. 227 Lay the ruler from 2 to 5 ; move it parallel to 4 ; and mark the temporary line at 3. Lay the ruler from 3 to 6 ; move it parallel to 5 ; and mark the temporary line at 4. Lay the ruler from 4 to 7 ; move it parallel to 6 ; and mark the temporary line at 5. Draw a line from 7 to 5, and it will reduce the figure A B C D, to two trapeziums ; hence their respective areas may be found by measuring diagonals and perpendiculars. The following general Rule for the Parallel Ruler, will be found of considerable service to learners ; and may be easily committed to memory. GENERAL RULE. 1 . Lay the ruler from the first to the third angle ; move it parallel to the second angle ; and you will have the first mark on the temporary line. 2. Lay the ruler from the first mark on the temporary line, to the fourth angle ; move it parallel to the third angle ; and you will have the second mark on the temporary line. 3. Lay the ruler from the second mark on the temporary line, to the fifth angle ; move it parallel to the fourth angle ; and you will have the third mark on the temporary line. 4. Lay the ruler from the third mark on the temporary line, to the sixth angle ; move it parallel to the fifth angle ; and you will have the fourth mark on the temporary line. 5. Lay the ruler from the fourth mark on the temporary line, to the seventh angle ; move it parallel to the sixth angle ; and you will have the fifth mark on the temporary line. 6. Lay the ruler from the fifth mark on the temporary line, to the eighth angle ; move it parallel to the seventh angle ; and you will have the sixth mark on the temporary line. Q2 228 LAND-SURVEYING. (Part V. 7. Lay the ruler from the sixth mark on the temporary line, to the ninth angle ; move it parallel to the eighth angle ; and you will have the seventh mark on the temporary line. 8. Lay the ruler from the seventh mark on the temporary line, to the tenth angle ; move it parallel to the ninth angle ; and you will have the eighth mark on the temporary line, &c. &c. Note. — As the operations of the parallel ruler, in straightening crooked fences, are founded upon a mathematical truth, it is certainly, in most cases, preferable to a lantern horn ; hut in large surveys, where the fences are much curved, it will be found that the latter may be applied with much more ex- pedition than the former ; and if it be used by a skilful hand, its results will be sufficiently correct for general practice. (See Problems I. and II. Part IV.) A BOOK of DIMENSIONS, CASTINGS, and AREAS, Belonging to Plate VIII. Names of the Proprietors. i H S3 rC| ■4-a C © ft 03 o 'IP 5 03 p-i u & Quantity " 1 . * \ : ," " " "I ' : !'■"/ 1 : 11 ; i (1 >^h_ ; V By a scale of 2 chains to an inch, draw the line AB = 7 chains. At A and B erect the perpendiculars A D and B C, each of which make =. 6 chains ; and join D C. Divide the lines A B and D C, each into 7 equal parts ; and the lines A D and B C, each into 6 equal parts ; join the opposite points of division, and the rectangle A B C D, will be divided into 42 equal squares, the side of each being one chain. 234 LAND-SURVEYING. (Part V. H G VT'r ■ \ XI X: ...;....)■ 1/ • ) E F Next, by a scale of 4 chains to an inch, draw tlie line EF^ 7 chains. At E and F erect the perpendiculars E H and F G, each of which make = 6 chains ; and join H G. Divide the lines E F and H G, each into 7 equal parts ; and the lines E H and F G each into 6 equal parts ; join the opposite points of division, and the rectangle E F G H will be divided into 42 equal squares, the sides of which will be exactly half the size of those in the rectangle A B C D. - Then, with your pencil, draw within the rectangle E F G H the fences contained within the rectangle A B C D ; making each fence pass through its proper situation in the corresponding squares, which may be done by observing where the lines forming the squares, intersect the fences. Afterward trace the fences with Indian ink, as before directed. Note. — In copying or reducing a large plan, by this method, you ought to number the corresponding squares, in the circumscribing rectangles, with the same figures, in order to prevent mistakes. These figures, as well as the lines forming the squares, should be made with a pencil, and effaced after the plan is copied. METHOD V. By the Pentagraph. No instrument that has hitherto been invented is equal to the pentagraph, for reducing, copying, or enlarging plans. It Part V.) LAND-SURVEYING. 235 is not only the most expeditious, but also the most correct ; as it copies every straight and curved line with the greatest ex- actness. It is as useful to an experienced draftsman, as to those who have had but little practice in drawing. It saves much time either in copying, reducing, or enlarging plans ; and may be used with equal facility for copying figures, profiles, sea- charts, maps, landscapes, &c. &c. Pentagraphs may be had of most of the Mathematical Instru- ment Makers ; and in Mr. Jones's Catalogue, the price is from 1/. 18s. to 61. 16s. 6d. DESCRIPTION OF THE PENTAGRAPH. See Plate V. The pentagraph is generally made of wood, or brass, from 12 inches to two feet in length, and consists of four flat bars or rulers ; two of them long, and two short. The two longer are joined at the end A, by a double pivot, which is fixed to one of the rulers ; and works in two small holes placed at the end of the other. Under the joint is an ivory castor, to support this end of the instrument. The two smaller rulers are fixed by pivots at E and H, near the middle of the larger rulers ; and are also joined together at their other end, G. By the construction of this instrument, the four rulers always form a parallelogram. There is a sliding box on the longer arm, and another on the shorter arm. These boxes may be fixed at any part of the rulers, by means of their milled screws ; and each of these boxes are furnished with a cylindric tube, to carry either the tracing point, pencil, or fulcrum. The fulcrum, or support K, is a leaden weight ; on this the whole instrument moves when in use. To the longer instruments are sometimes placed two move- able rollers, to support the pentagraph, and facilitate its motions. Their situation may be varied as occasion requires. The graduations are placed on two of the rulers, B and D, with the proportions of \, \, J, &c. to T ' 2 , marked on them. 236 LAND-SURVEYING. (Part V. The pencil-holder, tracer, and fulcrum, must in all cases be in a right line, so that when they are set to any number, if a string be stretched over them, and they do not coincide with it, there is an error either in the setting or gradations. The long tube which carries the pencil, or crayon, moves easily up or down in another tube ; there is a string affixed to the long, or inner tube, passing afterwards through the holes in the three small knobs to the tracing point, where it may, if necessary, be fastened. By pulling this string, the pencil is lifted up occasionally, and thus prevented from making false or improper marks upon the copy. THE USE OF THE PENTAGRAPH. To reduce a Plan in any of the Proportions \, i, \, J, fyc. as marked on the two Bars B and D. Suppose for example, \ Place the two sockets, at §, on the bars B and D, the ful- crum, or lead weight at B,.the pencil socket with the pencil, at D, and the tracing point at C. Fasten down upon a smooth board, or table, a sheet of white paper under the pencil D, and the original map, &c. under the tracing point C, allowing your- self room enough for the various openings of the instrument. Then with a steady hand carefully move the tracing point C, over all the lines on the map ; and the pencil at D will describe exactly the same figure as the original, but \ the size. In the same manner for any other proportion, by setting the two sockets to the number of the required proportion. The pencil-holder moves easily in the socket, to give way to any irregularity in the paper. There is a cup at the top for receiving an additional weight, either to keep down the pencil to the paper, or to increase the strength of its mark. A silken string is fastened to the pencil-holder, in order that the pencil may be drawn up off the paper, to prevent false marks when crossing the original plan, in the operation. ^M; Part V.) LAND-SURVEYING. 237 If the original should be so large, that the instrument will not extend over it at one operation, two or three points must be marked on the original, to correspond with the same upon the copy. The fulcrum and copy may then be removed into such situations as to admit the copying of the remaining part of the original ; first observing, that when the tracing point is applied to the three points marked on the original, the pencil falls on the three corresponding points upon the copy. In this manner, by repeated shiftings, a pentagraph may be made to copy an original of ever so large dimensions. To enlarge a Plan in any of the proportions, \,\, i, Sfc. Suppose h. Set the two sockets at |, as before, and change places of the pencil and tracing point ; namely, place the tracing point at D, and the pencil at C To copy a Plan the same size as the Original. Place the two sockets at J, the fulcrum at D, and the pencil at B. In this case, the lines upon the new plan will be re- versed, in copying. Note 1. — There are sometimes divisions of 100 unequal parts laid down on the bars B and D, to give any intex-mediate proportion, not shewn by the fractional numbers. 2. — Pentagraphs of a greater length than two feet are best made of hard wood, mounted in brass, with steel centres, upon the truth of which depends entirely the equable action of this useful instrument. 3. — Though I have given various methods of reducing plans, I would ad- vise the learner, after he has found the contents from a plan of 2 chains, or of 1 chain to an inch, to draw another rough plan, of the same size which he intends his finished one to be ; and then to transfer it to a clean sheet by any of the foregoing methods. This may appear a little tedious, but it will make the learner very expert in laying down his lines, which will be found of great advantage to him, when he enters upon the practical part of surveying. 238 LAND-SURVEYING. (Part V. TO EMBELLISH A PLAN. In order to make a neat, finished plan, some knowledge of drawing is absolutely necessary. The learner should also be a proficient in plain and ornamental penmanship ; or he will not be able to finish a plan, either with beauty or elegance. Every person who would excel in this art, should devote all his leisure hours to copying and making out drawings, either from plans or copperplates well executed ; as nothing but practice will make a good draftsman. METHOD I. Plans neatly finished with Indian Ink and Colours. Having transferred the plan to a clean sheet of drawing-paper, or to a skin of parchment or vellum, by any of the foregoing methods, draw ail the straight lines very finely, by the edge of a ruler, with a drawing-pen and Indian ink ; but the curved lines must be drawn by a steady hand. Proceed next to make the representation of hedges, bushes, trees, woods, gates, stiles, bridges, the bases of buildings, &c. &c. in their proper places ; running a single dotted line, in an open field, for a foot-path, and a double one for a carriage -road. Hills may be shaded with a brush or hair-pencil and Indian ink. The first wash should be weak, and the edges of the shade, particularly at the top and bottom of a hill, must be softened off with clear water, and a clean brush, kept for that purpose, at one end of the pencil-handle ; the other end being occupied by the Indian ink brush. When the hills are very steep, and rise one above another, as those in Wales, Derbyshire, Yorkshire, Westmoreland, Cum- berland, Northumberland, and Scotland, they must all be shaded according to their various inclinations ; always letting one wash dry before another is laid on ; and never neglecting to soften off the edges of each shade with Avater. Part V.) land-surveying. 239 If some parts of the hills be rocky, tint them with a colour resembling stone, after they have been shaded with Indian ink and a hair-pencil, in the manner exhibited in No. 2, Plate VII. It may also be observed that when the inclination of a hill is considerable, it is never noticed by Surveyors, in shadino- or finishing their plans ; and if hills be flat at the top, they are left nearly white. The method of shading high moorish ground, and hilly fields, may be seen in Plates VI. and VII. ; except they must not be done with lines, in imitation of engraving, but with repeated washes of Indian ink. After hills have been properly shaded with Indian ink, they may then be coloured in the manner hereafter directed for meadow, pasture, and arable land. Lakes, rivers, brooks, &c. may also be shaded with a brush and Indian ink, pretty strongly at the edges, and softened off towards the middle ; and when they are dry, they may be washed over with a light tint of Prussian blue. The shape of arrows should also be made in brooks and rivers, to shew in what direction the streams run. Meadow and pasture ground should be coloured with a trans- parent green, the pasture rather lighter than the meadow ; arable land with various shades of fine brown, so that too many fields may not appear exactly alike ; and some Surveyors use both red, blue, lake, and yellow, in colouring plans. If the quick-Avood hedges be not made with a pen and Indian ink, in imitation of bushes, they may be represented by run- ning narrow shades of colouring along the black lines w T hich form the boundaries of the different inclosures. Roads should be washed with a brownish tint, and the bases of buildings with a red one, or with Indian ink, laid on with a brush of a convenient size ; as it is difficult to manage large brushes in shading small spaces. Sands upon the sea-shore, may be washed over with a mixture of brown, lake, and gamboge. Greens of various shades may be composed of blue and yellow ; a pleasing variety of brownish tints may be produced by mixing 240 LAND-SURVEYING. (Part V. lake, red. or yellow, with a little brown ; and a shade for water may be formed of Indian ink and Prussian blue. All the washes should be made thin, and laid on in a very neat manner ; as nothing disfigures a plan or a map so much as daubing on the colours too thickly. If the estate be small, the area of each inclosure may be put down in some vacant part of the plan ; but if it be large, the areas must either be entered within the fields themselves, or in a book of particulars, which may also contain any remarks that the Surveyor may think necessary to make to his employer, concerning the estate. In some convenient part of the plan, write, in various hands, with Indian ink, the title of the estate, ornamented with a com- partment or device. In another vacancy, introduce the scale by which the plan has been laid down ; and also a meridian- line, with the compass or flower-de-luce pointing to the north. The whole may then be bordered with black lines, at a con- venient distance from each other ; and the space between them shaded with a hair-pencil and Indian ink. See Plates IX. and XI. (Also y vide Xotes 3. ±. 5, an d G, page 378. ) Note 1. — If the learner examine a well -finished, coloured map of England, or any other country, he will fully comprehend what has been said on the subject of embellishing plans. 2. — Indian ink must always be used in planning ; and as it is frequently of a very bad quality, it is advisable to try it before you purchase, by wetting one end of the cake, and rubbing it upon white paper. The blackest and freest is considered the best. 3. — The most convenient colours are those ready prepared in cakes, which must be used in the following manner : Dip one end of the cake in dear water, and rub a little of it upon a clean wedgewood or earthen plate ; then mix it with water, by your hair-pencil, until you have brought it to any con- sistency you please. Indian ink must be prepared for use in the same way. 4. — Mr. James Newmans water-colours, No. 24, Soho-Square, London, are considered the best. The following will be found quite sufficient for Land- Survey ors ; viz. Part V.) LAND-SURVEYING. 241 Vandyke Brown. Yellow Ochre. Vermillion. Raw Sienna. Indian Yellow. Prussian Blue. Burnt Sienna. Light Red. Prussian Green. Gamboge. Lake. Sap Green. By means of these colours, a great variety of tints may be formed ; and a little practice will soon enable the learner to produce any shade that may be wanted for plans, or maps. 5. — When the price for measuring and planning is very small, Surveyors generally finish their plans neatly ; but without either colours, compart- ments, or embellishments of any kind. 6. — Professional Surveyors always enter in their Field-Books, the day of the month and date of the year, when they begin to survey an estate ; and in finishing their Plans, they date them accordingly, and also insert their own names, in order that gentlemen may know when, and by whom their estates were surveyed. METHOD II. Plans highly finished with Indian Ink and Colours. The foregoing method of finishing plans, is very expeditious, and may suffice when the price allowed for surveying will not admit of much time being spent in making embellishments ; but when a highly finished plan is wanted, the following method must be adopted. Meadows. With a pen, or a very fine pointed hair-pencil, and light Indian ink, make perpendicular and inclining strokes over the whole meadow, as represented in No. 1, Plate VI. ; and then wash it with a fine, transparent green. The strokes must be of various lengths; but none of them should exceed the 10th part of an inch. Pasture Grounds. Pastures may be shaded with upright and sloping strokes, of various lengths, as represented in No. 2, Plate VI. ; and then R 242 LAND-SURVEYING. (Pari V. w i- ar with a green, somewhat inclining to yellow. H one of the strokes shonld ex _ \ art of an inch in lencrth. By the edge of a ruler, or by the hand, draw (in short da- fine parallel lines, at equal distances from each other, so aa _ the fields the appearance of being divided into ridges and farrows, as represented in Nos. 3 and 4, Plate VX ; and then wash each field over with a different tint of brown, inclining - yellow. n=£dds :.-: ..:. ; ::>.. : ] hi this ma:: a plan a fine appearance. 3f :■:■/'$. With a pen. or a hair-pencil, draw the representation of a few k :■.::;:■- Dc is, if there be any on the moor. Draw also here and there, small bushes, ta represent heath, broom, whins, and such like brushwood" as usually grow upon moors. Make likewise tofts of grass, if :he moor is pasturable; and :: fill up all the vacant spaces with perpendicular and in- clining strokes, as rej resented in Nos. 1 and 2. Plate VI If them: >i be high, hilly, and rugged, with pools of water, caverns, roads, &c. it must be shaded with lines, in imitation of engraving, is exhibited in X:. 5, Plate VX; if any parts be wet and marshy, they must be done in the same manner as marshy ground ; and if the moor contains large stones, re : or trees, they must not be omit: When vou have finished shading with Indian ink. you must then colour the different parts of the moor, in the same manner i- fchey appear in nature. The parts producing herbage, nrast be washed with a greenish colour, inclining to blue ; the dark parts with a brownish: tint ; the lighter parts with a yellowish on^. : and the shrubs and bushes maybe touched up th a fine, lightish green. I: the moor contains whins, first wash them with green : and Plate YJ . If////* Ufr//s// (wittid. Part V.) LAND-SURVEYING. 243 then touch them up on the west side Math yellow, which will give them the appearance of being in blossom. By proceeding as above directed, a variety of pleasing effects and shades will be produced : and you will be able to give your plan a very fine appearance, and make it resemble even nature itself. Marshy Ground. With a pen, or a fine pointed hair-pencil, and palish Indian ink, draw, by the hand, shortish horizontal strokes of various lengths, pretty closely to each other. Make also the representa- tion of reeds, rushes, sedges, and strong herbage, as exhibited in No. 1, Plate VII. ; wash the whole over with a palish green, inclining to blue; and then touch up the reeds, rushes, sedges, &c. with a stronger green, which soften off either towards the right or left, with a lighter one, or with clear water. (See the method of shading trees.) Sands and Rocks. Sands upon the sea-shore, &c. must be represented by small dots, with a pen and Indian ink; loose stones by figures re- sembling small circles and ovals, but more irregular ; and rocks must be made to appear rugged and rough, and to rise in suc- cession, one above another, as exhibited in No. 2, Plate VII. The sands may then be washed over with a mixture of brown, lake, and gamboge ; and the stones and rocks coloured with such tints as will give them the appearance of nature. Some stones and rocks are whitish, some yellowish, some greyish, others brownish, &c. ; hence the propriety of always taking their real colour into consideration, when we intend to give a faithful representation upon a plan. Trees. Trees always adorn and beautify the face of nature ; and when they are neatly drawn, with a fine pen and Indian ink, they give a plan a very beautiful and pleasing appearance. They must be made with vertical stems, neat, broadish tops, r2 244 land-surveying. (Part V. shaded darker cm one side than the other; and black, horizontal shades at the bottom, as represented in No. 3, Plate VII. The lighter parts of the trees represent that side upon which the light is supposed to fall ; and the horizontal shades at the bottom are intended to denote the shadows of the trees, upon the ground. These shadows must always be made on the darker sides of trees ; and also of every other object, where shadows are intended to be represented. It is not material which side of a tree be left light ; but we must take care to make all the trees in the same wood, light on the same side ; for we cannot suppose that the light can fall on the right of some trees, and on the left of others, at the same time. When a sufficient number of trees have been made to give the wood an agreeable appearance, the vacant spaces must be filled up with small hushes, to represent the underwood. The whole wood should then be washed over with a lightish green ; after which, the tops of the largest trees may be touched up with a darker green, and with a little brown or yellow, in order to produce that pleasing variety _of tints which we so often behold and admire in nature. Note 1. — When the Indian ink, composing the trees, is not perfectly dry, it will run in washing the wood with green ; in order to avoid this, the green wash may be laid on before the trees and bushes are made. — This observation also points out the propriety of colouring fields, before the quickwood fences, are made with Indian ink. 2. — The tops of trees are formed in various ways. Sometimes they are made with jagged edges, and filled up in the middle with irregular strokes, in different directions ; and some Surveyors form them entirely by hori- zontal lines of various lengths. 3. — When trees are small, and neatly made, it is unnecessary to touch them up with any colour. 4. — Quickwood hedges must be made with a pen and Indian ink, in imita- tion of bushes ; and when trees are properly introduced, they have a very good effect in the hedge-rows. (See Plates IX. and XI.) Lakes, Rivers, and the Sea-Shore. Water must first be coloured with a fine tint of Prussian blue ; Part V.) LAND-SURVEYING. 245 and then shaded, by a pen, and Indian ink, with crooked or waved lines, bold near the edges, and fainter towards the middle, as exhibited in No. 4, Plate VII., which is intended to represent a mere or lake. Rivers and brooks must also be shaded with waved lines, continued from one end to the other, as represented in Plate XI. ; and the sea-shore in a similar manner, but much stronger and bolder than either lakes or rivers. N t e l . — Some draftsmen do not wash with Prussian blue, until they have finished shading with Indian ink ; but it is much better to colour the water before it is shaded, as the ink frequently runs when a wash is laid upon it. 2. — Here it may not be improper to observe,, that in colouring lakes, rivers, &c. with Prussian blue, the wash should be pretty strong at the edges, and softened off with water, towards the middle. Hilly Ground. Meadow and pasture ground should first be washed w r ith a fine green, and ploughed land with a yellowish brown, as before directed ; the hills must then be shaded in lines, with a pen and Indian ink, as represented in Nos. 5 and 6, Plate VII. The sides of hills may be shaded in the manner represented in the lower part of No. G ; and when the top of a hill is level, it must be left almost without shade. The greater the altitude of a hill, the deeper must be the shade ; but the level part of a valley between two hills, must be very faintly shaded. It will add greatly to the beauty of the plan or map, if all the hills be introduced in their proper places. When this is the case, and the hills are properly shaded, they form what is called a bird's eye mew ; it being supposed that the eye of the observer is elevated to some distance from the ground. What has been said on this subject will be fully comprehended by the learner, if he carefully examine the Plate to which I have already referred ; and also No. 5, Plate VI., which repre- sents a high, moorish district, shaded in a very neat and ex- pressive manner. b3 246 LAND-SURVEYING. (Part V. Pleasure Grounds. In order to draw a true plan of pleasure-grounds, it is ne- cessary to measure such lines, in taking the survey, as will enable you to lay down correctly, the shrubberies, grass-plots, and fish-ponds ; the bases of summer-houses and alcoves ; and the turnings and windings of all the gravel- walks, &c. &c. The trees, bushes, bases of buildings, &c. &c. must then be neatly made ; the fish-ponds and grass-plots properly coloured and shaded, as before directed, for lakes and meadows ; and the gravel-walks washed with a fine brown inclining to yellow. Note 1. — If the mansion-house, stables, gardens, &c. &c. be situated within the pleasure-grounds, the greatest care should be taken to lay them down cor- rectly ; as a gentleman will easily discover the smallest inaccuracy in a plan of those places with which he is so well acquainted. 2. — When pleasure-grounds are surveyed and planned with adjoining estates, the same scale must, of course, be used for the whole ; but when the former are measured separately, a large scale should be chosen, in order to allow sufficient room to plan every object distinctly.. Gardens. Gardens should be correctly and neatly planned ; and finished in a tasteful and elegant manner. The hot-houses, green-houses, grass-plots, gravel-walks, beds, &c. &c. should all be drawn and laid out, as they appear in the garden itself. The divisions between the different beds may be made with short dashes, as represented in Nos. 3 and 4, Plate VL ; the beds should then be lightly shaded with a pen and Indian ink ; rows of bushes inserted along the sides of the walks, and at the divisions of the various beds ; and here and there a few scat- tered trees should be made, as before directed, if there be any in the garden. Part V.) LAND-SURVEYING. 247 The gravel-walks must then be washed with a yellowish brown ; the grass-plots with green ; and the different beds with a light tint of yellow, red, lake, blue, green, or any other colours, so as to produce a pleasing variety ; and the trees may be touched up with a little dark green ; and occasionally a brownish or yellowish tint may be used, and give them an autumnal ap- pearance. Note. — When plans are to be finished with colours, it is not necessary to shade them so much with Indian ink, as when they are finished with Indian ink only. The Bases of Buildings. The outlines of the bases of buildings must be made with a drawing-pen and Indian ink, bold and black on the south and east sides, or on the north and west sides ; and the spaces in the middle filled up with oblique lines, as represented in No. 7, Plate VII., which is given expressly for the purpose of making the learner fully acquainted with the method of shading the bases of buildings, drawing the plans of villages, towns, &c. &c. Note 1. — When a proprietor wishes to have a plan of his buildings, offices, yards, &c. &c. upon a large scale, the dimensions should be taken in feet and inches, or in feet and tenths, which is preferable ; because the chains and tenths of a chain, upon the plotting-scale, may then be considered as feet and tenths, and used accordingly in planning ; or when it is more convenient, each chain may be called ten feet ; consequently, each division will then become one foot. (See Note 3, Prob. I. Part III.) 2. — When it is intended to lay down buildings by a large scale, the thick- ness of the walls, the lengths and breadths of rooms and passages, the widths of doors and windows, the projections of fire-places, and other necessary dimensions, should be taken, in order to produce a correct plan. 3. — After the base of a wall has been formed by parallel lines, drawn at such a distance from each other as to exhibit the wall's thickness, the space between these lines may then be shaded by oblique lines as before directed. The door- ways should be left open ; the window-bottoms represented by omit- tingto shade them with oblique lines ; the chimney bottoms or fire-places ex- hibited by making the inside of the wall to project into the room, at right- R 4 248 laxd-suhveyixg. (Part V. angles ; and the steps of the stairs denoted by parallel lines, drawn at proper distances from each other. The insides of the rooms may either be left white or coloured, at the option of the draftsmen ; and if it be thought tedious to ehade the bases of the waDs with oblique lines, they maybe done with a brush and Indian ink. 4. — The name of every room, office, yard, Jce. must be given, either within the rooms themselves, or in the margin of the plan ; and when the premises are extensive, the names of the rooms, out-offices, yard?, kc. will be numerous ; there will probably be the kitchen, back-kitchen,parlour, hall, breakfast -room, dining-room, drawing-room, dairy, pantry, stairs, brew-house, wash-house, coal-house, carriage-house, stables, cow-house, calf -house, hog-stye, soil-hole, barn, stable-yard, court -yard, orchard, garden, &c. &c. What has been said on this subject will be easily comprehended by inspecting No. 2, Plate V. ; which is the ground plan of a small house, laid down by a large scale, in order to show the learner how he must proceed with plans of a similar nature. 5. — "Whehpreniises are to be sold, every convenience should be pointed out, on the plan, in order to promote the sale ; and it wiil be found very advan- tageous to have plans of the cellars and the upper stories, and even the ele- vations ; but this is more properly the business of an Architect than that of a Land- Surveyor. Some persons, however, will find it of considerable advan- tage to obtain a knowledge of both these sciences ; as gentlemen frequently want not only plans of their estates, but also architectural draughts of their buildings. The Elevation s >f Buildings. In order to give & perspective view of the elevation of a build- ing, it is necessary to be acquainted with the art of drawing in perspective; but an architectural view may be produced by taking the dimensions of the building, and laying them down by a scale of equal parrs. "When it is intended to give the elevation of any buildings belon-dno- to a farm, or the elevation of a mansion-house and offices belonging to a gentleman's estate, the length from end to end. the perpendicular height from the ground to the . the height of the gable-ends, the height and breadth of the chimnev-tops, the height and width of the doors and windows, their situations in the walls, and every other necessary dimen- /'LATE 17/ /. Afa/y/tv Givund. '2. . S't/// ( /x am/ /ifi'ks. :&£■£' TlY,'.s\ Wutsr J. /run J FisMs. Part V.) LAND-SURVEYING. 249 sion must be measured ; then these dimensions being correctly laid down by a scale, will give an architectural view of the elevation of the building in question. AVhat has been advanced on this subject will be further illus- trated by referring to No. 8, Plate VII. , which is an architectural view of a gentleman's house, given for the inspection and im- provement of the learner. The house itself is built with gable- ends, but the roofs of both the wings are hipped at one end, which make a pleasing contrast in the elevation. Note 1. — After the outlines of an elevation are drawn, the common method of shading is by a brush and Indian ink ; as it is generally thought too tedious to shade with strokes, in imitation of engraving. The roof should be shaded pretty strongly at the ridge, and softened off towards the middle, with water. It may then be washed with Prussian blue ; and if the washes, both of Indian ink and colour, be light and often repeated, a more agreeable softness will be produced than by laying on only two or three strong washes. When the roof has been thus shaded, lines may be drawn parallel to the eaves, decreasing gradually in their distance from each other towards the ridge, to represent the edges of the slates. If the house be covered with tiles, the lines must be at equal distances from each other ; because tiles of different sizes are never laid upon the same house. 2. — If the front of a building project beyond the wings, it must be denoted by making its shadow fall upon one of the wings ; but if the wings project beyond the front, the shade of one of them must be made to fall upon the front. (See No. 8, Plate VII., where the shade of the front falls upon the right wing ; if the wings had projected, the shade of the left wing would have fallen upon the front.) 3. — If a house be built of brick, it may be coloured red ; if of stone, a colour may be chosen to resemble it ; and when a roof is covered with grey slates, blue slates, or red tiles, it may be coloured accordingly. Sometimes the front of a building is shaded with Indian ink, the roof tinted with blue, and the stone door-posts, window-jambs, string-courses,chimney-tops,&c.&c. coloured so as to resemble stone. Indian ink, however, is generally used for fronts, in preference to any colour ; as it is considered to give buildings a much richer appearance. 4. — If there be trees about the buildings, they may be etched with a pen and Indian ink, in imitation of engraving ; the ground in front should be properly shaded ; the gravel-walks coloured with a light brown ; and if the elevation be bordered with black lines, as in No. 8, Plate VII., the sky may be coloured with a fine blue, or shaded with Indian ink. 250 land-surveying. (Part V. 5. — The elevations of buildings belonging to estates that have been sur- veyed, should be given on vacant parts of the plan, as embellishments ; it is very seldom indeed that they are drawn in their true situations, because they would intercept the view of the ground plot ; and besides, they are generally laid down by a much larger scale. The mansion-house of a nobleman, well executed, on a vacant part of the plan of his estate, has a very pleasing effect ; and will never fail to gratify the proprietor. 6. — It is almost superfluous to remind the young draftsman that he should always keep his hands perfectly clean, and also cover his plans and maps with clean paper, (particularly under his hands,) to preserve them from being in tho least soiled in drawing them ; as nothing exhibits the carelessness of a draftsman in a more conspicuous light, than seeing his work besmeared with dust, ink, or colours. METHOD III. Plans highly finished with Indian ink. A plan highly finished with Indian ink only, has a very- elegant appearance, and is considered, by most persons, to ex- cel those done in colours ; hut the process is very tedious, and requires much time to do it neatly ; however, if the Surveyor be well paid for his time, he ought to finish his plans in that manner which is most likely to give satisfaction to his em- ployers. Many Surveyors keep plans by them, finished in various ways, as specimens, in order that gentlemen may have an op- portunity of choosing in what manner they will have the plans of their estates executed. Shading with the Pen. In finishing a plan with Indian ink, a fine pen ought to be used ; and the fields should be shaded in a great variety of forms, in imitation of engraving, as exhibited in Plate V. IX. and XI. Some fields should be done lighter, and others darker, so as to produce a pleasing contrast of light and shade. Some may be executed in such a manner as to resemble corn-fields, as in Nos. 1 and 6, Plate IX. ; and 13 and 16, Plate XI. ; and others may be shaded like meadow and pasture, as exhibited in Nos. 1 and 2, Plate VI. Part V.) LAND-SURVEYING. 251 High, moorish ground should be shaded as represented in No. 5, Plate VI. ; and marshy grounds, sands, loose stones, rocks, trees, water, hilly fields, and the bases of buildings, as denoted in Plate VII. ; and even the elevations of buildings look very elegant, when they are finely shaded with lines, as No. 8, in the Plate to which we last referred. Note. — In finishing a plan with Indian ink only, it is necessary to shade it much closer and deeper, than in finishing with Indian ink and colours. In making finished plans, no ornaments or embellishments will compensate for bad penmanship. Writing, German-text, Printing, and Figures, are all essen- tially necessary for a draftsman; and whoever would excel in the art of planning, should use his utmost endeavours to be- come a complete and elegant penman. He should practise the various hands, either by copies well written, or by good copper-plates, until he can make all the letters and figures correctly, and with true taste ; and it will save him much trouble in making compartments and devices, if he can acquire the art of flourishing and ornamenting neatly and elegantly with the pen. (See Notes 3, 4, 5, and 6, page 378.J Ornaments. Any compartment or device may be chosen to fill up the vacant corners of a plan, such as the compass, scrolls of paper, wreaths or festoons of leaves and flowers, branches or sprigs of oak, palm-tree, weeping-willow, myrtle, laurel, olive, &c. &c. Also shields, coats of arms, columns supporting vases or urns, mathematical instruments, cattle, sheep, or whatever else may please the fancy of the draftsman. Ornaments on Plate IX. In the N. W. corner is a device formed of an oak branch, leaves, and acorns on the left side ; and on the right side is a 252 LAND-SURVEYING. (Part V. branch of large pointed leaves resembling sedges or sweet flags, intertwined with a string of small leaves; and both branches are united at the bottom by a bunch of riband. In the S. W. corner is a scroll of paper, supported by a fluted column ; by the side of which are some ears of corn, and at the bottom a few blades of grass and herbage. In the N. E. corner is the sun in his meridian splendour, with a fancy device resembling an ogee cornice, fronted with reeds ; and from each end of the cornice is suspended a festoon of small leaves. In the S. E. corner is a plotting-scale ; a pair of compasses, two drawing-pens, and a writing-pen, interwoven with a gar- land of small leaves and berries, resembling those of the myrtle. Ornaments on Plate XL In the N. W. corner is a fancy device, in the form of an oval ; and in the N. E. corner is a rectangular device, with the exception of the arch at the top. This device is ornamented with a bunch of riband, and two festoons of small leaves and berries, hanging upon two scutcheons, or shields. In the S. W. corner is a column, at the top of which is a vase encircled with leaves and flowers. On the west of the column, Britannia is seated, leaning on her shield, holding a spear in her right-hand, and with her left-hand pointing out the science of Surveying. To the east of the column are two sheep, emblems of agriculture. The plotting-scale, drawing-pens, &c. are nearly similar to those in the last plate. In the S. E. corner is a parallel ruler, a plane table, a terres- trial globe, a crowing cock, and a youth seated upon a bee-hive, with a pair of compasses in his hand, at work upon plate XII. The cock is an emblem of early rising, and the bee -hive may be considered as an emblem of industry ; and it may here be re- marked that it is impossible to attain eminence in the art of Surveying, without early rising, industry, and perseverance. Part V.) LAND-SURVEYING. 253 MISCELLANEOUS INSTRUCTIONS RELATING TO SURVEYING, PLANNING, CASTING, VALUING, &c. &c. 1. The title of a plan should set forth the name of the pro- prietor ; and also the name of the township, hamlet, parish, and county, in which the estate is situated. 2. The names of the adjoining lordships, or the names of the proprietors of the adjoining lands, should be given on the plan, in order to point out clearly the situation of the estate, and cor- roberate the title. 3. All principal roads passing through the estate, from one highway to another, should be laid down ; and the places to which they lead, specified. 4. All foot-paths and bridle-roads should be pointed out, in order to determine the public right; and guard against en- croachments. 5. All occupation and privileged roads, through adjoining estates, should be noticed either on the plan, or in the reference- book. 6. All ancient highways leading through the estate, although not now in use, should be particularly specified, and the names of the proprietors given, to show in whom the privilege of re- opening them, if necessary, is vested. 7. The ancient and proper names of fields should be pre- served ; as it generally creates confusion and mistakes, when new ones are assigned without sufficient authority. 8. It has already been observed, that the extremities of the ditches are generally the boundaries between adjoining fields ; this, however, is not always the case, as the stem of the quick- wood sometimes forms the boundary; hence the necessity of obtaining an assistant who is well acquainted with all the local customs of the place. 9. The greatest care must be taken to find the area of each field correctly ; and particularly if the survey be taken for an inclosure, or to make a valuation for the land-tax, poor-rates, 254 LAND-SURVEYING. (Part V. county-rates, and other assessments ; for it is evident that if the surrey be incorrect, the valuation can never be equitable ; and will consequently produce nothing but disputes and dis- satisfaction among the proprietors and occupiers, instead of peace, harmony, and friendship. 10. In valuing for an assessment, great care should be taken not to over-rate the land that is of a poor quality, and lies far from the means of improvement ; for bad land costs the occupier as much in labour and seed, as good land, and is far less produc- tive. (See more observations on valuing land, in Part VI.) 11. In reducing a plan for portable use. care should be taken to choose a scale sufficiently large to exhibit all the irregularities in the fences, buildings, &c 12. Several small farms, or detached pieces of land, belonging to one proprietor, may be laid down upon the same sheet. They ought not, however, to be joined together, but planned as separate estates. 13. When one sheet of drawing-paper is too small to contain the survey, two or more must be neatly pasted together ; and when those parts that have been wet with the paste, are nearly dry, they may be made smooth by a warm iron. The edge of one of the sheets should be cut even, and laid nearly half an inch over the edge of the other sheet ; and a piece of clean paper should be laid under the iron, to prevent it from soiling the plan. 1-i. It has already been observed that the surveying-chain should frequently be measured. The readiest method of doing this, is to drive two stakes or pins into the ground, exactly at the distance of 22 yards from each other. Professional Sur- vevors measure their chains in this manner every morning, when they are engaged in extensive measurements. When the chain has become too long, it is better to cut a little from several of the links, than to take off the rings ; care, however, must be taken to keep each 10 links of an equal length, or the dimensions will be incorrect. 15. The book of particulars, before-mentioned, is generally called M A Terrier of the Survey," and should contain references corresponding to those upon the plan; also the name of each Part V.) LAND-SURVEYING. 255 field, or the name of the proprietor, or of the occupier ; and the area of each field, in acres, roods, and perches. If the Sur- veyor value the estate, the Terrier ought to contain the value per acre to let, or for sale ; the annual value of each field to let, or the total value for sale ; and also the cultivation of each field : thus will the proprietor be furnished with every neces- sary particular relating to his estate. 16. The Terrier may likewise contain remarks and obser- vations on the quality of the soil; and point out the method of improving wet marshy grounds, by draining them; com- mons and waste lands, by inclosing them ; large fields, by dividing them ; &c. &c. 17. Some Surveyors return three measurements of each field in the Terrier ; viz. the land in cultivation ; the hedges and waste land ; and the total quantity, or sum of both. 18. In giving the cultivation of each field, the permanent meadows, or those which the tenant is prohibited from breaking up, should be particularly noticed. 19. In writing out a valuation-book for the purpose of making assessments, all the lands and tenements in the occupation of the same tenant, should be collected together ; and put down on the left -hand page of the book. At the top of the page must appear the name of the tenant ; and in the first and second columns respectively, the names of the proprietors and the num- bers on the plan. The third, fourth, fifth, and sixth columns, must contain the name, measurement, value per acre, and total value of each field respectively. The right-hand page may be left blank for incidental remarks, when a change of occupation takes place ; or when any circumstance occurs that affects the arrangement of the book. 20. When the valuation is high, it is frequently thought pru- dent to calculate the assessments from one-fourth, one-half, or three-fourths of the amount ; this, however, is more properly the consideration of the occupiers, than that of the Land-Sur- veyor. Sometimes the assessments are calculated from one- half, or three-fourths of the valuation of the land ; and from one -fourth of the valuation of the buildings. 256 land-surveying. (Part V. A TERRIER OF THE SURVEY IN PLATE IX. j © o Names of the Fields. Cultivation of the Ground. Area in A. R. P. Value per Acre to rent. £. s. d. Total Value per Annum to rent. £. s. d. 1 Calf Garth ... Pasture 1 20 2 12 6 2 19 Of 2 Lane Close ... Arable 2 2 38 1 16 4 18 6£ 3 Low Close Permanent ) Meadow J 2 10 2 2 6 4 7 7} 4 Turnpike Close Arable 13 1 28 1 14 22 16 5^ 5 Daisy Field . . . Meadow 11 9 1 15 6 19 12 5{ 6 Triangle Pasture 12 2 18 2 3 6 27 8 7£ Sura Total 43 3 82 2 91 Note 1. — The annual value of each field may be found from the area, and the value per acre, by the Rule of Three' ; but when the calculations are numerous, much labour may be saved by using Hudson's Land Valuer's Assistant. 2. — If one tenant occupy all the foregoing estate, his rent will be 82/. 2«. 9±d. per annum ; and if the assessments be made from three-fourths of the annual value, he will be assessed at 62/. 12s. Id. 3. The Terrier may be divided into any number of columns, to suit the purpose of the Surveyor ; and when the observations, remarks, Lc. are too numerous to be contained in the columns of one page, each two opposite pages may be divided into columns, in which may be entered every necessary infor- mation relating to the estate. 4. — In extensive surveys and valuations, an alphabetical index should be annexed to the Terrier or Valuation-Book, in order that the name of any par- ticular proprietor or occupier may be more readily found. /qW ( 7j' A /////A -JjA wjetjDMOom:, */ff(JC /lie /jfiSfr. ('"ontercts. ,.v/.e,W Close <2 „ () , f0 I'lff S/ty//cers Close 13. / .. 26 ■ l//:l7/vr/,r//r Close. // » O .. '9 Mi- .Ml,, r,li Close J2 .. 2 „ /S Total. IS. O ., 3 7/f/n/f lor/// J/ir// ' s //r/// ///<■ i ■//fj/'trmt ( |N ontmt$ \h:J)„'>() y,:C v / . 10 .13 .. / .. 2S VI .. (> ,. & WtHMrrnfi Close 12 .. 2 „ 16 Total... A3* O .. ,3 Settle,. / Chrnt-s'lfuf/ifitr//. ___ r/«uix ) ^O 1 entente. e7/w / .. o ., so 3 E L Li Kl ESTATE 9 c °H ' V A ^ fc r-yv^j zm dwv csbit: £c*bit^ D A O ~^ ontcnfo.xV; ij / /)...■()., 10 73 .. / .. 2. vnm { I fc£ & \ la ^* '^ # -x LAND-SURVEYING. Part tf>t Mixfy. Rules and Directions for laying out any given Quan- tity of Land* in any proposed Figure ; for parting from any Field or Figure any Quantity of Land required ; and for dividing a Piece of Land among sundry Claim- ants in the Proportion of their respective Claims, or a Common, fyc* of variable Value, among any Number of Proprietors, in the Proportion of their respective Interests. Also, the Method of reducing Statute Measure to Cus- tomary, and vice versa. SECTION I. RULES AND DIRECTIONS FOR LAYING OUT ANY GIVEN QUANTITY OF LAND, IN ANY PROPOSED FIGURE; AND FOR PARTING FROM ANY FIELD OR FIGURE, ANY QUAN- TITY OF LAND REQUIRED. When the land to be laid out, or parted off, is given in acres, roods, and perches, it must first be reduced into square links ; in which process the following Table will be found extremely useful. When it is required to part off from any field, or figure, any quantity of land, it is generally necessary, first, to measure the whole, if the dimensions be not given. s 258 LAND-SURVEYING. (Part VL A Table for reducing Acres, Roods, and Perches, into Square Links. Acres. Sq. Links. [Perches. Sq. Lks. Perches. Sq. Lks. 1 100000 1 625 1 21 13125 2 200000 2 1250 22 13750 3 300000 3 1875 23 14375 4 400000 4 2500 24 15000 5 500000 5 3125 25 15625 6 600000 6 3750 26 16250 7 700000 7 4375 27 16875 8 800000 8 5000 28 17500 9 900000 9 5625 29 18125 10 1000000 10 6250 30 18750 20 2000000 11 6875 31 19375 30 3000000 12 7500 32 20000 40 4000000 13 8125 33 20625 50 5000000 14 8750 34 21250 GO 6000000 15 9375 j 35 21875 70 7000000 16 10000 i 36 22500 80 8000000 17 10625 37 23125 90 9000000 18 11250 38 23750 100 10000000 19 20 11875 12500 39 24375 Roods Sq. Links. ~ 25000 2 50000 3 75000 1 PROBLEM I. To reduce any number of Acres, Roods, and Perches, into Square Links. Rule. — Rednce the given quantity of land into perches, which multiply by 625, the number of square links in one perch, and the product will be the square links required. Or, find the equivalents of the acres, roods, and perches respectively, in the foregoing Table. Section I.) land-surveying. 259 EXAMPLES. 1 . Reduce 6 acres, 3 roods, and 25 perches, into square links. By the Rule. By the Table. a. R. P. sq. links. 6 3 25 6 a. = 600000 4 3 r. =. 75000 27 25 p. =£= 15625 40 690625 Ans. 1105 625 5525 2210 6630 690625 Ans. 2. Required the number of square links in 96 acres, 2 roods, and 36 perches. Ans. 9672500. PROBLEM II. To lay out, in a Square, any Quantity of Land proposed. Rule. — Extract the square root of the proposed area, and it will be the side of the square required. examples. 1. Lay out, in a square, 7 acres, 1 rood, and 24 perches. sq. links. 7 a. = 700000 1 r. = 25000 24 p. = 15000 740000(860.2 links, the side of the square, 64 166)1000 996 17202)40000 34404 •5596 s2 260 LAND-SURVEYING. D C (Part VI. In laying out the square, in the field, let A B represent one of its sides, which make = 860.2 links. At A, erect the per- pendicular A D, which make = AB; and at B, erect the per- pendicular B C, which make also = AB. Then measure the line C D, and if you find it = 860.2 links, the work is right. 2. Required the side of a square, which shall contain 15 acres, 2 roods, and 32 perches. Ans. 1253 links. PROBLEM III7 Upon a given Line, to make a Rectangle that shall contain any proposed Quantity of Land. Rule. — Divide the proposed area by the given side, and the quotient will be the other side of the rectangle. EXAMPLES. 1. Lay out 3a. 3r. 26p. in the form of a rectangle, one side ©f which must be 850 links. sq. links. 3a. = 300000 3r. = 75000 26p. = 16250 85,0)391250(460.3 links, the other side. 340 .512 510 ..250 255 Section I.) D LAND-SUKVEYING 261 In laying out the rectangle in the field, let A B represent the given side. At A, erect the perpendicular A D, which make = 460.3 links ; and at B, erect the perpendicular B C, which make = A D. Then measure the line C D, and if you find it = A B, the work is right. 2. If one side of a rectangle be 52.5 links ; required the other side, so that the figure may contain 6a. 2r. 23p. Ans. 1265.5 links. PROBLEM IV. To lay out any given Quantity of Land in a Rectangle, so that one of its sides shall be two, three, four, or any number of times as long as the other. Rule. — Divide the given area by the given number, and the square root of the quotient will be the shorter side, which multiply by the given number, and the product will be the longer side. EXAMPLES. 1. Lay out 3a. Or. 32p. in the form of a rectangle, one of the sides of which shall be twice as long as the other. sq. links. 3a. = 300000 32p. = 20000 2) 320000 160000(400 links, the shorter side. 16 2 . . 0000 800 links, the longer do. s~3 262 LAND-SURVEYING. (Part VI. B D Let ABCD represent the rectangle, which you must lay out according to the directions in the last problem ; A D being 800, and A B 400 links. 2. A rectangle contains 7a. 2r. Op. ; what are its sides, one of them being three times the length of the other ? Ans. 1500 and 500 links. PROBLEM V. Upon a given Base, to lay out a Triangle that shall contain any given number of Acres, fyc. Rule. — Divide the area by half the base, or twice the area by the whole base, and the quotient will be the perpendicular of the triangle. EXAMPLES. 1. Lay out 3a. 2r. 16p. in the form of a triangle, the base of which must be 1200 links. sq. links. 3a. = 300000 2r. = 50000 16p. z= 10000 6,00)3600,00 600 links, the perpendicular. Section I.) land-surveying. C E 263 Upon any part of the given base A B, suppose at D, erect the perpendicular D 0, which make = 600 links ; then stake out the line A C and BC; so will A B C be the required tri- angle. But if the perpendicular be erected at either end of the base, as at B, then the line A E must be staked out ; and ABE will be the triangle required. 2. Required the perpendicular of a triangle, which contains 6a. 2r. 37p., its base being 1556 links. Ans. 865.2 links. PROBLEM VI. To lay out a Trapezium, that shall contain any Number of Acres, fyc. ; having one of its Sides or a base Line given. Rule 1. — Divide the given area into two parts, either equal or unequal ; and .then, by the last problem, find the perpen- dicular, that will lay out one of these parts in a right-angled triangle, upon the given base. You must then consider this perpendicular as one of the dia- gonals of the trapezium, and also the base upon which you must lay out the other triangle. Rule 2. — Divide the given area into any two parts, as before; and then, find the perpendicular that will lay out one of these parts in a right-angled triangle, upon the given base. Add the square of the perpendicular thus found, to the square of the given base, and the square root of the sum will be the hypothenuse. Consider this hypothenuse as one of the diagonals of the trapezium, and also the base upon which the other triangle must be laid out. 84 164 LAND-SURVEYING. (Part VI. EXAMPLES. 1. Lay out Ba. in a trapezium, upon a given side of 800 Kb BY THE FIRST RULE. I>i~:."r :he given :.: 5 and 3 acres, and let the triangle upon the given side contain th _ 5a. =. 500000 square links. 2 1250 -..:-. :he perpendicular of the first triangle. I also the base of the - 3a. = 300000 square links. _2 125.0)600000(480 links, the perpendicular of the second 500 triangle. 1000 In laving out the trapezium, in the field, let A B represent the given s:. if. A: B. a frpendicular B C. which make = 1250 links. Then any part of the line B C. as ar I>. the perpendicular D E. vrhich make = 4> Kniks. Hi€ four out- line- -ill be completed. Section I.) land-surveying. 265 BY THE SECOND RULE. 5a. = 500000 square links. 2 8,00)1000000 1250 links, tlie perpendicular of the first triangle. Then, \/l250 2 + 800 2 = v 1562500 + 640000 =V2202500 = 1484 links, the hypothenuse of the first, and also the base of the second triangle. 3a. = 300000 square links. 2 1484)600000(404.3 links, the perpendicular of the 5936 second triangle. • • 6400 5936 •4640 4452 188 c 13 Having laid out the triangle A B C, as before directed ; upon any part of the line A C, as at D, erect the perpendicular D E, which make = 404.3 links. Stake all the outlines, and the work will be completed. 2. Lay out 12a. in a trapezium, upon a given side of 1400 links. Ans. Supposing the given area divided into 7 and 5 acres ; 266 land-surveying. (Part VI. then, by the first Rule, the perpendicular of the first triangle is found to be 1000 links ; and that of the second the same. By the second Rule, the perpendicular of the first triangle is found to be 1000 links ; the base of the second 1720.5, and its perpendicular 581.2 links. PROBLEM VII. Upon a given Base, to lay out a Rhomlus of any Content less than the Square of the Base. Rule. — Divide the content by the base, and the quotient will be the perpendicular. Then, from the square of the base, sub- tract the square of the perpendicular, and find the square root of the remainder. Upon the base, from one of its extremities, measure a line equal to this root, and at this point erect a per- pendicular. Note. — It is evident from the foregoing Rule, that the area of a rhombus or rhomboides may be found by multiplying the base by the perpendicular breadth. EXAMPLES. 1. Lay out in a rhombus, 5a. 2r. 16p. its base being 800 links. sq. links. 5a. = 500000 2b. = 50000 16p. — 10000 8,00]5G00,00 700 links, the perpendicular. Then, \/s00 2 - 700 2 =V 640000 - 490000=^150000=387.3 links, at which distance, from one of the extremities of the base, the perpendicular must be erected. E C / D B Section I.) land-surveying. 267 In laying out the rhombus, in the field, let A B represent the given base. From A, on the line A B, measure 387.3 links to D ; and at D erect the perpendicular D E, which make =. 700 links. At E, erect the perpendicular E C, which make = the base A B. Measure the lines C B and A E, and, if you find each of them = AB, the work is right. 2. Lay out a rhombus, which shall contain 6a. 1b. 8p., upon a base measuring 900 links. Ans. The perpendicular is found to be 700 links, and the distance at which it must be erected from one of the extremities of the base 565.7 links. PROBLEM VIII. To lay out any given Quantity of Land in a Circle. Rule 1. — If we multiply the square of the diameter of any circle by .7854, the product will be the area ; consequently, if we divide the area by .7854, the quotient will be the square of the diameter. 2. Multiply the square root of the area by 1.12837, and the product will be the diameter. EXAMPLES. 1. Lay out one acre of land in a circle. sq. links. .7854)100000.000000(127323.65 links, the square of 7854 the diameter. 21460 15708 . 57520 54978 25420 23562 77s580 15708 . 28720 23562 .51580 47124 . 44560 39270 5200 7i : : - vetey i 1 Or r bjtfeS X 1.1283? = : : . la laying oak tie eirde in. tie field- provide a strong end. in £if :-.:r-i:: A mi — _-_ — zzr A I — -J: ~i :i>i - -_:_ -:~ z.:-: 5tzi>t :~: -_t Oe^ at prefer mfcem!^ stretek die radios A B. :-i>T- ~ i~:l i n_zzr: i: - :': m "Jl-r 9L Beqidredfhe Jmwmjh «f aeirefe, PROBLEM D -r ±i rilf _:, zi -1- .~i - Section I.) land surveying. 269 A Table of regular Polygons, with their Areas ; and the Radii of their circumscribing Circles, when the side of the Polygon is 1. 1 No. Sides. Names. Areas. Radii. 3 Triangle 0.433 0.577 4 Square 1. 0.707 5 Pentagon 1.72 0.851 6 Hexagon 2.598 1. 7 Heptagon 3.G34 1.152 8 Octagon 4.828 1.306 9 Nonagon 6.182 1.462 10 Decagon 7.694 1.619 11 Undecagon 9.365 1.775 12 Duodecagon 11.196 1.932 Note.—li the square of the side of any polygon, be multiplied by the area standing opposite to its name, in the preceding Table, the product will be the area of the polygon. EXAMPLES. 1. Lay out one acre of land in a regular hexagon. 100000 HerG "2T98 = 38491.147; and ^38491.147 = 196.191 links, the side of the required polygon, and also 'the radius of the circumscribing circle, because the side of a regular hexagon and the radius of its circumscribing circle are always equal to each other ; hence the multiplier in the Table is 1. <>B 270 land-suuveying. (Part VI. To lay out the hexagon, in the field, draw the circumscribing circle as directed in the last problem. Then, the radius A B, which is equal to the side of the hexagon, being applied six times, will just go round the circumference, and form the polygon required. 2. Lay out half an acre of land in a regular octagon. Ans. The side of the required octagon is 101.76, and the radius of its circumscribing circle 132.898 links. PROBLEM X. To lay out any given Quantity of Land, in an Ellipsis, having one of the Diameters given. Rule. — If we multiply the rectangle of the two diameters of an ellipsis by .7854, the product will be the area ; consequently, if we divide the area by .7854, and that quotient by the given diameter, the latter quotient will be the diameter required. EXAMPLES. 1. Lay out an ellipse, which shall contain one acre, with a transverse diameter of 450 links. sq. links. .7854)100000.00000(127323.6 quotient. 7854 21460 15708 57520 54978 • 25420 23562 • 18580 15708 28720 23562 •"51580 47124 • 4456 Section I.) land-surveying. 127323.G 271 Then, 450 z=. 283 links, the conjugate diameter. By Prob. 15, Part I., construct the ellipse ABCD; then by a property of the ellipse, (see my Mensuration, page 318,) the square of the distance of the focus from the centre, is equal to the difference of the squares of the semi-diameters : hence, we have v /225 2 -141.'5 i = v/ 30602.75 = 175 links, equal F o, or f o : and, 225-175 = 50 links, equal A F, or B f. Again, by another property of the ellipse, the sum of two lines drawn from the foci, and meeting in any point in the cir- cumference, is equal to the transverse diameter ; that is, F m -+- f m = A B. Procure, therefore, a cord, and upon it make two loops, so that the distance between them may be equal to the transverse diameter ; then measure, in the field, the diameter A B ; putting down a stake at each focus, and one at the centre o. At o, erect the perpendiculars o C and o D, making each = 141.5 links. Put the two loops over the stakes at F, f, and stretch the cord, so that the two parts F m, f m, may be equally tight ; at m put down a stake, as one point in the circumference of the ellipse ; and, in the same manner, determine as many others as you please. But if the ellipse be very large, so that you cannot conveni- ently procure a cord as long as the transverse diameter ; you must, then erect perpendiculars, called ordinates, at every 50 links, or at every chain's length, &c. upon that diameter, and measure the lengths of these perpendiculars by the scale. 272 laxd-suuvkying. (Part VI, Then measure, in the field, the transverse and conjugate dia- meters, and erect the perpendiculars in their proper places ; always remembering to put down a stake at the end of each perpendicular. 2. Lay out an ellipse which shall contain 8a. 3r. 8 p., one of the diameters being given equal to 800 links. Ans. The other diameter is = 1400 links. Xote. — As Surveyors are frequently requested to lay out, in various figures, small quantities of land for plantations, &c. it is presumed that the foregoing problems will be found not without their use. PROBLEM XI. To part from a Square or Rectangle, any proposed Quantity of Land, by a Line parallel to one of its sides. Rule. — Divide the proposed area by the side upon which it is to be parted off, and the quotient will be the length of the other side of the figure required. EXAMPLES. 1. From the square A B C D containing 6a. 1r, 26p., part off 3a. by a line parallel to A B. Section L) LAND-SURVEYING. sq. links. 6a. = 600000 1r. = 25000 24p. = 15000 273 640000(800 links, the side of the square. 64 . . 0000 — - 300000 ,. , . , . „ „ „ . , Then, = 375 links, the side A E, or B F required. 800 2. From the rectangle ABCD containing 8 a. 1r. 24p., part off 2a. 1r. 32p. by a line parallel to A D = 700 links. Then, from the remainder of the rectangle, part off 2a. 3r. 25p. by a line parallel to A B. sq. links. 2a. = 200000 1r. = 25000 32p. = 20000 7,00] 2450,00 . 350 links, the side A E, or D F. sq. links. 8a. = 800000 1r. = 25000 24p. = 15000 7,00(8400,00 1200lTnks, the side A B. 350 the side A E. 850 the difference = EB. 2? 4 land-surveying, (Part VI. sq. links. 2a. = 200000 3r. = 75000 25p. = 15625 850)290625(342 links, the side E G, or B H. 2550 73562 3400 .1625 1700 3. Part off 6a. 3r. 12p. from a rectangle, containing 15a. bv a line parallel to the longer side ; the shorter being 1000 links. Ans. The longer side of the given rectangle is 1500, and the shorter side of the rectangle required is 455 links. PROBLEM XII. To part from a Square or Rectangle^ any proposed Quantity of Land, either in a right-angled Triangle or Trapezoid, by a Line drawn from any of the Angles to either of the opposite Sides. R rLF ,. — TThen the proposed area is to be parted off in a tri- angle, divide double this area by the base or side upon which it is to be parted off, and the quotient will be the perpendicular. When the proposed area is to be parted off in a trapezoid, subtract it from the area of the square or rectangle, and part off the remainder in a triangle, as above directed. EXAMPLES. 1. From A B C D representing a square, whose side is 900 links, part off a triangle which shall contain 2a. 1b. 36p. by a line drawn from the angle B to the side A D. Section I.) land-surveying. I> C 275 2 a. 1r. 36p. = 247500 square links. 2 9,0014950,00 550 links, the perpendicular A E. Hence A B E is the triangle required. 2. From A B C D representing a rectangle, whose length is 1265,andbreadth 758 links, part off a trapezoid which shall contain 7a. 3r. 24p., by a line drawn from the angle B to the side C D. D E A B sq. links. 958870 the area of the rectangle. 790000 ditto of the trapezoid. 168870 difference, the area of the triangle. 2 758)337740(445.5 links, the perpendicular C E. 3032 Hence A B E D is the trapezoid required. .3454 3032 .4220 3790 .4300 3790 .510 T 2 276 land-surveying. (Part VI. 3. From a rectangular field, whose length is 1560, and breadth 1000 links, it is required to part off a trapezoid, which shall contain 12a. 3r. 12p., by a line drawn from any of the angles to the longer opposite side. Ans. The area of the rectangle is 15a. 2r. 16p. j conse- quently, the area of the triangle is 2a. 3r. 4p., and its perpen- dicular 555 links. PROBLEM XIII. To part from a Triangle, upon the bam or longest side, any proposed Quantity of Land, by a Line drawn from either of the Angles at tfa I&fse, to the opposite Side. Rule. — Divide twice the proposed area by the base upon which it is to be parted off, and the quotient will be the per- pendicular. Or, if the proposed area be divided by half the base, the quo- tient will be the perpendicular. Note. — A Parallel Ruler may be used with advantage in this, and several of the following Problems. EXAMPLES. 1. From ABC representing a triangle, whose base A Bis 1200, and sides A C and B C, 1000 and 800 links respectively, part off 2a. 2r. 24p. by a line drawn from the angle B to the side A C. A D 2a. 2r. 24p. = 265000 square links. 2 12,00)53001)0 44l76 links, the perpendiculars D E. Section I.) land-surveying. 277 At A, erect the perpendicular A F, which make = 441.6 links ; then draw F E parallel to A B, and it will intersect the side A C, in the point to which the division-fence B E must he made. Or, by the plotting-scale, erect the perpendicular DE = 441.6 links, which will determine the point E. By the scale, you will find AE = 664 links ; measure, there- fore, in the field, 664 links from A to E ; stake out the line B E, and ABE will be the triangle required. • 2. From ABC representing a triangle, whose base A B is 1300, and sides B C and AC, 1100 and 900 links respectively, part off Ia. 3r. 36p. by a line drawn from the angle A to the side B C, so that the triangle A E C may contain the proposed quantity. From the three sides, b>y Note 4, Part IV., the area of the given triangle is found = 488076 square links. And,lA.3R. 36f. = 197500 square links. The difference = 290576, the area of the triangle ABE. 1300)581152(447 links, the perpendicular D E. 5200 .6115 5200 .9152 9100 ..52 By the mode described in the last example, determine the point E, which you will find at the distance of 658 links from the angle B ; measure this distance in the field, from B to E, and proceed as before. t3 278 land-surveying. (Part VI. 3. From a triangular field, whose sides are 1500, 1200, and 1000 links respectively, part off 3a. 2r. 16p. by a fence made from the greater angle at the base, to the opposite side. Ans. The perpendicular of the triangle required, is found to be 480 links ; and it rises upon the base, at the distance of 537 links from the less angle. PROBLEM XIV. To part from a Triangle, any proposed Quantity of Land, by a Line parallel to any one of its Sides. Rule. — The areas of similar triangles are to one another in the duplicate ratio of their homologous sides : hence, as the area of the triangle A B C is to the square of the side A C, or B C, so is the area of the triangle D E C to the square of the side DC or E C respectively. (See Theo. 13, Part I.) EXAMPLES. 1. Suppose the base A B = 1200, the side A C = 1000, and the side B C = 800 links; part off 1a. 2r. 16p. by the line D E parallel to A B. From the three sides, by Note 4, Part IV., we find the area of the triangle. ABC = 396863 square links. And, I a. 2r. 16p. = 160000 square links. The difference = 236863, the area of the triangle DEC. Section I.) land-surveying. 279 Then, as 3968G3 : 1000 X 1000 :: 236863 : 596838.20; and V 59683^20=772.5 links =DC; hence 1000 - 772.5=227.5 links=AD. Again, as 396863 : 800x800 :: 236863 : 381976.45; and v/ 38 1976*45 = 618 links = EC; then 800-618 = 182 links = B E. Measure, therefore, in the field, 227.5 links from A to D ; and from B to E measure 182 links ; stake out the line D E, and the work will be completed. 2. From a triangular field, whose sides are 1800, 1500, and 1200 links respectively, part off 3a. 2r. 32p. by a line parallel to the shortest side. Ans. The area of the given triangle is 892941 square links ; the area of the triangle made by the line of division is 522941 square links ; and one of its sides, from the angle opposite the line of division, to the commencement of that line, is 1147.9, and the other 1377.4 links. PROBLEM XV. To part from a Rectangle or Triangle, any proposed Quantity of Land, upon a Line on which there are Offsets, when the Area of those Offsets is to be considered as Part of the Portion to be parted off. Hule. — Find the area of the offsets, which subtract from the portion to be parted off, and then proceed with the remainder, as directed in the preceding problems. But, in a rectangle, when there are offsets on one, or both of the lines adjoining that upon which the given quantity is to be parted off, reject these offsets, and proceed as before directed. Then, having found the distance at which the line of division must be from that upon which the given quantity is to be parted off ; find the area of the offsets contained between those lines, which area divide by the latter line ; and the quotient will be the distance by which the former line must be approximated to the latter. x 4 280 LAND-SURVEYING. (Part VI. EXAMPLES. 1. From a rectangular field, whose dimensions are contained in the following notes, part off 2a. 3r. 32p. upon the chain-line A B, so that the offsets taken upon that line may be included. Begin DA - 560 L. off D. CD 1200 1000 L. off C. BC 560 L. off B. A B 1200 1000 900 60 600 SO 300 50 000 at A. Range E sq. links. 2a. 3r. 32p. = 295000 57000 the area of the offsets. 1 2,00 1 23807>0 the difference. 198.4~links = A E, or B F. Hence the irregular figure, A G B F E, contains 2a. 3r. 32p. Section I.) land-surveying. 281 2. From a rectangular field, whose dimensions are contained in the following notes, part off 2a. 2r. 8p. by a line parallel to the chain-line AB; so that the offsets taken upon this line, and also those upon the two adjoining lines, contained between the chain-line A B and the line of division, may be included. DA, 500 40 350 55 250 45 150 000 R. off D. CD 1000 R. off C. BC 500 40 400 60 250 45 150 000 R. off B. AB 1000 50 700 70 450 40 200 000 Begin at A. Range W. 282 land-surveying. (Part VI. sq. links. 2a. 2r. 8p. = 255000 _40250 the area of the offsets taken on A B. 1 ,00 01214 750 the difference. 214.750 links = BaorAm, which we may call 215 links. Now 215 - 150 = 65 = r a = c m ; and, by the scale, a e is found to measure 58, and m n, 53 links ; hence the area of the offset B a e + the area of the offset A m n = 13282, which divided by 1000, gives 13 links, the distance by which the line e n must be approximated to A B. Conse- quently, E F is the true line of division ; and the irregular figure A G B E F contains 2a. 2r. 8p. minus the two shaded offsets. PROBLEM XVI. To part from a Trapezium, or any irregular Polygon whatever, any proposed Quantity of Land, by a Line drawn parallel to any of the Sides, or by a Line drawn from any of the Angles, or from any assigned Point in one of the Sides, to any of the opposite Sides. Rule 1 . — Having laid down the whole figure, draw a guess- line in the direction required, parting off, as nearly as can be judged, the proposed quantity ; after which, by the scale, mea- sure, with the greatest accuracy, the guess-line, and also the quantity thus parted off. Then, if the guess-line or line of division be drawn from an angle, or from any assigned point in a side, divide the difference between the proposed quantity and the quantity parted off, by half the guess-line, and the quotient will be the perpendicular to be set off, on one side, or the other, of the guess-line, accord- ingly as the quantity parted off is more or less than the quantity proposed. To the end of this perpendicular, from the point assigned, draw a new line of division ; and it will part off the quantity required. 2. But if the guess -line be drawn parallel to any of the sides, divide the difference before mentioned, by the whole guess-line, Section 1.) land-surveying. 283 and the quotient will be the perpendicular to be set off from each end of the guess-line, on one side, or the other, as above. Note 1. — When from a trapezium, approaching very nearly to a rect- angle, it is required to part off any number of acres, &c. by a line parallel to one of its sides ; it may be done as directed in Prob. XI. ; and if there be offsets upon any of the lines, they must be treated as in the last Problem. 2. — In using guess-lines, it is not necessary that the learner should draw them so as to coincide in measure, with those of the examples which he is performing. It will be sufficient for him to proceed in a similar manner. EXAMPLES. 1. From a trapezium, whose dimensions are contained in the following notes, part off 2a. 2r. 24p. by a line parallel to the side A B. Return Begin BD 1249 1000 toB. 1112 1000 R. off A. D A 550 R. off D. CD 979 R. off C. BC 557 R. off B. AB 1114 1000 at A. Diag. Diag. Range W. 284 LAND-SURVEYING. (Part VI. Having laid down the figure, draw the guess-line m n parallel to A B ; and from n, let fall the perpendicular a n ; then, sup- pose m n = 1058 links, a n will be = 230, and A a = 1052 links; therefore, Ba = 1114 -1052 = 62 links, sq. links. Then, 1055x230 = 242650 the area of the trapezoid A a n m. And, 230x 31= 7130 the area of the triangle Ban. The sum - =249780 the area of the trapezium A Bnm. 2a. 2r. 24p.=265000 15220 the difference between the quan- tity proposed, and the quantity parted off by the guess-line ; which, divided by 1058, gives 14.4 links, to be set off perpen- dicularly from m and n toward D and C. Hence, E F is the true line of division ; and the trapezium A B E F contains 2a. 2r. 24p. As A is very nearly a right-angle, measure, in the field, 230 -f- 14.4 = 244.4 links, from A to F. Then, upon any part of the line A B, (toward B) as at e, erect the perpendicular e r, which make = 244.4 links ; stake out the line E r F, and the work will be completed. 2. From a trapezium, whose dimensions are contained in the following notes, part off, in a triangle, Ia. 3r. 12p. by a line drawn from the angle C to the side A B. Return Diag. Section I.) land-surveying. 285 Having laid down the figure, draw the guess-line C m, which suppose = 638 links. From m let fall the perpendicular m a, which will be = 417 links. sq. links. Then, 410 X 417 = 170070 the area of the triangle BCm. 1a. 3r. 12p. = 182500 11530 the difference between the quantity proposed, and the quantity parted off by the guess- line, which is divided by 319 (half the guess-line) gives 36 links, to be set off from m toward A. Hence, E C is the true line of division ; and the triangle B C E contains 1a. 3r. 12p. 286 land-surveying. (Part VI. Also, A E is found =731 links : measure, therefore, in the field, 731 links from A to E; stake out the line E C, and the work will be completed. Note. — The Rules given in this problem, for parting off land from irregu- lar figures, are generally adopted by Practical Surveyors ; because they may be applied to any irregular figure whatever. Land, however, may sometimes be parted off more directly : for instance, the foregoing exam- ple may be performed by the mode followed in Prob. XIII., i. e. if the given quantity, in square links, be divided by half the line B C, the quotient will be the perpendicular of the triangle BCE; then, at the distance of this perpendicular, a line drawn parallel to B C, will intersect the line A B in E, the point to which the division-fence must be made. 3. From a field, whose dimensions are contained in the fol- lowing notes, part off 3a. 2r. 1 6p. toward A D, by a fence made from the side A B to the side C D, so that the fence may com- mence at the distance of 600 links from A. Return BD 1050 to B. AC 1708 1000 L. off A. DA 790 L. off D. CD 1130 1000 l. off a BC 640 L. off B. Begin AB 1320 1000 at A. Diag. Diag. Range E. Section I.) land-surveying. 287 Having constructed the figure, set off 600 links from A to E, and draw the guess-line E m, which suppose — 702 links ; the diagonal A m will be = 1 132, the perpendicular Daz: 278, and the perpendicular E a = 318 links. Hence, the area of the trapezium A D m E, is found =: 337336 square links ; but the quantity proposed (360000 square links) exceeds the quantity- parted off by 22664 square links : this divided by 351 (half the guess-line) gives 64.5 links, to be set off from the line E m, per- pendicularly toward B C. Now, continue the line E m, and upon it erect the perpen- dicular nF = 64.5 links. The line F E will be the true line of division; and the trapezium ADFE contains 3a. 2r. 16p. If it had been required to set off the perpendicular on the other side of the line E m, you must still have erected it so that its end might have touched the line C D. Now, by the scale, D F is found = 553 links. Measure, there- fore, in the field, 600 links from A to E, and 553 from D to F ; stake out the line F E, and the work will be completed. Note. — The last example may also be performed by finding the area of the triangle A D E, and subtracting it from the given quantity ; then, if the remainder be divided by half the line D E, the quotient will be the per- pendicular of the triangle D E F. 288 LAND-SURVEYING. (Part VI % At the distance of this perpendicular, draw a line parallel toDE; and it will intersect the line C D in F, the point to which the division-fence must be made. 4. From an irregular field, whose dimensions are contained in the following notes, part off 2a. 3r. 20p. toward the line A E, by a fence made from the angle D to the side A B. EB 1398 1000 R. off E. CE 1240 1000 500 R. off C. AC 1260 1000 R. off A. E A 400 80 200 000 R. offE. DE 600 25 450 35 300 20 150 000 R. off D. CD 740 R. off C. BC 550 R. offB. Diag. Diag. m, proof-line, goes to D, and measures 324. Diag. Section I.) land-surveying 289 AB 1250 35 1000 50 800 60 600 50 400 30 200 000 Begin at A. Range W. H J 1 the area of the offsets taken on the different lines. Having laid down the figure, draw the guess-line D n, which suppose = 766 links ; then the diagonal A D will he = 824, the perpendicular Ea = 278, and the perpendicular r a = 372 links ; r e also will be = 228, and r n = 52 links. sq. links. 267800 the area of the trapezium ArDE, 12000) DE(,? 16000 EA " 123 48 j A r { 308148 the area of the irregular figure A n D E. 2a. 3r. 20p. z= 287500 20648 the difference between the quantity proposed, and the quantity parted off by the guess-line, which divided by 383 (half the guess-line) gives 54 links, to be set off from n toward A. Hence, D F is the true line of division; and the irregular figure A F D E contains 2a. 3r. 2 Op. u 290 land-surveying. (Part VI. Now, by the scale, A c is found = 377 links. Measure, therefore, in the field, 377 links from A to c; stake out the line D c F, and the work will be completed. Note 1. — If the area of the irregular figure A D E, be subtracted from the given quantity, and the remainder divided by half the bine A D ; the quotient will be the perpendicular of the triangle A D F ; the side A B being nearly straight from A to F, Now, at the distance of this perpendicular, draw a line parallel toAD ; and it will intersect the side A B in F, the point to which the division- fence must be made. 2. — It is not absolutely necessary to survey and plan a whole field, in order to part a portion from it, as the guess-line and portion parted off may be measured in the field ; but, in my opinion, the former, in general, is a more eligible method than the latter ; as you have a better opportunity of proving vour work. SECTION II. THE METHOD OF DIVIDING A PIECE OF LAND AMONG SUNDRY CLAIMANTS, IN THE PROPORTION OF THEIR RESPECTIVE CLAIMS, OR A COMMON, §c. OF VARIABLE VALUE, AMONG ANY NUMBER OF PROPRIETORS, IN THE PROPORTION OF THEIR RESPECTIVE INTERESTS. "When land becomes the property of coheirs, copartners, joint purchasers, &c. it is generally divided into such shares, as the coparties are entitled to ; and this cannot possibly be accurately effected without the assistance^ of some person, who is not only well acquainted with surveying, but also with the method of dividing land. In this process an error is evidently much more material than one committed in surveying. — When a field, &c. is to be di- vided into any number of parts, equal or unequal, it is neces- sary, first, to ascertain its dimensions ; and next to inquire of the parties concerned, in what part of the property in question, they wish their respective shares to lie. Section II.) land-surveying. 291 PROBLEM I. To divide a Square or Rectangle, either equally or unequally, among any Number of Persons, by Lines parallel to one of its Sides. Rule. — If the parts, into which the field is required to he divided, he equal, divide the side which will he cut hy the di- vision-fences, hy the numher of those parts, and the quotient will be the distance at which the division-fences must be placed from each other, and from the outsides to which they are pa- rallel. But, if the parts be unequal, you must then part off each person's share as directed in Sect. I. Prob. XI. EXAMPLES. 1 . Divide the square A B C D containing 5a. 2r. 20p. into three equal parts, by fences parallel to the side A B. C B Here 5a. 2r. 20p. =562500 square links; and *J 562500 = 750 links, the side of the square. This, divided by 3, the num- ber of parts, gives 250 links, the distance at which the first di- vision-fence must be placed from A B, &c. From A and B, therefore, set off 250 links to E and F; join E F, and the rect- angle A B F E, will be one of the parts required. u 2 292 land-surveying. (Part VI. Again, from E and F set off 250 links to G and H ; join G H, and the rectangles E F G H, and G H C D will be the two other parts required. 2. Divide ABCD representing a rectangular field, whose length is 1500, and breadth 800 links, among three men, A, B, and C, by fences parallel to the side A D, so that A may have 3a. B 4a. and C the remainder. D F H C EG B Here 3a. = 300000 square links, which divided by 800, gives 3? 5 links = A E or D F : hence the rectangle A E F D contains A's share. Again, 4a. = 400000 square links, which divided by 800, gives 500 links — E G or F H : hence the rectangle E G H F contains B's share. Xow, the rectangle A B C D, is found to contain 12a. ; con- sequently, the rectangle GBCH containing 5a. is C's share. Note. — This and similar examples may also be performed by the following proportion : As the area of the whole rectangle is to the whole base, or side cut by the division-fences, so is each person's share of the rectangle to his share of the base. PROBLEM II. To divide a triangular Field, either equally or unequally, among any Number of Persons, by Fences made from any of its A nales to the opposite > Rule. — If the parts, into which the field is required to be Section II) land-surveying. 293 divided, be equal, divide the base, or side to which the division- fences are to be made, by the number of those parts, and the quotient will be each persons share of the base. But, if the parts be unequal, say, as the area of the whole triangle is to the whole base, so is each person's share of the triangle to his share of the base. (See Simpson's Geom. IV. 7. ; Reynard's Geom. V. 1. ; and Euclid VI. L) EXAMPLES. 1. Divide ABC, representing a triangular field, whose sides A B, A C, and B C are 1500, 1200, and 1000 links respectively, into three equal parts, by fences made from the angle C to the side A B. Here AB= 1500 links, which divided by 3 (the number of parts) gives 500 links, each person's share of the base. From A, therefore, set off 500 links to D, and from D 500 links to E ; draw the lines C D and C E, to represent the division- fences ; and the triangles A D C, D E C, and E B C, are the three equal parts required. 2. Divide ABC, representing a triangular field, whose sides A B, A C, and B C are 1450, 1150, and 960 links respectively, into three equal parts, by fences made from the angle A to the side B C. u 3 "d-subvey: ri VL parte) gh-es 920 links, eack person's dare tf Ike side B C. From B, tneref are, set off 320 finla - I . and fiwD set off Dhide A B C, representing a triangular field, A 1 A C. iii I I :: T .. Section II.) LAND-SURVEYING . 295 Having the three sides of the triangle, we find its area = 1272792.2 square links; then, as 1272792.2 : A B = 2200 :: A's share = 300000 square links : 518.5 links, A's share of the base. Again, as 1272792.2 : 2200 :: 400000 : 691.3 links, B's share of the base. The remainder of the base, which is 990.2 links, belongs to C ; and, deducting 7a., the sum of A and B's shares, from the area of the whole triangle, we find remaining for C's share 572792.2 square links = 5a. 2r. 36p. From A, therefore, set off 518.5 links to D, and from D set of 691.3 links to E ; and the lines CD and C E will be the lines of division required. PROBLEM III. To divide a triangular Fields either equally or unequally, among any Number of Persons, by Fences proceeding from any as- signed Point in one of its Sides. Rule. — Divide the base or side of the triangle from which the division-fences are to be run, as directed in the last problem. From the assigned point, draw a line to the opposite angle ; and parallel to this line, draw a line from each point of division on the base, until it intersects the opposite side. From these points of intersection draw lines to the point assigned ; and they will be the lines of division required. (See Dr. Hutton's Course of Mathematics, Vol. III. Chap. 7, Prob. 2.) EXAMPLES. 1. Divide ABC, representing a triangular field, whose sides A B, B C, and A C are 1500, 1150, and 950 links respectively, equally among three persons, by fences proceeding from a gate, 700 links distant from A on the base, leading into a lane, through which alone a road can be had to the field. u 4 296 LANL-SURVEYIV - Pari VI he question AB = 1500 links, divided by 3, grres 500 I •'-'-'?. -:.\'l '::■::.- ~_:f :: :~_t i-z F::z A. :!:::::::. ^: z~ ■:'.'. ~ >> :: I iii f::n I —: :z ":"_.- z: :; E. TlrZ fr.zi Tie _ -. !t '. :lr Li^r G C: i^E ririllfl :•:■ ::. Ike Hues D H and E F. E: ::~ E -id F draw the lines H G cm x G\ n. . "_r~ ""'. t zjLr :t~:t- :: :^~.«: z :•: N ~. j b juilar triangles, (Theo. 11. Part L) as A G : A C : AD:AH = :^.:Eis:-:. E 1:B( 3E:BF = Tlf "'"Vs. Measure, therefore, in the field, 6T8.5 links from A to H. and 71S.7 from B to F : stake ont the tines H G .. 7 >. z -jl ■ \: ". ' . : mler, the fines A H and B F may he l _':— if A B C. ~i^~m--zz.z i :nizrEir ~-\i. ~i:fr iiif* A B. A C. ni B C are 1400, 1200, and 1000 Knks respeciiTelT. among dree persons. A _ md C. by fences proceeding from a pond which is at the distance of 600 links from A on the base ; so that each person partaking of the pond, A may have 1 acre, 2 roods, and 10 perches ; B I acxe, 3 roods, and 20 perches; and C the remainder. Section II) land-surveying, 297 Having the three sides of the triangle, we find its area = 587877.5 square links. Then, as 587877.5 : A B = 1400 :: A's share == 156250 square links : 372 links, his share of the base. Again, as 587877.5 : 1400 :: 187500 : 446.5 links, B's share of the base. From A, therefore, set off 372 links to D, and from D set off 446.5 to E. Then from the pond P draw the line P C, and parallel to it, the line D G and E F. From G and F draw the lines G P and F P ; and the triangle A P G will contain A's share ; the trapezium P G C F, B's share ; and the triangle B P F, C's share = 244127.5 square links = 2 acres, 1 rood, and 30 perches. By similar triangles, we find A G — 744, and B F = 726.8 links : proceed, therefore, in the field, as directed in the last example. PROBLEM IV. To divide a triangular Field, either equally or unequally, among any Number of Persons, by Fences made parallel to one of its Sides. Rule.— By the rule given in Sect. I. Prob. 14, part off the first person's share ; proceed with the remainder of the triangle, :*5 i rEYB P • : r/. A B, A C. and B C are 1500, 1300, aai 1000 fiats itay ttt liit s lj ; tt- _■ _:_ l_~ iri "•_- ?. _--- : . . ~_ ; 5 _■!_•_- - '.-- Vi : : r .:- ::':lr -- — A I G ~: = :::, * iriis = a E Arn^ as 59S11&4 : 1200 X ISO* : 960000; and n ~ = Vr ? ^ZlVf - A G lz ■• T* iJ ~r = - znVs - A I and ^4800OM>2 = 6&2.S Knks = AF. Hasce, the liim^V ABC is divided ioto tferee equal par Section II.) land-surveying. 299 2. Divide ABC, representing a triangular field, whose sides A B, B C, and A C are 2200, 1700, and 1500 links respectively, among three persons, A, B, and C, by fences made parallel to the base A B, so that A may have 3a. B 4a. and C the re- mainder. The area of the triangle A B C is found = 1272792.2 square links, from which taking 300000 square links, (= A's share) we leave 972792.2 square links, the area of the triangle D G C From this taking 400000 square links, (= B's share,) we leave 572792.2 square links, the area of the triangle EFC = 5a. 2b 36p. = C's share. Then, as 1272792.2 : 1700 x 1700 :: 972792.2 : 2208820.46 and ^2208820^46 = 1486.2 links = CG. And, as 1272792.2 : 1500 X 1500 :: 972792.2 : 1719669.91 and ^1719669^91 = 1311.3 links = CD. Again, as 972792.2 : 1486.2 x 1486.2 : : 572792.2 : 1300563.40 and J 1300563.40 = 1140.4 links = CF. And, as 972792.2 : 1311.3 x 1311.3 :: 572792.2 : 1012467.60 and ,y 1012467.60 = 1006.2 links = CE. Hence, the triangle A B C is divided into three parts, as required. 300 LAND-SURVEYING. (Part VI. PROBLEM V. To divide a Trapezium, or an irregular Polygon, equally or un- iffjr, among any number of P .ces made in a turn. Rrc.E. — By the Rules given in Sect. I. Prob. 16, part off the first person's share ; proceed with the remainder of the figure and the second persons share in the same manner ; and thus continue, till the whole figure is divided. EXAMPLES. 1. Divide a trapezium, whose dimensions are continued in the following notes, into three equal parts, by fences made from the side A B to the side C D. BD 1.542 Return to B, A C 1848 U R. off A. DA 91.5 R. offD. C D 1347 1000 R. off C B C 885 R. off B. Begin at AB 1547 1000 A. Range Diag. Diag. W. Section II) land-surveying, 301 mF xiH jy ,/""] .■••, i \ \ 1 &i W \ I- - \ ' 3 \ B G The area of the triangle A B C, is found = 681942, and the area of the triangle CDA = 585949 square links ; consequently, the area of the trapezium ABCD = 1267891 square links, which divided by 3, gives 422630 square links, for each person's share. Now, draw the guess-line E m, which suppose = 880 links ; then the diagonal E C will be found = 1028, the perpendicular Ba = 387, and the perpendicular m a = 424 links : hence, the area of the trapezium B C m E, is found s= 416854 square links^ which is too little by 5776 square links. This divided by 440 (half the guess-line) gives 13 links, to be set off from m toward D ; consequently, E F is the true line of division. Again, draw the guess-line G n, which suppose = 878 links ; then will the diagonal G F = 1017, the perpendicular Ear 430, and the perpendicular n a — 385 : hence, the area of the trapezium E F n G, is found = 414427 square links, which is too little by 3203 square links. This divided by 439 (half the guess-line) gives 19 links, to be set oft' from n toward D ; con- sequently, G H is the true line of division ; and the trapezium A B C D is divided into three equal parts, as required. Now, by the scale, we find BE=: 450, EG=500,CF = 508, and F H = 468 links, which distances must be measured in the field, in order to determine the situations of the division-fences. B02 LAXD-SUKVEYIXG, (Part VI. Note. — If we subtract the area of the triangle B C E, from the quantity to which each person is entitled, and divide the remainder by half the line C E, the quotient will be the perpendicular of the triangle C E F. By drawing a line parallel to C E, at the distance of this perpendicular, the point F may be determined. In a similar manner, may be parted off the trapezium E F H G. 2. Divide a field, -whose dimensions are contained in the fol- lowing notes, among three persons, A, B, and C, so that each partaking of a pond at P, A may have 3a. B 4a. and C the remainder. BD 1447 Diag. 1000 R. offB. EB 1603 Diag. 1000 ft. off E. CE 1300 Diag. 1000 R. off C, AC 1320 Diag. 1000 700 Pond. R. off A. E A 750 R. offE. DE 650 R, offD. CD 850 R. off C. BC 800 R. offB. — Section II.) land surveying. 303 Begin AB 1200 1000 at A. Range W. From the pond P, draw the line P D, and also the gness-line P m, which suppose = 558 links ; then will the diagonal D m he = 1025, the perpendicular Par: 400, and C a = 195 links : hence, the area of the trapezium P m C D is found = 304937 square links, which exceeds A's share by 4937 square links. This divided by 279 (half the guess-line) gives 17.7 links, to be set off from m toward C ; consequently, P F is the true line of division, and the trapezium P F C D contains A's share. Again, draw the guess-line P n, which suppose. = 696 links ; then, the diagonal P E will be = 848, the perpendicular n a = 247, and D a = 552 links : hence, the area of the trapezium P n E D, is found = 338776 square links, which is less than B's share, by 61224 square links. This divided by 348 (half the guess-line) gives 176 links, to be set off from the line P n per- 304 LAND-SUB TRYING. PmWt VI. pendicularlr toward A iie true line of nd the trapezium P G E D con- hare. irregular polygon A B F P G c :-:_:_- B's V % 128 2569078 25 2 30.5 C's * ^ 5659999 56 2 15.8 proof. Each person's share thus determined, the common may easily be divided by the methods already described, 2. Three gentlemen, A, B, and C, have each an estate consist- ting of 300a. ; divide among them, according to the values of their estates, 75a. 3r. 32p. ; A's estate being valued at 25s., B's at 32s., and C's at 40s. per acre, per annum. (25) ( 7500 the value of A's estate. Here 300 X < 32 V = ^ 9600 ditto of B's. ( 40 ) [ 1 2000 ditto of C's. 29100 sum. And 75a. 3r. 32p. = 7595000 square links. Then, s. sq. links. a. r. p. s. sq. links. ( 7500 ) ( 1957474 ) ( 19 2 12 ) A's ( <- a829100:7595000::-< 9600 V : <( 2505567 V = <^ 25 9VB's^S ( 12000 j ( 3131958 ) ( 31 111 j C's {-% 7594999 75 3 32 proof. 306 land-surveying. (Pari VI Note. — It sometimes happens that two, three, or more persons join in taking a common pasture, and agree to pay in proportion to the number of cattle with which each person depastures. In such cases, when the whole of the cattle graze an equal time, you must make use of the rule of Single Fellowship, by saying, as the whole of the cattle, is to the rent of the whole parture,so each person's cattle to his share of the rent. But when the cattle graze an unequal time, you must then have recourse to the rule of Double Fellowship, \ ; f the products of each person's cattle and time, is to the whole ren- :li person's product to his share of the rent. PROBLEM VII. To divide a Gammon, . if :irioble Value, among any numher of Propr. :\e Pro p or ti on to their respective I In a work of this kind, the quantity of every different quality is required, not only of the land to be divided, but also of each proprietor s estate ; consequently, the Surveyor, accompanied by the persons appointed to value, generally called 4i Commis- sioners." must examine each persons estate, and also the Com- mon, previously to the survey being taken. In doing this, they must stake out lines between the different qualities of the soil ; and. in surveying, these lines (called by Surveyors, " Quality-lines") must be considered as boundaries, and represented in the field-book, and upon the plan, by small By way of distinction, there ought to be two stakes put down at each angle formed, by the quality-lines : and also marks cut in the ground, pointing in the direction of these lines, so that if the stakes should be pulled up, thesr marts maj serve as directors. When the survey is finished, and laid down, every different quality. re] resented upon the plan, must be sot num- bered, 1, 2, -3, Sec The Sti rr eyor must then require the Com- missioners to put the different valuations upon the land ; and, in doing this, he must accompany them with the plan, in order that both he and they may know the ground corresponding with each number. Surveyors generally asc letters to repre- sent the different values of land : Section II) land-surveying. 307 Thus, a, may denote 1 shilling. b 2 c 8 d 4 e 5 f 6 g 7 h 8 i 9 o 10 s 20 and x 30 shillings. By putting three of these letters together, and adding their separate values, the value per acre per annum, may he set down as high as sixty shillings ; and, hy adding more letters, it may be carried to any height required. By the use of these letters the confusion, arising from a multiplicity of figures, is avoided. The land being valued, you must then proceed to find the quantity contained under each number on the plan ; and also its value. In doing this, it is unnecessary to bring the decimals into roods and perches, or to retain more of them than the three next the acres ; as the operation is thus considerably simplified. If the fourth figure in the decimals be 5, or greater, add 1 to the third : that is, if the content be 3.54585, set down 3.54>6. When the content does not amount to an acre, and the number of decimals is under five, add as many ciphers to the left, as will complete that number : that is, if the content be .8626, set down .086. Then, multiply the acres and decimals, contained in each number, by the valuation per acre, put upon the respective num- bers, and the product will be the value in shillings and decimals. MISCELLANEOUS OBSERVATIONS ON VALUING LAND. 1 . Proprietors ought to be very judicious in appointing com- missioners, to value for an inclosure. They should not only be well acquainted with the quality of the soil ; but should also be x2 308 LAND-SURVEYING. (Part VI. able to judge how far every part of the Common is capable of being improved, after it has been inclosed, or they will not be able to put a just valuation upon it. 2. In valuing, not only the quality of the land, but also its situation, must be attended to ; for, if one part of the land to be divided, lies in a valley, (not subject to be flooded.) near a pro- prietor's messuage, and another part upon a hill, at the distance of two or three miles : it is evident, allowing the land to be all of the same quality, that the former situation is much more de- sirable than the latter : because it is nearer the house-stead, and consequently better situated for receiving agricultural improve- ments. 3. The manner in which the climate and seasons may operate upon the produce of the ground, in consequence of its local situation, should always be taken into consideration. If one field lies towards the south, and another towards the north, and both be of the same quality ; the field that faces the south is more valuable than the other, as the crops on the former will not only be brought to a greater degree of perfection by the benign influence of the sum, but will also be ready for the sithe or sickle much sooner ; and consequently may be brought to an earlier, and frequently to a better market. 4. In valuing a Common for an inclosure, the improvements that may be made by fencing, draining, and cultivation, should never be overlooked. If one person should have an allotment awarded to him in the best part of the Common, but where no improvement can be made ; and another person's allotment, of equal value, be laid out in the worst part of the Common, but where much improvement may easily be made by cultivation, it is manifest that the latter allotment will, in a few years, be more valuable than the former. Besides, as quantity is always given to compensate for any deficiency in quality, the proprietor who has his common-right laid out in the worst part of the ground, will not only receive more land than the other : but will soon be able, by a trifling expense in cultivation, to make it worth more per acre. 5. In valuing either old inclosed lands or commons, the dis- tance of the ground from good springs of water should be re- Section II.) land-surveying. 309 garded. In many parts of England, and particularly upon the Wolds in Yorkshire, the occupiers of land frequently suffer great inconvenience in driving their cattle a considerable dis- tance to watering -places ; and the cattle themselves are some- times much injured, in droughty summers, for -want of a re- gular supply of wholesome water. Hence a farm that is well watered is worth more to rent, than another farm of equal quantity and quality, but destitute of water. 0. The distance of farms, common-rights, &c. from market- towns is also of considerable importance ; because land always increases in value as it approaches the vicinity of large towns. Besides, as tillage abounds in such places, the means of im- provement may be obtained at a much less expense, for ground situated in the environs of towns, than for that which lies at the distance of several miles. It may also be remarked, that the occupiers of the former can always find a ready market for the produce of their land, while the occupiers of the latter are under the necessity of being at a considerable expense in trans- porting their goods to market; and in procuring the various articles that are indispensably necessary for the use of their families. Note. — Here It may not be improper to explain to the young Surveyor, a few of those terms by which commons and uninclosed lands are usually de. nominated. Appellations given to Commons. 1 . Moors are large, uncultivated tracts of ground, generally overgrown with furze, broom, heath, and other small shrubs, as Rumbles-moor in Yorkshire, and Blackstone-edge, partly in Yorkshire, and partly in Lancashire. 2. A Fell is a large, open portion of land, generally less overrun with shrubs than a moor, as Gateshead Fell in the county of Durham. 3. A Heath is any open ground, abounding with the plant called heath, or any other shrubs, as Hounslow Heath in Mid- dlesex. 4. "Wolds are high, open grounds, as the Wolds in York- shire and Lincolnshire. x3 310 land-surveying. (Part VI. 5. Downs are fine, open, pasture grounds, as the Downs in Kent, Sussex, and Surrey. 6. Fens are low, wet, tracts of ground, as the Fens in Lin- colnshire. 7. Marshes are low, swampy grounds ; and when adjoining the sea, or the sides of rivers, they are mostly excellent pastures ; as the Marshes in the counties of Durham and York, contiguous to the river Tees : those in the counties of York and Lincoln, contiguous to the river Humber ; and the rich marsh of Romney, in the county of Kent, adjoining the straits of Dover. 8. Mosses are black, turfy, boggy moors, as Ashton Moss, and many others in Lancashire. 9. Forests are wild, uncultivated tracts of ground, generally abounding with trees, as Sherwood Forest, in Nottinghamshire, and the New Forest, and that of East Bere, in Hampshire. 10. Ings are large, open meadows, generally situated on low, level grounds. Fields and tracts of land known by the local name of u The Ings," abound in almost every county of Eng- land. 11. Holmes are hilly, fenny, or level grounds, adjoining to, or encompassed by rivulets or brooks. Many rich and fertile pasture grounds, in this country, are known under the local appellation of i; The Holmes." 12. Ope>*-fields are uninclosed lands, generally divided into furlongs, by mereforms ; and occupied by different tenants. Some furlongs are usually in corn, some in meadow, and others in pasture ; and the cattle and sheep which depasture, are tended by shepherds. Large tracts of land upon the Wolds, in Y'orkshire, are cultivated in this manner. 13. A Furlong of land is used, in some old books, to express the eighth part of an acre ; hence 20 perches or 605 square yards, make a furlong. The term is also used to denote anv number of lands ad- Section II.) LAND-SURVEYING. 311 joining each other, in open fields, and running in the same di- rection from one head-land to another; and known by some particular name, in order to distinguish the different parts of the field from each other. 14. Mereforms are narrow pieces of swarth, dividing lands, or furlongs, in open-fields, from each other. 15. An Ox-gang, or Ax-gate of land is usually taken for 15 acres ; being as much land as it is supposed one ox can plough in a year. In Scotland, 13 acres are denominated an Ox-gang ; and in some places, the term is used to denote as much land as will summer one ox. This word is corruptly called Osken in Lincolnshire, and some other counties. 16. A Hide of land, sometimes met with in old books, was such a quantity as might be cultivated, in the compass of a year, with one plough ; having meadow and pasture sufficient to feed the cattle belonging thereto. The term was also frequently used to denote as much land as would maintain a family. Some writers make the hide to contain 60, some 80, some 100, and others 120 acres. Sir William Dugdale, the antiquarian, says that a Barony, in former ages, was a certain portion of land held immediately of the king, and contained not less than 40 hides, or 3840 acres ; a statement that gives 96 acres to a hide. Directions for setting out new Roads, Sand- Pits, Quarries, Water- ing-Places, §c. fyc. ; and for dividing Commons and Waste Lands into Allotments. 1. Before commons and waste lands are divided and allotted, new roads must be set out upon them, in the most convenient and advantageous manner. They should, whenever it is prac- ticable, be set out in such directions as to form right-angles, or as nearly right-angles as possible, as the places where they meet or x4 312 land-surveying. (Part VI. intersect each other, or come in contact with ancient highways. They should not be less than thirty feet in breadth; and set out in right-lines ; because straight roads not only look better than crooked ones, but also occupy less ground. 2. All old roads leading over commons or waste lands about to be inclosed, may be stopped or diverted, at the discretion of the commissioners ; and such old roads must be surveyed and allotted as part of the commons or waste lands. 3. Certain portions of commons should always be set out for sand or gravel -pits, and for quarries ; if the commons contain either sand, gravel, or stone. The portions of ground thus set out are considered as public property, from which every person who receives a common-right, may take materials for building houses, making fences, and repairing roads. 4. If there be any good springs of water on commons, they must either be left uninclosed, for public watering-places ; or the water must be conveyed to more convenient situations, by means of drains or channels ; and troughs or reservoirs made for its reception. 5. In some places the lord of the manor claims one-twelfth, in some one sixteenth, in others only one-twentieth, of all commons and waste lands ; whatever be his claim, however, it must be set out before any other allotment, after its value has been ascer- tained from the quantity and value of the whole common. Be- sides this allotment, the lord of the manor, will, of course, be entitled to his proportional share of the remainder of the waste lands, in the same manner as any other proprietor. 6. When it .can be done, it is very desirable to ascertain the value of all the tythes, and to set out, for the proprietor of the tythes, an allotment of equivalent value ; thus will the whole place become tythe-free ; and the occupiers of lands be exempt from what they generally deem an unpleasant tax upon their industry ; but which is, nevertheless, as justly due to the pro- prietor of the tythes, as the rent of a farm is to the landlord. 7. If the clerk's salary arise from the lands, Avhich is the case Section II.) land-surveying. 318 in some places, a common-right may also be set out in lieu of it ; and if another can be obtained as a small endowment for a town's school, the inhabitants will not have cause to repent, if they be judicious in the choice of a master. 8. After the roads, sand-pits, quarries, watering-places, mano- rial right, &c. &c. have been set out, the remainder of the com- mon or waste lands must be equitably divided, (quantity, qua- lity, and situation of place being regarded,) among the owners and proprietors of messuages, cottages, lands, tenements, and hereditaments situated in the township or place where the in- closure is to be made and executed. Note 1 . — The first step towards inclosing wet, marshy grounds, is to have them well drained ; for without this be done, every attempt at improvement will be vain. Mr. Elkington's method of draining land, drawn up by Mr. Johnstone, (price twelve shillings in boards,) and published under the direction of the Board of Agriculture, has eclipsed every other work on this subject. See my Treatise on Practical Mensuration, Part V I ., for a particular account of Mr. Elkington's manner of draining ; for the great agricultural improve- ments lately made in the counties of York and Lincoln, by means of exten- sive drainages ; and for the method of measuring hay-stacks, drains, canals, marl-pits, ponds, mill-dams, embankments, cpuarries, and coal-heaps. 2. — As Land-Surveyors are frequently employed to measure and value standing-timber, in gentlemen's estates, I beg leave to refer them to my Mensuration, Part IV., where I hope they will find these subjects satisfac- torily treated. The work also contains the Mensuration of Superficies and Solids in general ; the method of measuring Artificers' Works ; Conic Sections and their Solids ; and the most useful Problems in Gauging. To determine the Value of each Proprietors Allotment, or claim upon the Common. In doing this, the value only can be used ; for, if we make use of the quantity, in allotting land of different qualities, the proprietor who has his allotment in land of the best quality, will obviously receive more than his just right ; while those, whose allotments fall in land of inferior quality, lose part of their pro- s 14 LAND-SURVEYING. (Part VI. perty. Hence, you must say, as the value of the whole estates, is to the value of the Common, or land to be divided, so is the value of each person's estate to the value of his allotment, or claim upon the Common. To set off\ upon the Plan, each Proprietor's Allotment, or Share of the Common. When you find that a proprietor's allotment falls in that part of the Common, which is of uniform quality, you may easily determine the quantity to which he is entitled, by saying, as the value put upon the number in which his allotment falls, is to 1 acre, so is the value of his claim, to the quantity of land which his allotment must contain. Then set off the allotment upon the plan, by some of the methods already described. But it commonly happens that a proprietor's allotment falls in different numbers. In such a case, you must draw a guess-line, or lines, and measure separately, by the scale, the pieces cut off belonging to the different numbers : then multiply the different quantities by their respective values, and if the sum of the pro- duets be equal to the value of the claim in question, the guess- line or lines, are right ; if not, they must be altered, until they part off the exact portion. After each proprietor's allotment is set off upon the plan, if you find the quantity and value of all the allotments equal to the quantity and value of the whole Common, the division is right. EXAMPLE. Lay down a Plan from the engraven Field-Book, belonging to Plate XII. ; and divide the Common among the three Pro- prietors, A, B, and C, according to the different qualities of their Estates, and of the Common. Section II.) land-surveying 315 A Book of Quantities, Qualities, Values, #e. Belonging to Plate XII. No. on the Plan. A's Estate. Quantity. ~V7DecT Qua- lity. Value. Shil. Dec. 1 2 3 Total 7.565 7.609 7.301 x s X xh 378.250 304.360 277.438 22.475 960.048 4 5 6 "Total B's Estate. 7.858 7.892 8.223 X c X o 290.746 260.436 328.920 ~~ 8807f02~" 23.973 Tf 1 8 9 Total C's Estate. 7.819 7.078 7.481 xh X so X s 297.122 424.680 374.050 22.378 1095.852 10 11 12 13 Total The value whole Esl ofthe ates. 2936.002 The Common. 10.061 4.680 4.446 5.995 "25.182 X xd xh sh 301.830 159.120 168.948 167.860 797.758 Note 1.— The learner should lay down the plan, from the field-notes, by a scale of two chains to an inch ; and find the areas of all the fields from his own dimensions, as directed in Part V. The diagonals and perpendiculars from which the above areas were found, are not given, as this would have rendered the work too easy to exercise the genius of the student ; he may, however, retain his own dimensions, and enter them in " a Book of Dimen- sions, Castings, Quantities, Qualities, and Values, adapted to Plate XII." (See the Bool s of Dimensions and Castings, in Part V., belonging to Plates VIII. and X.) 316 land-surveying. (Part VI. 2. — If the learner should not be able to find such dimensions as will make his areas agree exactly with those given in the foregoing book of quantities, it will be a matter of no consequence, provided the difference be not too considerable ; and as any difference in the areas will also produce a dif- ference in the values, all the numbers in his book will differ from the given numbers. This, however, will tend much to his improvement, as he will be under the necessity of making all his own calculations, both in finding the areas and- values of the different fields, and also in dividing the Common, and proving the Division. The Operation of finding the Value of each Proprietors Share of the Common ; and Directions for setting out the Allotments in the Field. s s s. s. ( 960.048 ) ( 260.860 ) A's ) As 2936 : 797.758 :: - 880.102 V : \ 239.137 >B's value. 1095.852 j ( 297.761 ) C's j 797.758 proof. As the whole of A's allotment will fall in No 10, we say, as 30 : 1 :: 260.860 : 8.695 acres, the quantity of land which A's allotment must contain. From 10.061 take 8.695, and we have 1.366, the remainder of No. 10, in value = 40.980, which will form part of B's allot- ment. Then, from 239.137, take 40.980, and there remains 198.157; consequently, B must have land equivalent to this value, from Nos. 11 and 12. The remainder of these Nos. and the whole of No. 13, will be C's allotment, which you must measure, &c. as a proof. In setting off the allotments upon the plan, we find that one end of the division-fence between the allotments of A and B, falls at the distance of 827 links from + 8 toAvard -J- 1 ; and the other end at the same distance from -f- 7 toward -j- 2. We find, likewise, that one end of the division-fence between the allotments of B and C, falls at the distance of 1465 links from -f 8 toward -j- 1 ; and the other end at the distance of 1478 Mrf/rXi jL ^ /^ ■ — / ,v 1 3?J 5 JO 4 .r r 6 11 12 ■>.') .^v/ \ .••/ ' 7 >— 8 9 ._/•./ 13 j, - 5 fe J /, //, / / //,////■ i //' •/// Z///70. Section II.) LAND-SURVEYING. 317 links from + 7 toward -f 2. Measure, therefore, these dis- tances in the field, stake out the division-fences, and the work will be completed. Note. — The fences of old inclosures are generally very crooked ; but the fences of new inclosures are always set out in straight lines, when it is prac- ticable. THE PROOF OF THE DIVISION. No. on the Plan. A's Allotment. Quantity. A. Dec. Quantity. A. R. P. Qua- lity. Value. Shil. Dec. Part of 10 8.695 8 2 31 1 X i 260.850 Part of 10 11 B's Allotment. 1.366 2.580 2.910 X X d TT h 40.980 87.720 110.580 1° I ■"■ " Total 6.856 I 6 3 16 | 239.280 Part of 11 12 C's Allotment. 2.100 1.536 5.995 X d X h s h 71.400 58.368 167.860 Whole of 13 Total 9.631 9 2 22 297.628 1 Sum total 25.182 25 29 797.758 Note 1. — In dividing land by this irregular method, (the only one practica- ble, when an allotment falls in land of different qualities,) it is almost impos- sible to get the quantity and value of all the allotments to agree exactly with the quantity and value of the whole Common ; but when the difference is trifling, we may rely upon the accuracy of the division. 2. — All the fences of the estate in Plate XII. are made straight, in order to avoid trouble in casting the contents ; and as the allotments are small, neither roads, sand-pits, quarries, nor watering-places, are set out ; but as copious directions have been given on these and other subjects, the Author is persuaded that if these directions be well understood, the learner will find no difficulty in performing any operation that may be wanted in conducting an extensive inclosure, so far as appertains to the business of a Land-Sur- veyor. ais LAND-SURVEYING. (Part VI. 9rt* of parliament FOR INCLOSING COMMONS AND WASTE LANDS. All commons and waste lands are inclosed under Special Acts of Parlia- ment obtained for that purpose ; and the Commissioners and Surveyors are always appointed by name, in such Acts. The preamble of a Special Act, sets forth the manor, township, parish, and county in which the commons or waste lands are situated ; specifies the names of such commons and waste lands, and the quantity of ground they contain, either by survey or estimation ; notices the little profit and ad- vantage they afford in their present state ; and points out the improve- ments they are capable of receiving, if they be divided, allotted, and inclosed. In order to diminish the expense attending the passing of Special Acts of Inclosure, for particular places, a General Act was passed in the year one thousand eight hundred and one, consolidating and containing certain pro- visions usually inserted in Special Acts of Inclosure. This Aet is made the foundation of all Special Acts, and contains the same provisions, with the exception of particular clauses that are always inserted in Special Acts of Inclosure, relating to, and making provision for, local circumstances. Now, in order that no necessary instructions may be wanting m this Work, relating to Inclosures, it has been thought advisable to give an ab- stract of the General Inclosure Act, for the information of those readers who may not have an opportunity of consulting the Aet itself. It will be found from this statute, that no person can act as a Commis- sioner, until he has first taken an oath that he will faithfully, impartially, and honestly, according to the best of his skill and ability, execute and perform all the trusts, powers, and authorities vested and reposed in him, as a Commissioner. It also appears by this Act that every person making a survey, plan, and valuation for an inclo. r : ..:. -.., shall verify the same upon oath, to the Commissioners. The Act likewise points out the method of ascertaining the boundaries of manors or lordships ; making out claims ; settling disputes ; setting out roads ; fencing allotments ; defraying the expenses of the inclosure, &c. &c. Besides giving an abstract of the General Act, a few particular clauses are selected from Special Acts, obtained for inclosing certain commons and waste lands in the West Riding of the County of York. Section II.) LAND-SURVEYING. 319 GENERAL ACT. An Abstract of an Act for consolidating in one Act, certain Pi*ovisions usually inserted in Acts of Inclosure ; and for facilitating the Mode of proving the several Facts usually required on the passing of such Acts. (July 2nd, 1801.) Whereas, in order to diminish the expense attending the passing of Acts of Inclosure, it is expedient that clauses usually contained in such Acts should be comprised in one law, and certain regulations adopted for facili- tating the mode of proving the several facts usually required by Parliament, on the passing of such Acts : May it, therefore, please your Majesty, that jt may be enacted ; and be it enacted by the King's most excellent Majesty, by and with the advice and consent of the Lords Spiritual and Temporal, and Commons, in this present Parliament assembled, and by the authority of the same, that no person shall be capable of acting as a Commissioner in the execution of any of the powers to be given by any Act hereafter to be passed for dividing, allotting, or inclosing any lands or grounds, except the power of signing, and giving notice of the first meeting of the Commissioner or Commissioners for executing any such Act, and of administering the oath or affirmation hereinafter directed, until he shall have taken and subscribed the oath or affirmation following : * I, A. B. do swear, (or being one of the people called Quakers, do solemnly ' affirm), that I will faithfully, impartially, and honestly, according to the ' best of my skill and ability, execute and perform the several trusts, powers, ' and authorities vested and reposed in me as a Commissioner, by virtue of 1 an Act for (here insert the title of the Act), according to equity and good ' conscience, and without favour or affection, prejudice or partiality, to any ' person or persons whomsoever. So help me God.' Which oath or affirmation it shall be lawful for any one of the Commis- sioners, where more than one shall be appointed by any such Aet, or any one Justice of the Peace for the County within which the said lands or grounds shall be situated, where only one Commissioner shall be so ap- pointed, to administer, and the said oath and also the appointment of every new Commissioner, shall be enrolled with the award, and a copy of the enrollment admitted as evidence. 2. Commissioners declining to act, shall give notice, in writing, of such intention, to the other Commissioners ; and no Commissioner shall be ca- pable of purchasing any lands within any parish in which the inclosures are to be made, until five years after the date and execution of the award to be made by any such Commissioner, or Commissioners. 320 land-surveying. (Part VI. 3. And whereas disputes may arise concerning the boundaries of parishes, manors, hamlets, or districts, to be divided and inclosed, and of others ad- joining thereto, Commissioners shall inquire into the boundaries of parishes, and if not sufficiently ascertained, they shall fix them, giving previous notice of their intention so to do. The Commissioners shall cause a description of boundaries to be delivered to one of the Church- Wardens, or Overseers of the poor of the respective parishes, and to the Lords of Manors or their stewards ; and if any such person or persons be dissatisfied with the determination respecting the said boundaries, they may appeal to the quarter-sessions, the decision of which is to be final. 4. A true, exact, and particular survey, admeasurement, plan, and valua- tion of all the lands and grounds to be divided, allotted, and inclosed by any such Act ; and also of all the messuages, cottages, orchards, gardens, home- steads, ancient inclosed lands and grounds within any such parish or manor, shall be made, and kept by the Commissioners ; and the same shall be veri- fied upon oath or affirmation by the person making such survey, valuation, &c. at any meeting to be held after the making hereof. Proprietors, and their agents, may inspect admeasurements and plans, and take copies or extracts therefrom. 5. Until the division shall be completed, the lands may be entered by the Commissioners, or any persons they may appoint to make surveys, valua- tions, &c. &c. Maps made at the time of passing Acts, may be used, without making new ones, if the Commissioners shall think fit. 6. All persons who shall have or claim any common or other right to or in any such lands to be inclosed, shall deliver to the Commissioners schedules of particulars, or shall be excluded ; and such claims may be inspected, and copies taken. Objections to claims to be delivered to the Commissioners at or before the meeting appointed for that purpose, or they shall not be received, ex- cept for special causes 7. Commissioners are not hereby authorised to determine disputes touch- ing rights ; but they shall assign the allotments to the persons in actual possession of the land. 8. Commissioners before making any allotments are to set out and appoint the public carriage-roads and high- way s through and over the lands and grounds intended to be divided, allotted, and inclosed ; and to divert, turn, and stop up Section 1 1. J land-surveying. 321 any of the roads and tracts upon any part of the said lands, as they shall judge necessary, so as such roads and highways shall be and remain thirty feet wide at the least, and the same shall be set out in such directions as shall appear to them most commodious to the public. They shall also ascertain the same by marks and bounds ; and prepare a map thereof to be deposited with their Clerk, and give notice thereof, and appoint a meeting, at which, if any person shall object, the Commissioners with a Justice of the Division shall determine the matter. If the Commissioners by any Bill shall be empowered to stop up any old road, it shall not be done without the order of two Justices, which order shall be subject to appeal to the Quarter Sessions. 9. The carriage-roads shall be well fenced on both sides, by such of the land-owners as the Commissioners shall direct ; and no person shall erect any gate across any road, or plant any trees on the sides, at less than fifty yards distance. The Commissioners shall appoint Surveyors of the roads, and if with a salary, such salary, and the expense of making the road, over and above the statute duty, shall be raised in the same manner as the charges and ex- penses of obtaining and passing any such Act ; and shall be directed to be raised and paid to such Surveyors on or before the execution of the award. Surveyors of roads are directed to be in all respects subject to the controul of the Justices of the Peace, acting in and for the county in which such roads shall respectively lie ; and shall account to such Justices for all monies re- ceived and expended ; and for the re-payment of any surplus which may remain in their hands, to such persons as shall have been made liable to con- tribute thereto, according to the proportion so as above ascertained by such Commissioners ; and such Justices shall have the power of levying any such rates as may be thought necessary for the purpose aforesaid, according to the proportions previously ascertained by the Commissioners. If Surveyors neglect to complete roads within a limited time, they shall forfeit £20, and the inhabitants shall not be charged or chargeable towards forming or repairing the said roads, (except statute duty,) till such time as the same shall be declared to be completed, at a Special Sessions. 10. Commissioners are empowered and required to set out and appoint such private roads, bridleways, footways, ditches, drains, watercourses, watering-places, quarries, bridges, gates, stiles, mounds, fences, banks, bounds, and land-marks, in, over, upon, and through or by the sides of the al- lotments to be made, as they shall think requisite, giving such notice, and sub- ject to such examination as may be required. And the same shall be made and at all times kept in repair, by the owners and proprietors, for the time being, of the lands and grounds directed to be divided and inclosed, in such proportion as the Commissioners shall, by their award, order and direct. Y 322 land-surveying. (Part VI. II. The grass and herbage on roads shall belong to the proprietors of the lands adjoining on either side ; and all roads which shall not be set out as aforesaid, shall be stopped op, and be deemed and taken as part of the lands and grounds to be inclosed ; and shall be drvid :. and in- closed accordingly. -mpike-road shall be altered or diverted, without the consent of the trustees of such turnpike-road. 12. Commissioners, in making the several allotments, shall have due re- gard as well to the situation of the respective houses or homesteads of proprietc : - if the lands and grounds to be allotted to them respective Iy, bo fin - be consistent with the general convenience of the said proprietors ; and the Commissioners, in making the said allotments, choJI have par:. ,-^rd to the convenience of the owners or proprietors of the smalles: m the lands and grounds directed to be allotted and exchanged. 13. And whereas the proprietors and persons interested in open common- fields, meadows, pastures, commons, and waste lands, directed to be divided and allotted, whose allotments thereof will be small, and expensive to in- close, may he desirous of stocking and depasturing their allotments in com- mon, and of sharing such produce as may grow thereon, under proper regulations ; therefore the Commissioners shall be fully authorised and empowered, on application of the parties interested, at their : :ond meeting for receiving claims, and on an attentive view and full consideration of the prrii. ises, to a ~ ard, order, and direct any such allotments to be laid together, and ring-fenced, and to be stocked and depastured in common, and to make such orders and regulations for the equitable enjoyment thereof, and for the participation of any produce growing or to grow thereon, as the Co m missioners may think beneficial and proper for the said several parties Interested therein. 14. The several shares of and in any lands or grounds which shall, upon any such division, be assigned, set out, allotted, and applied unto and for the several persons who shall be entitled to the same, shall, when so allotted, be and be taken in full compensation for all rights in the lane:- rights of commons, and ail other rights and properties whatsoever, which they respectively had, and were entitled to, in and over the said lands and grounds ; which rights shall cease on notice from the Co mmis sioners being affixed on the doors of the parish church ; in which the said lands and grounds shall be situated. 15. Commissioners shall, and they are hereby authorised, to set out, allot, and award any messuages, buildings, lands, tenements, hereditaments, new allotments, or old inclosures, within such parish or manors, in lieu of or in Section II) LAND-SURVEYING. 323 exchange for any othermessuages,buildings,lands,tenements,hereditaments, new allotments, or old inclosures, within the said parish or manors, or within any adjoining parish or place ; so that all such exchanges be made with the consent of the respective owners and proprietors, seized of the lands, &c, which shall respectively be so exchanged : or if belonging to or held in right of any church, chapel, or ecclesiastical benefice, shall also be made with the like consent, in writing, of the bishop, the patron, &c. for the time being ; and all such exchanges shall be for ever good, valid, and effectual in the law, to all intents and purposes whatsoever. 16. Commissioners may make allotments in severalty to joint tenants, or tenants in common ; and immediately after the said allotments shall be made and declared, the same shall be holden and enjoyed by the person or persons to whom the same shall be allotted in severalty, in the same manner, and subject to the same uses, as the undivided part or shares of such estates would have been held in case such partition and division had not been made. 17. All persons to whom any allotments shall be made, are required to accept of their respective allotments within the space of two calendar months next after the execution of the award, directed to be made, and in case any persons shall neglect or refuse to accept of their share or allot- ment within the time before-mentioned, such persons so neglecting or re- fusing shall be totally excluded from having or receiving any estate or interest, or right of common whatsoever, in any part of the lands and grounds to be divided and inclosed. 18. It shall and may be lawful for the respective guardians, husbands, trustees, committees, or attorneys, of any persons being minors, femes covert, lunatics, beyond the seas, or otherwise incapable by law, to accept any such allotments as shall be made by any such act, to and for the use of such persons so incapacitated as aforesaid ; and also that any persons entitled to any allotments as tenants for lives, shall be, and are hereby respectively enabled and required to accept of and take such allotments. The non-acceptance of any guardians, husbands, &c. &c, shall not ex- clude, or in any way prejudice the right of any person, incapacitated as aforesaid, who shall claim or accept such share or allotment within twelve calendar months next after such incapacity shall be removed. 19. After the allotments shall be set out by such Commissioners, and at any time before the execution of their award, it shall be lawful for any per- sons to whom any allotments shall be so made, and staked, and marked out, by and with the consent of such Commissioners, in writing under their hands, to ditch, fence off, and inclose their respective allotments, in such manner as such Commissioners shall so direct and appoint. Y 2 324 land-surveying. (Part VI. 20. The timber trees and other trees, thorns, and bushes, standing and growing upon any waste lands, or other lands to be allotted by such act, shall be allotted and go along with the lands whereon they respectively stand, and shall be deemed the property of the several persons to whom the same lands shall be respectively allotted, such persons paying to the owner or respective owners of the said trees, such sums of money for the same, and at such times, and places, as the said Commissioners shall, by writing under their hands, direct ; but if the said parties, who are to make such respective payments, shall neglect or refuse to make the same accordingly, then it shall be lawful to and for the respective parties who shall be entitled to have and receive such payments, to enter on the said lands, and cut down, take, and carry away to their own use, the said trees, thorns, or bushes, in respect of which the said payments were respectively to be made to them, at any sea- sonable time, within one year next after such neglect or default, they doing as little damage on the said lands as may be. 21. Whenever any sum of money is, under the provision of this Act, or any such Bill, to be paid for the purchase or exchange of any lands, tene- ments, or hereditaments, or of any timber or wood growing thereon, and which sum of money ought to be laid out in other purchases, to be settled to the same uses, it shall and may be lawful for the Commissioners, out of such sum, to defray such proportion of the expense of passing such Act, and of carrying the same into execution, as shall, if any, be charged upon any of the lands, tenements, or hereditaments so sold or exchanged. And if the surplus money shall amount to the sum of £200, it shall, as soon as convenient, be laid out in other purchases, and in the mean time, until such purchase can be made, such money shall be paid into the Bank of England, in the name and with the privity of the Accountant General of the High Court of Chancery, to be placed to his account there. And such money shall be applied under the direction, and with the approbation of the Court of Chancery. 22. If such money be less than £200, and shall exceed the sum of £20, it shall, at the option of the persons entitled to the rents and profits of the lands, be paid into the Bank, as aforesaid, in order to be applied in the man- ner before directed ; or otherwise the same shall be paid at the like option, to two trustees to be named by the person making such option, and to be approved of by the Commissioners, (such nomination and approbation to be signified in writing under the hands of the nominating and approving parties,) in order that the money be applied as before directed. 23. Where such money shall be less than £20, it shall be applied to the use of the persons who would for the time being have been entitled to the rents and profits of the lands, in such manner as the Commissioners shall think proper. Section II.) land-surveying. 325 24. If any persons to whom any allotments shall be made, do not accept, inclose, and fence their allotments as the Commissioners 'shall direct, they may cause such allotments to be inclosed and fenced, and let the same to any persons they may think proper ; and they may receive the rents and profits thereof, until the expenses attending the inclosure and fencing thereof are paid ; or they may charge such expenses npon the proprietors of the allot- ments, by any such writing as aforesaid, or by their award, appoint to whom, and at what times the same shall be paid. 25. It shall be lawful for the several proprietors of the allotments to be made in pursuance of any such Aet, their agents or workmen, at any sea- sonable times, within the space of seven years next after the fencing of any allotments, to set up and erect posts and rails, or other dead fences, on the outside of the ditches bounding their respective allotments, not exceeding three feet from such ditches, for the preservation of their quickset-hedges ; and at any seasonable tunes, before the expiration of the said term, to take and carry away the materials of such outside fences, when they shall think prober. 26. No fences or hedges standing when any act is passed, shall be cut down or destroyed by the owners thereof, until the execution of the award, without the consent of the Commissioners ; and if assigned by them as a boundary or division-fence to and for any of the allotments, all such fences or hedges shall be left uncut, for the benefit of the persons to whom such allotments shall belong ; and they shall make such compensation to the former owners thereof, as the Commissioners shall, by writing under their hands, hi that behalf order and appoint, 27. No proprietor whose allotments or shares shall, upon any such inclo- sure, lie and be situated next and adjoining to any common-fields, or inclosed grounds, the boundary of which shall be fenced by any mound, fence, brook, or rivulet, shall be compelled to make or erect any hedges, ditches, or fences, next adjoining to any such common-fields, or inclosed grounds, for inclosing such their allotments or shares ; but that the whole mound, fence, brook, or rivulet, or other sufficient fences which divide any such common-fields, or in- closed grounds from such allotments, shall for ever be and remain a boundary fence for the purpose of such division : and shall from time to time be main- tained, kept, cleansed, scoured, and repaired by the respective proprietors thereof, in the same manner as the Commissioners shall order and direct. In case it shall happen that some of the proprietors shall have a greater proportion of fences to make and maintain upon any of the lands directed to be divided and inclosed, than, in the judgment of the Commissioners, they ought to be charged with, it shall be lawful for the Commissioners, where they shall judge it proper, to ascertain and appoint such sum of money to be paid to every such proprietor, towards making and maintaining such fences, by such Yd 326 LAND-SUE YE V I xg. (Part VI other of the proprietors who may have a less proportion of fencing, according to the value and quantity of the lands to be allotted to them ; and to grant such other relief in respect thereof, out of the money to be raised for de- _- the expenses of carrying such Act into execution, as they shall think reasonable, in order that the said boundary fences may be brought as near as may be to a just and equal proportion. 28. In case any person shall wilfully and unlawfully break down, destroy, carry away, or damage any fence, stile, post, rail, gate, bridge, or tunnel, which may be put or placed under the authority of any such Act, every person so offending, and being thereof convicted before any Justice of the Peace for the County in which the lands or grounds to be inclosed shall be situated, on confession or on proof of the offence, by oath of one or more credible witnesses, (which oath the said Justice is hereby authorised to ad- minister,) shall for every such offence forfeit and pay any sum not exceed- ing £5 ; and every person shall be allowed to give evidence of such offence, notwithstanding he may be a proprietor or occupier of lands within, or an inhabitant of such parish, and notwithstanding he may be the owner of any such fence, stile, ice. &c. to be recovered as hereinafter provided. 29. If it shall be provided by any such Act, that the expenses of obtain- ing and carrying the same into execution, shall be paid in proportion, by the proprietors of lands or grounds to whom any allotments shall be made ; then and in such case, when and so often as any such persons, except those ex- empted from payment of any such charges and expenses, shall refuse or neglect to pay their proportion of the charges or expenses, or shall refuse or neglect to pay the expenses attending the inclosing and fencing of any such allotments, as upon the neglect or refusal of the proprietors, shall be inclosed and fenced by the Commissioners, as hereinafter mentioned, at the respective days and rimes to be appointed for payment of such charges and expenses, k shall be lawful for such Commissioners, by any warrants under their hands and seals, -directed to any persons whomsoever, to cause the said costs, charges, and expenses, and sum or sums of money respectively, to be levied by distress and sale of the goods and chattels of the persons so making default in payment as aforesaid, their guardians, husbands, trustees, com- mittees, or attorneys, wheresoever the same shall be found, rendering the overplus (if any) on demand, to the owners of such goods and chattels, the reasonable charges of such warrant, distress, and sale, being first deducted, together with the interest, after the rate of £5 per centum per annum, to be computed on such shares or proportions, from the time the same shall be directed to be paid by such Commissioners as aforesaid ; or otherwise it shall be lawful for such Commissioners, or any persons authorised by them, to enter upon and take possession of the premises so to be allotted to such persons refusing or neglecting to pay as aforesaid, and to receive and take Section II) land-surveying. 327 the rents and profits thereof, until thereby, therewith, or otherwise, the shares or proportions, and the said costs and charges so ordered and directed by such Commissioners to be paid by such persons as aforesaid, and all in- terest on such shares or proportions, to be oomputed from the time the same shall, by such Commissioners, be directed to be paid as aforesaid ; and also all costs, charges, and expenses occasioned by or attending such entry upon and perception of the rents and profits of the said premises, shall be fully paid and satisfied. BO. And in such case as last aforesaid, it shall T3e lawful for the husbands, guardians, trustees, committees, or attorneys of any of the owners or proprie- tors of such allotments or exchanged lauds, (except the rector or vicar of such parish) to charge such allotments or exchanged lands and premises, with such sums of money as such Commissioners shall, by their award, or by writing under their hands, either before or after the execution of such award, adjudge necessary to pay and defray the said respective shares of the^harges and expenses incident to and attending the obtaining such Act, and carrying the same into execution, and of charging the said lands as -aforesaid, so that the same shall not exceed £5 for every acre of such allotments or exchanged lands ; and -to grant, mortgage, surrender, lease, or demise, or otherwise sub- ject the lands, tenements, and hereditaments so to be charged, unto such per- sons who shall advance and lend the same respectively, their executors, ad- ministrators, and assigns, for any term or number of years ; or in case any person in possession, who shall or may be liable to and charged with a share of the expenses as aforesaid, shall choose to advance, pay, and discharge such sums of money, then it shall be lawful for the Commissioners, by any deed of writing under their hands and seals, to be attested by two or more credible witnesses, in like manner to grant, mortgage, surrender, lease, demise, or otherwise subject the said lands, tenements, and hereditaments, to such per- sons, respectively paying and discharging the same, for any term or number of years, to and for the payment of such sums of money so advanced, paid and discharged by them, with interest for the same, to commence on the ter- mination of their right in the premises ; so that every such grant, mortgage, surrender, lease, or demise, be made with a proviso or condition to cease and "be void, or with an express trust to be surrendered or re-assigned, when such sums of money thereby to be secured, should be fully paid and satisfied ; and also with a covenant to pay and keep down the interest, so that no per- sons afterwards becoming possessed or entitled to any such lands, &c. shall be liable to pay any further or larger arrear of interest than for six calen- dar months preceding the time when the title to such possession shall have commenced ; and that every such charge, grant, mortgage, &c. shall be good, valid, and effectual in the law, for the purpose thereby intended. 31 . And whereas in such cases as aforesaid, where provision may be made in any such Act for charging the expenses of passing such Act, or of executing y 4 328 land-surveying. (Part VI. the powers therein contained, or of fencing the respectire allotments, on the several proprietors thereof, it may be more convenient for the feoffees or trustees of any charity lands or school lands, to have lands deducted from the respective allotments, to he made for such charity or school lands, for paying the proportionate share in respect of such allotments, of such expenses re- spectively, than to raise money on mortgage for those purposes ; therefore, it shall be lawful for any such Commissioners, if they shall judge it right or expedient, to deduct from the respective allotments to be made to such feoffees or trustees, as aforesaid, so much land as shall, in the judgment of such Commissioners, be equal in value to their respective proportions of the said expenses ; and to allot, assign, and award the same to such persons as such Commissioners shall think proper, and who will undertake to pay and defray, and shall pay and defray, all such expenses. 32. In case it shall be provided by any such Act, that the expenses at- tending the same shall be paid by sale of any part of the lands so to be in- closed, the said Commissioners shall mark and set out such parts of the said waste or common lands, as in their opinion, will by sale thereof raise a sum of money sufficient to pay and discharge all such charges and expenses, as may, by any such Act, be directed to be paid and discharged out of the same ; and the Commissioners shall sell such parts of the said lands to any persons for the best prices that can be gotten for the same, by private con- tract, or by public auctions, to be holden for that purpose, of which six weeks' previous notice shall be given. And the persons so purchasing the same shall immediately pay (by way of deposit) into the hands of the said Commissioners, or such persons as they shall appoint, one-tenth part pf-their purchase-money, and pay the remainder thereof within three calendar months next after, or at such other time as the said Commissioners shall appoint. And in default thereof, the money so deposited, shall be forfeited, and shall be applied in carrying such Act into execution ; and the said allotments for which the whole of such purchase-money shall not have been so paid, or for which there shall be no bidding at such auction, shall be again put up to sale, and sold in manner aforesaid, for the best prices that can be gotten for the same, or be sold by the said Commissioners, by private contract, for any sums not less than the remaining nine-tenths of the prices for which the same were respectively sold before, or the amount of one bidding above the sums at which the same were respectively put up in the said former auction ; and every allot- ment for which the full purchase-money shall be paid,shall immediately there- upon be absolutely discharged of andfromall common and other right thereon, and be vested in fee simple in, and be inclosed, and thenceforth held in severalty by such purchasers thereof respectively,astheirprivate and absolute property ; and shall be allotted accordingly, by the said Commissioners ; and the said pur- chase-money shall be applied in defraying such charges and expenses as may be in any such Act directed to be paid and discharged by the sale of such land. Section II.) land-surveying. 329 33. And, for the better enabling such Commissioners to determine the several matters and things, by this or any such Act, referred to their determi- nation, it shall be lawful for the said Commissioners, from time to time, as they shall see occasion, by any writings under their hands, to summon and require any persons to appear before them at any time and place in such writing to be appointed, to testify the truth touching the matter in dispute between any proprietors or interested persons, or otherwise relating to the execution of the powers given by this or any such Act ; and to cause a copy of such writing to be served on such persons required to give evidence, or to be left at their usual or last place of abode. And all persons so summoned, who shall not appear before the said Commissioners pursuant to such sum- mons, (without assigning some reasonable excuse for not appearing,) or who appearing, shall refuse to be sworn or examined on oath or affirmation, which oath or affirmation the said Commissioners are hereby empowered and re- quired to administer, (such persons having been paid the reasonable charges of their attendance,) and being thereof convicted before one of his Majesty's Justices of the Peace of the county or district in which such lands are situated, upon information thereof upon oath made before any such Justice, shall for every such neglect or refusal, forfeit and pay such sum of money, not ex- ceeding £10, nor less than £5, as such Justice shall think fit and order. 34. Provided always, That no witness summoned to attend such Commis- sioners shall be obliged to travel above eight miles from the boundary of the parish, manor, or district to be inclosed by any such Act. 35. And be it further enacted, That as soon as conveniently may be after the division and allotment of the said lands and grounds shall be finished, pursuant to the purport and directions of this or any such Act, the said Com- missioners shall form and draw up, or cause to be formed and drawn up, an award in writing, which shall express the quantity of acres, roods, and perches, in statute-measure, contained in the said lands and grounds, and the quantity of each and every part and parcel thereof which shall be so allotted, assigned, or exchanged, and the situations and descriptions of the same respectively ; and shall also contain a description of the roads, ways, foot-paths, water- courses, watering-places, quarries, bridges, fences, and land-marks, set out and appointed by the said Commissioners, as aforesaid ; and all such other rules, orders, agreements, regulations, directions, and determinations, as the said Commissioners shall think necessary, proper, or beneficial to the parties ; which said award shall be fairly ingrossed or written on parchment, and shall be read and executed by the Commissioners, in the presence of the proprietors, who may attend at a special general meeting called for that purpose, of which ten days' notice at least shall be given in some paper to be named in such Act, and circulating in the county ; which execution of such award shall be pro- claimed the next Sunday in the church of the parish in which such lands shall 330 LAND-SURVEYING. (Part VI, be ; from the time of which proclamation only, and not before, such award shall be considered as complete ; and shall, within twelve calendar months after the same shall be so signed and sealed, or so soon as conveniently may be, be enrolled in one of his Majesty's Courts of Record at Westminster, or with the Clerk of the Peace for the county in which such lands shall be situated, to the end that recourse maybe had thereto by any persons interested therein, for the inspection and perusal whereof no more than one shilling shall be paid ; and a copy of the said award, or any part thereof, signed by the proper Officer of the Court wherein the same shall be enrolled, or by the Clerk of the Peace for such county, or his Deputy, purporting the same to be a true copy, shall from time to time be made and delivered by such Officer or Clerk of the Peace for the time being, as aforesaid, to any person requesting the same, for which no more shall be paid than two-pence for every sheet of seventy -two words ; and the said award, and each copy of the same, or of any part thereof signed as aforesaid, shall at all times be admitted and allowed in all courts whatever, as legal evidence ; and the said award or instrument, and the several allotments-, partitions, regulations, agreements, exchanges, orders, directions, determinations, and all other matters and things therein mentioned and con- tained, shall, to all intents and purposes, be binding and conclusive, except where some provision to the contrary is herein or shall be by any such Act contained, unto and upon the said proprietors, and all parties and persons con- cerned or interested in the same, or in any of the lands, grounds, or premises aforesaid ; and also that the said respective Commissioners, if they think it necessary, shall form or draw, or cause to be formed and drawn on parch- ment or vellum, such maps or plans of the said lands and grounds, the better -to describe the several new allotments or divisions to be made, and premises that shall be exchanged by virtue of this Act, and which shall express the quantity of each allotment in acres, roods, and perches, together with the names of the respective proprietors at the time of such division and allotment ; winch said maps and plans shall be annexed to and enrolled with the said respective award, and shall be deemed and construed in every respect as and for part of the said award. 36. Commissioners shall, and they are hereby recmired to enter in a book to be provided for that purpose, a particular account of all sums of money received from the proprietors or others during the progress of the inclosure ; and also of all the charges, expenses, and disbursements which shall accrue or be made by virtue of any such Act, and in carrying the same into execution ; which book of accounts shall be kept at the office of their Clerk, open at all seasonable times during the progress of the inclosure, and till all the accounts are finally settled, for the inspection of any of the proprietors, without fee or reward ; and in case any such Commissioners, or their Clerk, shall neglect to provide and keep such book of accounts as aforesaid, or refuse the inspection thereof to any of the proprietors at seasonable times in manner before men- Section II.) land-surveying. 331 tioned, and shall be convicted thereof, upon the oath of one or more credible witnesses, not interested in the intended division and inclosure, before any Justice of the Peace of the County in which the lands or grounds to be in- closed shall be situate, or of any such other county or place where such Com- missioners or Clerk so causing such neglect or refusal, and convicted as afore- said, shall forfeit and pay for every such offence any sum not exceeding £1 0, nor less than £5, to be levied, recovered, and applied in the same manner as other penalties are by this Act directed to be levied, recovered, and applied. 37. All monies raised under any Act shall from time to time, as often as the same shall amount to the sum of £50, be deposited in the hands of some banker or such persons as shall be approved by a majority in value of the pro- prietors, at the first meeting of the Commissioners, in the notice of which meeting shall be expressed the intention of then appointing such banker, or such other persons, and no monies deposited or paid into the hands of such banker or other persons, to be appointed as aforesaid, shall be issued or paid by them, without an order in writing under the hands of such Commissioners, specifying the persons to whom the same are respectively payable, and the service or consideration for which the same are due ; and the balance, if any, upon the final settlement of accounts, shall be immediately repaid to the landowners in proportion to the sums respectively paid by them. 38. It shall be lawful for the rector or vicar of any parish wherein the lands and grounds intended to be inclosed shall be situate, by indenture under his hand and seal, with the consent of the bishop of the diocese, and of the patron of the living, to lease or demise all or any part or parts of the allot- ments to be set out and allotted to any such rector or vicar, to any persons whomsoever, for any term not exceeding twenty-one years, to commence within twelve calendar months next after the executing the award ; so that the rents for the same shall be thereby reserved to the rector or vicar for the time being, by four equal quarterly payments in every year ; and so that there be thereby also reserved and made payable to such rector or vicar, the best and most approved rents that can reasonably be gotten for the same, without taking any fine, foregift, premium, sum of money, or other consideration for the making or granting any such lease or demise ; and so that no such lessee by any such lease or demise be made dispunishable for waste, and so that there be inserted in every such lease, power of re-entry on non-payment of the rents to be thereby reserved, within a reasonable time to be therein limited, after the same shall become due ; and so that a counterpart of such lease be duly executed by the lessee or lessees to whom such lease shall be so made as aforesaid ; and every such lease shall be valid and effectual. 39. All penalties and forfeitures imposed by virtue of this or any other such Act, shall be levied and recovered before any one Justice of the Peace I3S : axd-surveyikg. Purl r/. for the county in which the lands or grounds to be inclosed shall be sitnate, **-'- ~>-::"- : i" :-f i: =".:: .'. " f 7i~-:il : r . r; - 7: 7 .-- : f ■:' :'.: : 7 -:. : ■-. -- -- made to him, to sawn die party accused, and the witnesses on of the party accused. (winch oath any snch Justice is hereby em- . - ari :•■ :^iriiz 7ir -. ir:;- i::iirl n =~;^- :ii7: ^ 1 = " :' r:' .: _r - ^ -.'--. :'- •ri::: siill 11-f z:r:T 7 n 1 :: !f-y - i .7 : fnlr.f- n '. : .::':::_-:- ;- lii- 1 sale of the offe nd e r ' s goods and chattels, together with reasonable : ■:>-; ■ .. " .. _ ---\- ..:.:..-.:. - "... . - ' - 7_ri. -7. -."_ 5-: si:i i= Tif sin f 7n7 ': t If-lf-i. if :i:: ::r ri 7: i.^f-5 i- 7if ; shall by writing under their hands or by their award, order i-iir rlilf, :r ±:er-r=- ::' ill" l:ri :r 111;- : J n;-ini :r :: l-rdilir;.— riTi.7 f are situate; or to the seniorities, rights, and royalties incident or belonging to snch manor or lordship, or to the lord or lady thereof. ■ any person : :i: :if sin f 7n7 r-fnm. n :. - rill. :r-'.r. n :':-:;■ i- 1 jnr-i^fs. :--1t"i::1- :r :i-7:i: ii-f if 11 =-; f 1 mi r:l:s ':-ff:r-f 7if : .■.■^n: : : ' 5i7i A ::. :r n :ifr :7t Mnf 7_ 1 4 '_ ?i -vi : ~ - - : 7 . . :~*s:r«. ::::: ill "It: ; n- i=. 1:- : :'irl: mi : :rr :riif. n 1 ::fi : : ::-. ?i::fff ::•;. r-r ■;:::-. i~ 1 i innim: :rs. ill sr:7 frme .: -..•'.:- rif.ii.ln- .fr-~: i- -if; ii 1 :r fi; :;fi .in.::. :r .:: :i :r n rr i:; ::' :if =ili in is. rriil-. n 1 :rnil-f- ?•: Tif ::f 1 : " f in If i ii::if 7 i 1 1 i;rvi :r fx:'nrifi is r if-:: 1. ' -•-::'- if 7if :r ; i; .:" - :i .-..-. r :■: ill :r nlr'i: ii~f fi; if 1 n iff :if snf 7. 49 I: shall and may be lawful &r any two or more Justieesof tbf 7 ■- f to take affidavits on oath or affirmation (which oath or affirmation snch Jus- ::' r.f r:i.e> rf- ::' -if illf -ir_:if ..... . - •f ■:: :r n'if :: n; : r:r : i-i :7i: -i:i;.riln r- ;i .... i : : ' r s 7:- _ "ii .T-:-f " z'z :7 li-r:f :r ■ i Trii: ii" Section II.) land-surveying. 333 matter ortlring which shall be false or untrue ; every such person so offending shall, on conviction thereof, be deemed guilty of perjury, and shall suffer the like pains and penalties, to which persons guilty of wilful and corrupt perjury j are now liable. 44. And be it enacted, that all and every of the powers, authorities, direc- tions, and provisions in this Act contained, shall be only so far effective and binding in each particular case, as they or any of them shall not be other- wise provided and enacted in any such Act hereafter to be passed as aforesaid. SPECIAL ACTS. Clauses selected from Special Acts, obtained for Inclosing cer- tain Commons and Waste Lands in the West Biding of the County of York. 1. And be it enacted, That if any difference of opinion shall arise between the Commissioners appointed for setting outvaluing, dividing, and allotting the said commons and waste grounds, touching or concerning any matter or thing to be done by them by virtue of the said recited General Act, or this Act, the said Commissioners from time to time, and when and so often as such difference of opinion shall arise, shall, by writing under their hands, appoint some person (not interested in the premises) to be an umpire between them ; and the matter upon which such difference of opinion may arise, shall be set- tled and determined by such umpire, whose determination in writing shall be binding and conclusive. Provided always, that no person shall be capable of acting as an umpire, until he shall have taken the oath usual on such occasions. 2. And be it enacted, That the said Commissioners and the said umpire shall be paid and allowed one guinea each, and no more, for every day they shall respectively travel or attend for the purpose of this Act, over and besides all their reasonable expenses at the times of such their journeys and attendances. 3. And after the said Commissioners shall have set out and appointed the public carriage-roads and highways through and over the said commons and waste grounds, they shall set out such parts of the same, as they shall think proper, not exceeding five acres in the whole, to be used and enjoyed by the respective proprietors of the said lands, for the purposes of common watering- places for cattle, and getting stones and other materials for erectingand repair- ing buildings, bridges, walls, fences, and other works, for the reparation of the public and private roads. And the Commissioners shall in the next place assign, set out, allot, and award unto and for the lord of the manor, such part and parcel of the residue and remainder of the said commons and waste grounds, as shall in their judgment be equal in value to one full sixteenth part 334 land-suiiveyixg. (Part VI. of the said residue of the said common ar. md-?, in lieu of and as a full recompense for all such right and interest in and to the soil of the said commons ar. 1 waste g rer expressly saved and re- served ; and that after set L:h part to the said lord of the manner, the Commissioners shall set out, assign, and allot the residue of the said commons an I waste grounds unto and amongst the said lord of the manor, and the said several other persons entitled to right of common or other rights and interests in and upon the said commons and waste grounds.accordingtothevalueoftheancientmessua. . >tfc ges, mills, old inclosed lands, tenements, and hereditaments, in respect whereof thev are so respectfully entitled to such right of common, as aforesaid, and according to the true and real value of such o : :r interests, as aforesaid, esti- mating lands at their full and fair value as they are worth to be let, and mes- 50 .. - ? : : wires, mills, and other buildings at one-half only of such their re- spective values : hut in estimating the value of m w - ;■ : w. _■ w . .:: i mills, no regard shall be had to any additions or improvements made within forty years last past. Provided always, that no person shall be entitled to any al- lotment from the said commons and waste grounds, or any part thereof, for or in respect of any messuage, cottage, mill, or other building which shall be proved to the satisfaction of the said Commissioners to have been er : any time within sixty years next before the passing of this Act, uniw erection shall have been made upon the scite'of some ancient messuage, eot- : :, . will, or other building which shall have been originally erected sixty years or upwards before the passing of this Act. -4. Ail encroachments which at any time within twenty years now last past have been made upon the said commons and waste grounds shall be deemed part thereof, and shall be divided and allotted accordingly ; and in case any dispute or difference shall arise, touching any such encroachments or the extent thereof, such dispute or difference shall be determined by the said - 5. Provided always, that the lands and grounds comprised in such encroach- ments shall be aliened to the persons who shall be in;: OBSession thereof, with- : : : e wrd to the value of such improvements as shall or may have been made thereon since such encroachments were made, in case the persons so in pos- session shall desire the same to be so allotted, and shall signify such desire by writing signed by them to be deliveredto the said Commissioners at th-ir first or second meeting to be holden in pursuance of this, and the said general Act ; and the value of such encroachments shall be deducted from the allotments to which such persons shall be entitled under this Act, unless it shall happen that the value of such encroachments respectively (quantity and quality con- sidered) shall be greater than the allotments to which such persons shall be entitled by virtue of this and the said recited General Act : and in that case proportionable part only of such encroachments shall be deducted therefrom Section II. J LAND-SUltVEYING. 335 and the residue thereof shall be sold by the said Commissioners ; and if the persons in possession of such encroachments shall not be entitled to any allot- ments, then the whole of such encroachments shall be sold by the Commis- sioners, and conveyed by them in fee simple to the purchaser or purchasers thereof, and the money arising from such sales shall be applied towards de- fraying the expenses of obtaining and executing this Act. 6*. And from and immediately after the passing of this Act until the ex- ecution of the award of the said Commissioners, it shall not be lawful for any persons whomsoever to grave, dig, get, pare, cart, or carry away any sods or turves from any part of the commons or waste grounds aforesaid ; and every person so doing, shall for every such offence forfeit and pay any sum not exceeding twenty shillings. 7. And be it further enacted, That no sheep or lambs shall be kept in any of the new inclosures (except such as are not fenced by quicksets) during the space of nine years from the execution of the said award, unless the persons keeping such sheep or lambs do, at their own expense, fence their neighbour's quicksets, adjoining the inclosures where such sheep or lambs shall be kept, so as to prevent any damage being done to such quicksets by such sheep or lambs. 8. And be it further enacted, That convenient gaps and openings shall be left in the fences and inclosures to be made by virtue of this Act, during such time as shall be allowed and fixed for making such fences as aforesaid, for the passage of cattle, carts, and carriages in and through the same, unless the said Commissioners shall order and award to the contrary, and then for such time only as they shall so order and award. Note. — The foregoing clauses are not contained in the General Act. SECTION III. The Method of reducing Statute Measure to Customary, and vice versa. It has been before observed, that by custom the perch varies in different parts of England j and with it, consequently, varies the acre in proportion. In Devonshire and part of Somersetshire, 15 ; in Cornwall, 18 ; in Lancashire, 21 ; and in Cheshire and Staffordshire, 24 feet are accounted a perch. In the common field-lands of Wiltshire, and in some other counties, there is a customary measure of a different nature, viz. of 120, instead of 160, statute-perches to an acre ; consequently. 336 land-surveying. (Part VI. 30 perche9 of statute-measure, make I rood of customary, or 3 statute-roods 1 acre. In some places, an acre of this measure, is called a day-work, or day's-work of land. Note. — The utility of the following Problems will appear obvious, when we consider that in many places land is not only reaped and farmed, but also bought and sold by customary-measure. Besides, when persons have the contents of their estates in statute-measure, it is frequently necessary to reduce them to the customary-measure of the place ; and on the contrary, when the contents are in customary -measure, it may be desirable to reduce such contents to statute-measure. General Rules for reducing Statute-Measure to Customary ', and the contrary. Rule 1. — To reduce statute-measure to customary ; multiply the number of perches, statute-measure, by the square feet in a square perch, statute-measure ; divide the product by the square feet in a square perch, customary-measure, and the quotient will be the answer in square perches. Rule 2. — To reduce customary-measure to statute, multiply the number of perches, customary-measure, by the square feet in a square perch, customary-measure; divide the product by the square feet in a square perch, statute-measure, and the quotient will be the answer in square perches, which reduce to roods and acres by dividing by 40, and by 4. Note 1. — It is scarcely necessary to remark that the length of any perch mul- tiplied by itself, will give the number of square feet in a square perch of the same measure ; hence we have 16.5 x 16.5 = 272.25, the statute perch ; 15 x 15 = 225, the Devonshire and Somersetshire perch ; 18 x 18 = 324, the Cornwall perch ; 21 x 21 = 441, the Lancashire perch ; and 24 x 24 = 576, the Cheshire and Staffordshire perch. 2. — It may also be observed that 4840 square yards make 1 statute acre ; 4000 make 1 Devonshire or Somersetshire acre ; 5760 make 1 Cornwall acre ; 7840 make 1 Lancashire acre ; and 10240 square yards make 1 acre of the customary-measure of Cheshire or Staffordshire. Section III.) land-surveying. 337 PROBLEM I. To reduce Statute Measure to the Devonshire and Somersetshire Customary Measure, of 15 Feet to a Perch, and vice versa. TABLE I. Stat. Customary. Stat. Cust. I Stat. Cust. A. A. R. P. P. 1 R. P. P. 21 R. P. 25.4 1 1 33.6 1.2 2 2 1 27.2 2 2.4 22 26.6 3 3 2 20.8 3 3.6 23 27.8 4 4 3 14.4 4 4.8 24 29.0 5 6 8.0 5 6.0 25 30.2 6 7 1 1.6 6 7.2 26 31.4 7 8 1 35.2 7 8.4 27 32.6 8 9 2 28.8 8 9.6 28 33.8 9 10 3 22.4 9 10.8 29 35.0 10 12 16.0 10 12.1 30 36.3 20 24 32.0 11 13.3 31 37.5 30 36 1 8.0 12 14.5 32 38.7 40 48 1 24.0 13 15.7 33 39.9 50 60 2 0.0 14 16.9 34 1 1.1 100 121 0.0 15 16 17 18.1 19.3 20.5 35 36 37 1 2.3 1 3.5 1 4.7 Stat. Customary. R. J R. P. 18 19 21.7 22.9 38 39 1 5,9 1 7.1 1 8.4 2 2 16.8 20 24.2 3 3 25.2 Note 1. — To reduce customary -measure, of 15 feet to a perch, to statute, multiply the number of square links, customary-measure, by .826447, and the product will be the answer in square links, which must be brought into acres, roods, and perches. (See a table of square links in the first Section.) 2. — When it is intended to find the area of an estate in customary-mea- sure only, it is generally thought most convenient to take the dimensions by a chain properly adapted for that purpose. The Devonshire and Somer- set chain is 60 feet ; the Statute-chain 66 feet ; the Cornwall chain 72 feet ; the Lancashire-chain 84 feet ; and the Cheshire and Staffordshire chain 96 feet in length. Each of these chains is divided into 100 equal links, in the same manner as the statute-chain; consequently, the customary-mea- sure is found by the same rules as the statute-measure. z 338 LAND-SURVEYING. (Part VI. 3. — It may also be observed that the Devonshire and Somerset link is 7.2 inches ; the Statute link 7.92 inches ; the Cornwall link 8.G4 inches ; the Lancashire link 10.08 inches ; and the Cheshire and Staffordshire link is 11.52 inches in length. EXAMPLES. 1. In 25 a. 2r. 20p. statute, how many acres, &c. customary - measure ? BY RULE 1. A. R. p. 2.5 2 20 4 102 40 15 x 15 — 225)1116225.00 900 4 .2162 . 2025 4100 272.25 = 16.5 x 16.5 20500 8200 8200 28700 8200 4?0 4.96,1 124 1 31 A - ° R - 1p - Ans- . 1372 1350 .225 225 BY THE TABLE. A. R. p. 20a. = 24 32 5a. == 6 8 2r. = — 2 16.8 20p. = — 24.2 31 1 Ans Section III.) land-surveying. 339 2. In 31a. Or. 1p. customary, how many acres, &c. statute- measure ? BY RULE 2. A. R. P. 31 1 4 124 40 4961 225 24805 9922 9922 272.25)1116225.00 108900 4 410 102.20 2/225 25a. 2r. 20p. Ans. 27225 - 00 BY THE NOTE. sq. links. 30a. = 3000000 1a. = 100000 lp. = 625 3100625 . 82 6447 21704375 12402500 12402500 18603750 6201250 24805000 25.62502.229375 4 2.50008 40 20.00320 Ans. 25a. 2r. 20p. 3. In 159a. 3r. 26p. statute, how many acres, &c. customary- measure ? Ans> 193a. 1r. 39p. z2 340 land-surveying. (Pari VI PROBLEM II. . s Ut Meeuun to thi Cornwall C M of IS Feet to a Perch, and vice versa. TABLE II. Star. A. 1 2 3 4 5 6 7 8 9 10 20 30 40 50 100 StoL R. CusTomarv. A. R. P. 1 2 3 4 ■5 5 6 8 16 25 33 42 84 14.4 28.8 3.3 17.7 32.2 21.0 3.5.5 9.9 24.4 8.8 33.2 17.6 2.0 4.0 Customarv. R. P. 33.6 1 27.2 2 20.8 Stat. Cost P. P. 1 0.8 2 1.6 3 2.5 4 3.3 .5 4.2 6 5.0 : 5.8 8 <-.: 9 :.5 10 11 9.2 12 10.0 13 io.g 14 ii.: 15 12.6 16 13.4 i; 14.2 18 15.1 19 i5..;' 20 16.8 Stat. Oust P. P. 21 22 23 24 25 26 27 2s 29 30 31 32 33 34 35 36 3? 38 17.6 18.4 19.3 20.1 21.0 21.8 22.6 23.5 24.3 25.2 26.0 26.8 27.7 2S.5 1 A 3'"'. 2 31.0 31.9 32.7 Xote. — To reduce customary-measure, of 18 feet to a perch, to statute, multiply the number of square links, customary-measure, by 1.19, and the product will be the answer in square links, Section III.) land-surveying. 341 EXAMPLES. 1. Reduce 56a. 3r. 36p. statute, to customary-measure. BY RULE 1. A. R. P. 56 3 36 4 227" 40 9116 272.25 45580 18232 18232 63812 18232 18 X 18 = 324)2481831.00 2268 A 4,0 7659.9 191 19.9 2138 47a 3r i9.9p. Ans. 1944 •1943 1620 • 3231 2916 3150 2916 • 234 BY THE TABLE. A. R. P. 50a. = 42 2 6a. = 5 6.6 3r. = 02 20.8 36p. = 00 30.2 47 3 19.6 Ans z3 342 Land-surveying. (Part VI 2 - B* ' ' *■ - " bomai -measure. BY RULE 2. A. R. p. 4 4-0 3 124 I 1532 55 ."::■:" i^if^.oo nil o 246025 r — 56a. Sit. 36i Am - --'"■ ======== 43650 --225 i : a -: :be note. .inks. = 4000000 ~. = '00000 3ft. = 75000 20p. = 125: • *7875( 875 t7875 47875 4 J.88i 4 35.40000 Ana : : a. 3r. -S; '-■ 1; - . ■ . .- . r how many = customarv-me&V- Ans. 223a. Or. Section III.) land-surveying, 343 PROBLEM III. To reduce Statute Measure to the Lancashire Customary Measure, o/2\ Feet to a Perch, and vice versa. TABLE III. Stat. Customary. Stat. Cust. Stat. Cust. A. 1 A. R. P. P. 1 P. P. 21 P. 2 18.7 0.6 12.9 2 1 37.5 2 1.2 22 13.5 3 1 3 16.3 3 1.8 23 14.1 4 2 1 35.0 4 2.4 24 14.8 5 3 13.8 5 3.0 25 15.4 6 3 2 '32.6 6 3.7 26 16.0 7 4 1 11.4 7 4.3 27 16.6 8 4 3 30.1 8 4.9 28 17.2 9 5 2 8.9 9 5.5 29 17.9 10 6 27.7 10 6 1 30 18.5 20 12 1 15.4 11 6.7 31 19.1 30 18 2 3.1 12 7.4 32 19.7 40 24 2 30.8 13 8.0 33 20.3 50 30 3 18.5 14 8.6 34 20.9 100 Stat. R. 1 61 2 37.0 15 16 17 9.2 9.8 10.4 35 36 37 21.6 22.2 22.8 Customary. R. P. 18 19 11.1 11.7 38 39 23.4 24.0 24.7 2 1 9.4 20 12.3 3 1 34.1 Note 1. — To reduce customary-measure, of 21 feet to a perch, to statute, multiply the number of square links, customary-measure, by 1.62, and the product will be the answer in square-links. 2.— As the lineal Irish perch is 21 feet, and the Irish square perch 441 feet ; the method of reducing English to Irish, or Irish to English measure is precisely the same as shewn in this Problem. z 4 344 laxd-sulvzying. fPmi VI EXAMPLES. 11:1 -rate, how manr acres. &c. BY RITLE 1 . A. R. P. 36 i ic 1 rr 7 w 5810 272^5 29054 1 1 5 1 ::-": --\-r 1 1 : : M 1581772 5( 35S 132S 4 .2581 : . : - i - - - - 2205 - - A . I;. 3Si: 3528 . 2992 . — ." 1 :" 5 ::~- 17a - V THE TABLE, A. B, P. .. = If 2 3.1 - = 3 - J..- IB. = 24 '-'.:- = 22 1 26.5 Ails. Ar - Section 111,) land-surveying. 345 2. Reduce 22a. 1r. 27p. customary, to statute-measure. BY RULE 2. A. R. P. 22 1 27 4 89 40 3587 441 3587 14348 14348 4,0 272.25)1581867.000,581,03 136125 41 145* 1 0. 3 ..28170 27225 94500 816*75 12825 BY NOTE 1. sq. links. 20a. = 2000000 2a. = 200000 1r. = 25000 27p. = 16875 2241875 1.62 4483750 13451250 2241875 36.31837.50 4 1.27348 40 10.93920 Ans. 86a. 1r. 10.9p. 3. Reduce 116a. 3r. 32p. English measure, to Irish measure. Ans. 72a. Or. 31 p. 346 EYING. Pari PROBLE! I : stomary Measure, cf 24 Feet to a Perek, and -rice Ye: TABLE IV. >----. o l^T " hit v. >i: Cast. Srat, C-5T. A 3 R. P. "?.' P. P. P. 1 1 ■:". - 1 2 0.-=- _ g : : : I :■;.? _ : 1.4 -3 10.? 4 1 22 :' 1 1.? 24 11.3 2 1 is .: 5 25 11.7 2 - o : ? 6 2.S 26 IS I - : I 9.3 J :-.: 27 12.7 > n ■:. S 25 13.1 4 1 0.6 - . 29 i ; : 10 4 2 3'?. 2 10 30 :: 9 1 :. i II . 5 31 ! 14 I'S.-f' 12 :- 15 : 40 18 •3 24.8 11 6.1 I : : :" 23 o .:.: 14 6.6 M 1-f.O ::" *7 1 - 15 16 i: 35 13.4 1*.0 Cus:: :-.- R. i\. r. 1 s 5.4 33 17 15.3 : o i - •:■ 37-S 2 ; 3 1 5 i ie.7 Aofe. — To lednee cnstomaiy-roeasaie, of 24 feet to a perch, to statute, nildrlv :cf r"ir_r;r ::' ; ::itIh.I: = . •: _-::n^r- ■■~-.:i — i. v ; - .".I:". -il Section III.) land-surveying. 347 EXAMPLES. 1. Required the number of acres, &c. customary-measure, in 269a. 2r. 12p. statute -measure. BY RULE 1. A. R. P. 269 2 12 4 1078 40 43132 272.25 215660 ^6264 86264 301924 86264 4Q 24 x 24 = 576)11742687.0012038.6.6 1152 4| 509.26.6 . . 2226 127a. 1r. 26.6p. Ans. 1728 . 4988 4608 .3807 3456 .3510 3456 54 BY THE TABLE. A. R. P. 200a. = 94 2 4 50a. = 23 2 21 30a. = 4 2 36.2 9a. = 4 1 0.6 2r. = 37.8 12p. == 5.6 127 1 25.2 Ans. 348 land-surveying. (Part VI, 2. In 127a. 1b. 26p. customary, how many acre?. &c statute- measure ? BY RULE 2. A. R. P. 127 1 20 4 509 40 20386 57 6 122316 142702 101930 4,0 272.25)11742336.00 4313 0.7 108900 4 10 78 10.7 ' ' ff?.?? 269a. 2r. IO.Tp. An?. OlOiO — . 35586 27225 .83610 81675 193500 190575 2925 BY THE NOTE. sq. links, 00a. = 10000000 20a. = 2000000 7a. = 700000 1R. = 25000 26p. = 16250 12741250 2,4157 89188750 6370625 1274125 1274125 S 548250 269.56662.6250 4 2.26648 40 10.65920 Ans. 269A. 2p. 10.6p. Section III.) land-surveying. 349 3. Reduce 587a. 3r. 39p. statute, to customary-measure. Ans. 277a. 3r. 27p. PROBLEM V. To reduce Statute Measure to the Wiltshire customary Measure, of 120 Perches to an Acre, and vice versa. Rule 1. — To reduce statute-measure to customary, divide the number of perches, statute- measure, by 120, and the quotient will be acres ; then divide the remainder by 30, and the quotient will be roods ; and the last remainder, if any, will be perches. If the first remainder be under 30, it will be perches, and there will be no roods in the answer. Rule 2. — To reduce customary-measure to statute, divide the number of perches, customary-measure, by 160, and the quo- tient will be acres ; then, divide the remainder by 40, and the quotient will be roods ; and the last remainder, if any, will be perches. If the first remainder be under 40, it will be perches, and there will be no roods in the answer. Note 1. — To bring customary acres, &c. into perches, multiply the number of acres by 120, and the number of roods by 30 ; these two products, added to the number of given perches, will be the number of perches required. 2. — In some parts of England, land is not only reaped and farmed, but also bought and sold by this measure ; and as the customary acre of 120 statute perches, or three statute roods, is frequently denominated a day's work or day- work of land, Surveyors are sometimes required to return the areas of estates in day's works, roods, and perches. 350 LAND-SURVEYING (Part VI TABLE V. Stat. Customary. Stat. Oust. Stat. Cust. j A. A. R. P, P. R. P. P. P. P. 1 i 1 10 1 1 21 21 2 2 2 20 2 2 22 22 3 4 3 3 23 23 4 5 1 10 4 4 24 24 5 6 2 20 5 5 25 25 6 S 6 6 26 26 7 9 1 10 7 7 27 27 8 10 2 20 8 8 28 28 9 12 9 9 29 29 10 13 1 10 10 10 30 1 o 20 26 2 20 11 11 31 1 1 30 40 o 12 12 32 1 2 40 53 1 10 13 13 33 1 3 1 50 66 2 20 14 14 34 1 4 100 133 1 10 1.5 16 17 15 16 IT 35 36 37 1 5 1 6 1 7 Stat. Customary. R. 1 A. R. P. 18 19 • 18 19 38 39 1 8 1 9 1 10 2 2 20 20 20 3 1 Xote. — In adding up the numbers taken from the above table, you must divide the number of perches by 30, and the number of roods by -1 ; because 30 perches of this measure make 1 rood, and 4 roods 1 acre, or 1 day's work, EXAMPLES. 1. In 165a. 3r. 26p. statute-measure, how many acres, &c. customary ? BY RULE I. A. R. P. 165 3 26 663 40 120)26546(221 240 254 240 146 120 726 Ans. 221A. Or. 26'p. Section III.) land-surveying. 351 BY THE TABLE. A. R. P. 100a. = 133 1 10 50a. = 66 2 20 10a. = 13 1 10 5a. = 6 2 20 3r. = 10 26p. = 26 221 26 Ans. 2. Required the number of acres, &c. statute-measure, in 221a. Or. 26p. customary. by rule 2. p. 221 X 120 = 26520 26 = 26 160)26546(165 160 1054 960 ..946 800 40)146(3 120 ?26 Ans. 165a. 3r. 26p. 3. In 265a. 2r. 24p. statute, how many acres, &c. customary measure ? Ans. 354a. Or. 24p. GENERAL RULES For constructing the foregoing Tables, and for finding the Mul- tipliers given in the Notes. Rule 1. — Divide the number- of square feet in an acre, statute-measure, by the number of square feet in an acre, customary -measure, and the quotient will be an acre and decimals, or decimals of an acre. Multiply this quotient 3 52 LAI EYING, (Part VI by 2, and the product will be the acres and decimals, customary-mowne, in 2 acres, statute-measure. Bring the decimals to their proper quantity, and you will have the acres, roods, and perches, customary -measure, in 2 acres, statute-measure. In a similar manner you must proceed with 3 acres, 4 acres, &e. Rule 2. — Divide the number of square feet in a rood, statute-measure, by the number of square feet in a rood, customary-measure, and the quotient will be a rood and decimals, or decimals of a rood. This quotient being multiplied by 2, the product will be the roods and decimals, customary - measure, in 2 roods, statute-measure. In a similar manner you must pro- ceed with 3 roods. Rule 3. — Divide the number of square feet in a perch, statute-measure, by the number of square feet in a perch, customary-measure, and the quotient will be a perch and decimals, or decimals of a perch. Multiply this quotient by 2, and the product will be the perches and decimals, cus- tomary-measure, in 2 perches, statute-measure. In a similar manner you must proceed with 3 perches, 4 perches, &c. Rule 4. — To find the multipliers given in the notes, say, as the number of square feet in an acre, statute-measure, is to an acre, so is the number of square feet in an acre, customary-measure, to the multiplier. Or, divide the number of square feet in a perch, customary-measure, by the number of square feet in a perch, statute-measure, and the quotient will be the multiplier. JN'ofc. — Table V. was constructed by Role 1, given in tee last Problem. REMARKS. 1. If a tenant rents a farm of 100 acres, reckoning 120 perches to an acre of tenantry measure, which is but 3 roods, statute-measure ; he loses 1 acre in 4, or 25 acres in the whole, which reduces his farm to 75 acres, statute -measure. 2. If a tenant takes a farm, in Devonshire or Somersetshire, of 100 acres, at the customary-measure of 15 feet to a perch ; he loses nearly 1 statute acre in 6 customary acres, or IT acres, 1 rood, 17 perches, in the whole, which reduces his farm to 82 acres, 2 roods, 23 perches, statute -measure. 3. If a tenant rents a farm of 1 00 acres> in Cornwall, at the customary-measure of 1 8 feet to a perch ; he gains about 1 statute acre in 5 customary acres, or 19 acres, roods, 1 perch, in the whole ; consequently, his farm contains 119 acres, roods, 1 perch, statute-measure. ■i. If a tenant takes a farm of 100 acres, in Lancashire, reckoning 21 feet to a perch, customary-measure; he gains Section III.) land-surveying. 353 nearly 2 statute acres in three customary acres, or 61 acres, 3 roods, 37 perches, in the whole; hence, his farm contains 161 acres, 3 roods, 37 perches, statute-measure. 5. If a tenant rents a farm of 100 acres, in Cheshire or Staf- fordshire, reckoning 24 feet to a perch, customary-measure ; he gains nearly 16 statute acres in fourteen customary acres; or 111 acres, 2 roods, 1 1 perches, in the whole ; hence, his farm contains 211 acres, 2 roods 11 perches, statute-measure. 6. Three acres, statute-measure, are equal to 4 acres, Wilt- shire measure. — Fire acres, statute-measure, are equal to 6a. Or. 8p. Devonshire and Somersetshire measure. — Six acres, statute-measure, are equal to 5a. Or. 6£p. Cornwall measure. — Five acres, statute-measure, are equal to 3a. Or. 14p. Lancashire measure. — Thirty acres, statute-measure, are equal to 14a. Or. 28|p. Cheshire measure. SCOTCH MEASURE. In Scotland, land is generally measured by a chain of 74 feet in length, which is divided into 100 equal links, the same as the English chain. The area is given in acres, roods, and falls; 342.25 square feet making 1 fall, 40 falls 1 rood, and 4 roods 1 acre. TABLE YI. A Table of Scotch Lineal Measures. Inches. 8.88 1 Lk. 12 1.35 1 Foot. 1 Ell. 3? 4.16 3.08 222 25 18.5 6 l Rd. 88.8 100 74 24 4 1 Chain. 71040 8000 5920 1920 320 80 1 Mile. Note. — It appears by comparing the above Table with that given in Part III., that the Scotch ell is 1 inch more than the English yard ; and the Scotch mile 640 feet more than the English mile ; but by a statute of James II., it was enacted that the Scotch mile, like the English, should contain 1760 yards. A a 354 LAND-SURVEYING. TABLE VII. ^4 Table of Scotch Square Measures, (Part VI. Sq. Inches. 78.8544 144 1 Sq. Lk. 1.82 1 Sq. Ft. •v 1369 17.36 9.51 IS. Ell. 49284 625 342.25 36 IS. Fall. 1971360 25000 13690 1440 40 1 S.Rd. 7885440 100000 54760 5760 160 4 ■ lS.Acre. Note. — By comparing the above Table with that given in Part III., W8 find that the Scotch fall contains 70 square feet more than the English statute perch ; and the Scotch acre 1 1200 square feet more than the English statute acre ; hence 1089 Scotch acres are equal to 1369 English acres. TABLE VIII. A Table fen* reducing English to Scotch Measure, Eng. Scotch. Eng. Scotch. En£. Scotch. Acs. A. R. F. P. Falls. P. Falls. 1 3 7.3 1 0.8 r 21 16.8 2 1 2 14.5 2 1.6 22 17.5 3 2 1 21.8 3 2.4 23 18.3 4 3 29.1 4 3.2 24 19.1 5 3 3 36.4 5 | 4.0 25 20.0 6 4 3 3.7 6 4-8 26 20.8 7 5 2 10.9 7 5.6 27 21.5 8 6 1 18.2 8 6.4 28 22.3 9 7 25.5 9 7.2 29 23.1 10 7 3 32.8 10 8.0 30 24.0 20 15 3 25.5 11 8.8 31 24.8 30 23 3 18.3 12 9.6 32 25.4 40 31 3 11.0 13 10.3 33 26.2 50 39 3 3.8 14 11.1 34 27-0 100 79 2 7.5 15 16 17 12.0 12.8 13.5 35 36 37 27.8 28.6 29.4 Eng. Scotch Rds. R. F. 18 19 14.3 15.1 38 39 30.2 31.0 1 31.8 2 1 23.6 20 16.0 3 2 15.5 Section 111.) land-surveying. 355 Note 1 . — The General Rules given in the beginning of this Section, may be applied in reducing English to Scotch, or Scotch to English measure. 2. — Scotch measure may also be reduced to English statute-measure, by multiplying the number of square links, Scotch measure, by 1.2571 ; and the product will be the answer in square links. i EXAMPLES. 1. In 45a. 2r. 23p. English statute-measure, how_ much Scotch measure ? BY RULE I. A. R. P. 45 2 23 4 182 40 7303 272.25 = 16,5 36515 14606 14606 51121 14606 4,0 342 .25)1988241.75 171125 a 580,9.3 i ±k q r- X 16.5 ? 7 J 9 ?} 36a. 1r. 9.3f. An*. 319175 308025 111500 102675 . . 8825 BY TABLE VIII. A. R. F. 40a. = 31 3 11 5a. = 33 36.4 2r. = 1 23.6 23p. = 00 18.3 36 1 9.3 Ans. 2. In 36a. 1r. 9.3f. Scotch measure, how much English mea- sure ? A a 2 356 land-surveying. (Part VI. BY RULI .2, A. R. F, 36 1 9.3 4 145 40 5809.5 342.25 290465 116186 116186 232372 174279 272.25)1988232.925 190575 4 7302.9 182 22.9 45a. 2r, 22. yp. Am 81675 ■ 80792 54450 263425 24502 5 18400" BY NOTE. 2 30a. = 3000000 6a. = 600000 1r. = 25000 9p. = 5625 ^p. = 187.5 3630812.5 1.2571 36308125 254156875 181540625 72616250 36308125 45.64294.39375 4 2.57176 40 22.87040 Am 45a. 2r. 22.gr. Section III.) land-surveying. 357 3. Reduce 102a. 3r. 38p. of English statute-measure, to Scotch measure. Ans. 81a. 3r. 27.7p. 4. In 52a. 2r. 3Gf. Scotch measure, how many acres, &c. English measure ? Ans. 66a. Ir. 5 p. IRISH MEASURE. In Ireland, land is measured by a chain of 84 feet in length, which is divided into 100 equal links, the same as the English chain. The area is given in acres, roods, and perches, the same as in England; but the Irish perch contains 168.75 square feet more than the English perch ; and 98.75 square feet more than the Scotch fall ; consequently, the Irish measure is greater than either the English or the Scotch measure. TABLE IX. A Table of Irish Lineal Measures. Inches. 10.08 1 Link. 12 1.19 1 Ft. 36 3.57 3 1 Yd. 252 25 21 7 lPch. 1008 100 84 28 4 lChn. 80640 8000 6720 2240 320 80 1 Mile. Note. — By comparing the above Table with that given in Part III., we find that the Irish mile is 480 yards more than the English mile J hence 11 Irish miles are equal to 14 English miles. a a 3 358 land-surveying. (Fart VI. TABLE x. A Table of Irish Square Measures. Sq. Indies. | 101.6064 1 Sq. Lk. 144 1.42 1 Sq. Ft. 1 1296 12.78 9 lS.Yd. 49 1 63504 625 441 lS.Ph. 1 2540160 25000 17640 1960 40 lS.Rd. 10160640 100000 70560 7840 160 4 IS. Ac! • Note 1. — By comparing the above Table with that given in Part III., we find that the Irish perch contains 168.75 square feet more than the English statute perch ; and the Irish acre 3000 square yards more than the English acre j hence 121 Irish acres are equal to 196 English acres. 2. — Irish measure may be reduced to English, or English measure to Irish, by Problem III. 3. — Scotch measure may be reduced to Irish, or Irish measure to Scotch, by the following rule : As the square feet in a square perch of the required measure, is to the given area in perches ; so is the square feet in a square perch of the given measure, to the required area in perches. 4. — The rule given in the last note, is the substance of the two General Rules given in the beginning of this Section : and will hold good for all kinds of measures. The Rules given in this Wo?~k,for Jin ding the Areas of Figures, and Dividing Land, are applicable in all cases of Land- Surveying. As both the Scotch and Irish chains are divided into 100 equal parts, the same as the English chain ; it is manifest that Section III.) land-surveying. 359 the Rules given in this Work, for finding the areas of figures, and for laying out, parting-ofF, and dividing land, are applicable in all cases of Surveying, whether the dimensions be taken with the English, Scotch, or Irish chain. They also hold equally true, if the dimensions be taken in yards, tenths, and hundredths ; in feet and tenths ; or in any other denominations. EXAMPLES ENGLISH, SCOTCH, and IRISH MEASURES. 1. The base of a triangular field, measured by the English chain, is found to be 1252 links, and the perpendicular 684 links ; what is the area of the field, in statute-measure ? links. 1252 684. 5008 -1 . 10016 7512 2) 856368 4.28184 4 1.12736 40 5.09440 Ans. 4A. Ir. 5p. 2. Reduce 4a. Ir. 5p. English measure, to Scotch and Irish measure. Reduced to Scotch Measure by Table VIII* A. R. F. 4a. = 3 29.1 Ir. = 31.8 5p. =0 4.0 3 1 24.9 Ans. A a 4 360 land- surveying. (Part VI. Reduced to Irish Measure, by Talk III. A. it. p. 4a. = 2 1 35.0 lR. = 24.7 5p. = 3.0 2 2 22.7 Ans. — 3. The base of a triangular field, measured by the Scotch chain, is 1252 links, and the perpendicular 084 links; required the area of the field in Scotch measure. links. 1252 084 5008 10016 7512 2)856308 4.28184 4 1.12730 40 5.09440 Ans. 4a. 1r. 5p. Note. — Here the area is the same as that found in the first example. 4. Reduce 4a. 1r. 5f. Scotch measure, to English and Irish measure. Reduced to English Measure, by Note 2, under Table VIII. sq. links. 4a. = 400000 1r. = 25000 5f. = 3125 428125 1.2571 428125 2990875 2140025 850250 428125 5.38195.9375 4 1.52780 40 21.11200 Ans. 5a. 1r. 21. 1p, Section III.) LAND-SURVEYING. 36 1 Reduced to Irish Measure by Note 3, under Table X. A. R. F. 4 1 5 4 vT sq. ft. J5 sq.ft. As 441 : 685 :: 342.25 342.25 3425 1370 1370 2740 2055 4i0 441)234441. 25j53,1.61 2205 4 I 13 16.1 . 1394 3A . 1r. 16. lp. An&, 1323 ~711 441 2702 2646 "565 441 124 5. The base of a triangular field, measured by the Irish chain, is 1252 links, and the perpendicular 684 links; what is the area of the field in Irish measure ? links. 1252 684 5008 10016 7512 2)856368 4.28184 4 1.12736 40 5.09440 Ans. 4a. 1r. 5p. Note. — Here the area is the same as that found in the first and third ex- amples, which proves that the Rules for finding the areas of figures hold good for all kinds of measures. o62 UNI- SO] LVKYTS P H VJ 6. Redoce 4a. 1b. dp. Irish measure, to flogHiA and fit oil ■ !L- :.::::. F-. ; :-'.-■ ;■. £■■/ _'/ • ;/ . ■-. ." . V -. -. ■ /•_.', _T B. P. I ' I r: i_ ;,- :'- 141 685 274 - - - 1 ' - «o U 4i 27 2 27 225 - 1 : . ; : i - - • : : _. ' ".23625 Reduced to Scotch Measure lu ." .nder TaV X r sq. p. sq. : K3 25 »5 :: 141 I4J — 5 *74 !^ 1 -7 - : 7 .i_ j _ _ f r 7 — The length of a rectangular field, measured by the English chain .. i its breadth 923 link*; required the area of the field, in English, Scotch, and Irisk measnre. Section III.) land-surveying. 363 Ans.' 13a. Or. 39p. English measure ; 10a. 2r. 5. 6f. Scotch measure ; and 8a. Or. 2 8 p. Irish measure. 8. A Land-Surveyor is required to measure a triangular field, and to return the area in English statute-measure ; but not having an English chain, he found the base of the field to mea- sure 1548 links, and the perpendicular 924 links, by a Scotch chain; required the area of the field in English statute-mea- sure. Ans. 8a. 3r. 38. 4p. GAD MEASURE. In some places the dimensions of land are taken, by farmers, workmen, &c. with a pole or staff of 8, 9, or 10 feet in length, called a Gad ; hence the square gad of 8 feet, contains 64 square feet ; the square gad of 9 feet, 81 square feet ; and the square gad of 10 feet, 100 square feet. When the area of a piece of land is wanted in gad -measure, the dimensions, taken in gads and feet, must be brought into feet ; from which the area, in square feet, may be obtained, by the rules already given. Divide this area by 64, 81, or 100, respectively; and the quotient will be the number of square gads ; and the remainder will be square feet. If the remainder be multiplied by 4, and divided as before, the quotient will be I, i, or | of a gad. If, however, the gad be decimally divided, the dimensions mil be taken in gads and tenths, and the rules will then give the area, in square gads and decimal parts. The decimals may be reduced to their proper quantity by multiplying them by the number of square feet in a gad ; or to quarters of a gad, by multiplying them by 4, as before directed. Note 1. — Gad-measure may be reduced to English statute-measure, by the following Rule : As 272.25, the square feet in a square perch, statute-mea- sure, is to the given area in gads ; so is the square feet in a gad of the given measure, to the required area in perches. Or, divide the square feet in the given area, by 272.25 ; and the quotient will be the answer in square perches, statute-measure. 2. — To reduce statute-measure to gad-measure, divide the given area in 364 land-surveying. (Part VI. square feet, by the number of square feet in a gad \ and the quotient will be the answer in square gads. EXAMPLES. 1. The length of a rectangular piece of land, measured with the eight-feet gad, is 45 gads, 5 feet ; and its breadth 21 gads, 3 feet ; required its area in square gads. 8x8 G. F. G. F. 45 5 21 3 8 8 365 171 171 365 2555 365 C4)62415)975g. 15f. Ans. ^7ft : — : — — 481 448 335 320 . 15 rem. 2. The area of a piece of ground, measured by the eight-feet gad, is found to be 975 gads, 1 5 feet; required its area in sta- tute-measure ? BY NOTE 1. G. F. 975 15 64 3905 5851 4 ?0 272.25)62415.00| 22 ( 9.25 54450 4 | 5 29 i 79650 54450 : 252000 245025 69750 54450 153000 136125 7l6875 rem. 1a. 1r. 29ip. Ans. Section III.) land-surveying. 365 3. The area of a piece of land is 1a. 1r. 29|p. statute-mea- sure ; what will be its area in square gads, if it be measured by the eight-feet gad ? by note 2, A. R. P. 1 1 29.25 4 40 229.25 272.25 114625 45850 45850 160475 45850 64)62413.3125(9750. 13.3F. Ans, 576 =z= .481 448 ~333 320 . 13.3 rem. 4. The base of a triangular field, measured with the nine -feet gad, decimally divided, is 58.7 gads, and the perpendicular 26.9 gads; required the area of the field, in gad, and also in statute-measure ? Here, 58.7x26.9=1579.03; and ^ — = 789.515, the area in gads; and by Note 1, as 272.25 feet : 789.515 gads :: 81 feet : 234.89 perches = 1a. 1r. 34.89p. the area in statute-mea- sure. 5. The length of eight lands, forming a furlong in an open field, is found, by the ten-feet gad, to be 118.7 gads, and their breadth 12.4 gads ; what is the area of the furlong ? Ans. 1471.88 gads = 3a. Ir. 20.6p. statute-measure. 6. The diagonal of a trapezium measures 56.2 gads, by the 366 LAND-SURVEYING. (Part VI. ten-feet gad, one of the perpendiculars 21.4 gads, and the other 18.3 gads; required the area of the trapezium? Ans. 11 15. 57 gads = 2a. 2r. 9.?p. statute-measure. ESTIMATING LAND BY THE MILE. The Method of making a rough Calculation of the Number of Acres contained in a Common, Moor. Lordship, County, or Kingdom, Endeavour to ascertain, in miles, as nearly as you can, either by your own observations, or from the information of others, the mean length and breadth of the land to be estimated ; then multiply the length by the breadth, and the product will be the area in square miles. Multiply this area by 640, the number of acres in a square mile ; and the product thus obtained will be the area in acres, according to this method of calculating. Note 1. — The mean length and breadth of a county or a kingdom, may be found from a map, in the following manner : Measure several lengths, by the scale of miles, upon the map ; add them together ; and divide their sum by their number, for a mean length. A mean breadth may be obtained by a similar process, 2. — The foregoing method of finding the area of counties and kingdoms, must of course, be liable to considerable inaccuracy, not only as regards the method of taking the dimensions, but also as respects the correctness of the map and scale ; for it is evident that if these be not truly delineated, the dimensions can never be obtained to any degree of accuracy. 3. — When you have a correct map and scale of a county or a kingdom, its content may be found to a considerable degree of accuracy by the following method : Divide the map into triangles and trapeziums in the most convenient manner ; and straighten the crooked shores or coasts, either with a lantern horn, as directed in Part IV., or by the parallel ruler, as directed in Part V. Measure the bases, diagonals, and perpendiculars correctly, by the scale of miles belonging to the map ; find the area of each figure separately • and the sum of these areas will be the whole area required* Section III.) land-surveying. 367 EXAMPLES. 1 . Suppose the mean length of a common or moor be esti- mated at 3} miles, and its mean breadth at 2± miles ; what is the area in acres, according to this estimation ? miles. 3.75 2.25 1875 750 750 8.4375 miles. 640 3375000 506250 5400.0000 acres. Ans. 5400 acres. 2. If the mean length of a lordship be estimated at 4| miles, and its mean breadth at 2 J miles; what is the content in miles and acres? Ans. 10.625 miles, and 6800 acres. 3. The mean length of a county, found from a map, is 63 miles, and its mean breadth 42 miles ; what is its area in miles and acres ? Ans. 2646 miles, and 1693440 acres. 4. Mr. Pinkerton says, in his Geography, that the content of Ireland is computed at 27457 square miles ; Avhat is its area in acres? Ans. 17,572,480 acres. 5. According to Mr. Pinkerton, the content of Scotland is computed at 27793 square miles ; required its area in acres. Ans. 17,787,520 acres. 6. The same author observes, that the extent of England and "Wales is computed at 58335 square miles ; what is the area in acres ? Ans. 37,334,400 acres. 368 land-surveying. (Part VI. Note. — The real quantity of land in England is very uncertain ; and dif- ferent writers have given very different statements. Dr. Greve, in the Philo- sophical Transactions, No. 330, states the number of acres in England at 46,000,000 ; but Sir William Petty, in his Political Arithmetic, states them at no more than 39,000,000. Dr. Halley's statement is also 39,000,000 acres ; but Zimmerman's statement, in his Political Survey, is only 34,631,080. Dr. Grew's statement stands at 46,800,000 ; and in the Gentleman's Maga- zine, for July, 1804, is a statement made from Smith's County Maps, by which the area is estimated at 32,134,400 acres. Now, if we take this number from the area of England and Wales, found in the last example, we shall have 5,200,000 acres for the area of Wales, LAND-SURVEYING. The Method of Measuring and Planning Villages, Towns, and Cities ; Directions for Measuring and Planning Building Ground, and Dividing it into con- venient Lots for Sale ; and Miscellaneous Questions relating to Surveying, Laying-out, Parting-ojf, and Dividing Land. SECTION I. THE METHOD OF MEASURING AND PLANNING VILLAGES, TOWNS, AND CITIES. As villages, towns, or cities, present themselves in almost every extensive survey, and are generally measured and planned with the adjoining or surrounding lands, it is highly necessary that something should be said on the method of taking and laying down the dimensions of such places, and finishing the plans. Besides, the plans of towns and cities are so essentially neces- sary for the purposes of commercial and general reference, that Surveyors are not unfrequently employed in forming correct drawings of the same, in order to have them engraved and published in copperplates. Without this art, we could not obtain the ichnography of towns and cities ; neither could we have any just idea of the shape, extent, and direction of the streets ; the size and number of the public buildings ; the local conveniences enjoyed by the inhabitants, &c. &c. of those places which circumstances will not permit us to visit. Bb 370 LAND-SURVEYING. (Part VII. Directions for taking the Dimensions of Villages, Toicns, and Cities. The dimensions of villages, towns, and cities, may generally be obtained by the chain only ; as the streets are usually wide enough to admit of angles or tie-lines being taken -with the chain, at the meetings or intersections of the streets, in the same manner as directed in Problems 4 and 5, Part IV. In these Problems the methods of measuring meres, woods, roads, rivers, and canals, are clearly illustrated and exemplified ; and if the learner make himself completely master of those depart- ments of Surveying, any difficulties which may present them- selves in measuring villages, towns, or cities, will be easily sur • mounted. It will sometimes happen that the tie-lines cannot be mea- sured at a greater distance from the angular points than 30 or 40 links. In such cases, the tie-lines must be taken to a quar- ter of a link, and both them and the angular distances must be multiplied by 2, 3, 4, or any larger number, as circumstances may require ; and the products used in laying down the chain- lines. (See Prob. 2, Part IV.) The notes taken in measuring towns and cities must be en- tered precisely in the same manner as in surveying estates ; and in measuring along the streets, offsets must be taken to the houses on both sides of the chain-line ; and particularly to every corner and projection ; even the small projections of bow-windows must not be omitted. Sketches of the bases of the buildings, particularly the corners and projections, must be made in the margin of the note-book, in order to assist the Surveyor in drawing a correct plan. All public buildings, such as churches, prisons, castles, court- houses, market-places, halls, colleges, mansion-houses, &c. &c. must be distinctly noticed ; and the range of the first line should be taken with the compass, in order that the Draftsman may be able to lay down every street in its true direction. Note 1 . — In measuring alonj: the streets, all the offsets to the buildings must be taken at right-angles to the chain-lines. The bases of the buildings, and all the projections must be sketched, as you proceed ; and the breadths r»f the buildings, the lengths and breadths of the projection?, fee. fee. must Sectio?l I.) LAND-SURVEYING. 371 be correctly measured, and entered opposite to those parts of the sketch to which they respectively belong. The sign 4- (plus) is usually placed between the breadth of a building, at its perpendicular distance from the chain-line- The method of sketching the bases of buildings, and entering the notes, is exemplified in pages 4, 10, and 12, of the engraven Field-book, to which the learner is referred. 2. — When a town and the surrounding or adjoining lands are both to be measured and planned together, the dimensions must be taken with Gunter's chain ; and the lines measured along the streets must be properly connected with those measured in surveying the adjoining estates ; but if the plan of a town only is required, it is more convenient to take the dimensions with a chain of 50 feet in length, divided into 50 links, and an offset staff of 10 feet in length. 3. — As station staves cannot be fixed in the streets, in consequence of the pavement, they must either be set in wooden pedestals, made for that pur- pose, or two or more assistants must each hold a staff in those places that are pointed out by the Surveyor. 4. — Sometimes it is most convenient to measure external or main-lines, on the outside of the town, as in surveying a mere or wood, Prob. 4, Part IV. ; and in running such lines, stations must be left at the ends of the streets, as you pass them, in order that lines may be run from one station to another in measuring the streets. 5. — In some situations, and under certain circumstances, it is more eligible to measure the first line along one of the principal streets ; and to intersect this line by another, measured along some other principal street, nearly at right-angles with the former ; then these two lines being tied together by a connecting line, measured in the most convenient manner, will divide the town into four parts, each of which may be measured separately, by running lines in the most advantageous manner. (See a similar remark in Note 5, Method I. Part V.) 6. — In putting down stations at the ends of the streets, &c. the number of the station may be made upon the wall of the opposite building, (if there be one,) with red or white chalk, in such a situation that an offset may be taken, at right-angles to the building, from the station marked upon the wall, to the station on the chain-line. This offset being entered in the book, and again measured from the station on the wall, at right-angles to the building, will give you the station on. the chain-line, whenever you may want to find it. 7. — When the foregoing method cannot be adopted in consequence of not being able to take a right angled offset from any building to the station which you wish to fix, then two lines may be measured from the statiou to Bb 2 b~2 i.A\'D-suRvtv.\\- (Part VII. or to any other parts of two adjoining buildings ; and the in- of these lines, when measured from the buildings, will give the r -: _ --. : - — _-_--.}r :.'.'. -'z- 77.7 - - ■ ' ---::- = '::.-- '~: ^7 7- -: ; :7 ; : . :'r.r- 77: :f:i :: the smaller and intermediate streets ; and lastly to the lanes, alleys, courts, yards, and every other part which it may be thought necessary to r c sent upon the plan. 9. — When any of the streets are so narrow as not to admit of tie-lines "7.7.7. :ik-7~7:7 "7_r ••" ~.z- . t_t:-t; ~z:.z :z: :'. z~-Z-~zzz--. 77777 ~ .:::;:: ■:t.t7. 7: -Zz 77.7 :7.:r- 7 :::::-::: .75 : 77 77777: - 77:.: '^ -.zziz zz If- grees and minutes, by a theodolite ; and in planning, they most be hud down as directed in Problems 20 and 21, Part I. (See the Description of die T~-e: i'l.r. 7777 : 74 10. — "VThas has been advanced on tins subject will, no doubt, be aecepi- - .7 :: 't77t_77- "__: : = : :~ :_- 7: - ' zz: : ::77 -7:7. z z^z_- ::' 7 ".; 7-. 77:1 : 7— 7777- ■ - 77 - : —_:J7 177 :Ji7ir :': 7777=. n: I7 ::. : n= zzzz '7 z\~-z\ :'zz: -■_". 7 7 7 7: 1- : . *:_7 :: 7-777 7-~ -— - ::-•: '-'- '~ t zz~: ~z:~z 77 77^:77:7. A 7: :-:: ii-zl ~zLL z~z\ 7 777777 ~: :~ -7.7 777.: 777 7:77777: :: :'z- ~ 77-77 :r. who should, after duly examining every part of the town, endeavour to run 7.r \\Z\-- 77 :77 77!-: 7 Z':ZZ': Z~ 7: 7_77 77 7 7 Let it be required to measure the >~ 1 nra, No. 7, r -: VII. _:. -z-: :: :''. ~ -.:_--- : l-> ._-_' -; ". in X::-r -r. " r 5J12II begin at the south-west corner, as in Problem 4, Fir: TV.; -■.'.-.'l: '-Li- :i: - : :- I - zi ::;->". 7 in :"-f sin:- manner. if we begun at any other corner. F 1 z ■:.-. "."Ti — 1. : -Ir •" •iris :'z~ z I rz\-z : : :..._ f- ;-> :■: :i_f ' .:. tere- r it is necessary ; and sketching their bases in the margin of the note-book. At the end of High Street, 1 ui down — _ :-.: '^:..7 S: : i: L ; n-:. — ^ . -.- :L-r >. E. corner, -f- 5 ; and produce the Kne at pleasure, to — Second Lime. From -f 5, proceed towards the N . W. corner; but when you arrive at the end of Y rk Street, put down -f- and thence run a tie-line to -f- 6. From -f- ?, proceed with the main-line : and ax Km, Street, put down -{- 8 ; at George Street, + 9 ; at the N. W. comer, — 10; and continue the Hue to -f 11. Section I.) land-surveying. 373 Third Line. From + 10, go towards the N. "W. corner; but when you come to the end of Low Street, put down + 12, from which run a tie -line to +11. Proceed from + 12 ; and at the end of Queen Street, put down + 13 ; at High Street, + 14 ; and at the N. W. corner, + 15. Fourth Line. From + 15, proceed towards the S. W. cor- ner ; and at the end of George Street, put down + 16; at King Street, + 17 ; at York Street, + 18 ; and continuing the line to + 1, you will have circumscribed the town with four main-lines, into which the lines measured along the streets must be run. Note. — After the first three lines are laid down, it is evident that the fourth line will serve as a check ; and will reach exactly from + 15 to + 1, if all the operations have been conducted with accuracy. Fifth Line. From + 18, through York Street, to + 7. Sixth Line. From + 8, along King Street, to + 17. Seventh Line. From + 16, through George Street, to + 9. Eighth Line. From + 12, along Loav Street, to + 4. Ninth Line. From + 3, through Queen Street, to + 13. Tenth Line. From + 14, along High Street, to + 2 ; thus the survey of the town is completed. Note 1. — The chain-lines and stations do not appear upon the plan, as they could not have been conveniently entered without increasing its size ; the learner will, however, find no difficulty in making a similar plan, two or three times as large ; drawing the chain-lines, and putting down the stations in their proper places. Or he may take the dimensions of the given plan with a small scale ; enter them in a note-book ; and then draw a rough plan by a larger scale, and after that a finished one, which will be an exercise that will tend much to his improvement. 2. — The survey of this town might have been carried on according to the directions given in Note 5, by measuring a line through King Street, and another through Queen Street ; and then connecting these two lines together by tie-lines taken at the point of intersection. Thus would the town be di- vided into four parts, each of which might be measured separately. 3. — Here it will be proper to observe, that in taking an angle with the chain or theodolite, at the intersection or meeting of two lines, either the external or internal angle may be taken, as circumstances may make it most convenient ; but it should always be remembered, that neither very acute nor very obtuse angles should be measured, if it can be avoided, as both are liable to errors, in laying down. Those angles which approach nearest to right-angles should always be preferred, as being most correct. B b 3 :J74- LAND-SURVEYING. (Pari VII. 4. — By way of proof, it is an excellent plan to take both the angles. If they be taken by the chain, you will have a check-line, by the scale ; and if taken by the theodolite, their sum should be 180 degrees ; and you will also have a proof in planning, in consequence of having measured an angle and its supplement. (See Definition 16, and Problems 20 and 21, Part I.) A Descry . ./" Theodolite. The theodolite is a mathematical instrument used by Sur- veyors, for taking horizontal-angles, in measuring meres, woods, roads, rivers, canals, villages, towns, cities, &c. Sec. when tie- lines cannot be taken by the chain, in consequence of ob- structions. It also enables us to take such angles as are neces- sary for calculating the heights and distances of remote objects by plane trigonometry. There are various forms of this instrument, arising from the successive improi sments of many eminent artists ; but the prin- eiple of its operation is the same in all, whatever difference may appear in the construction. A theodolite of the best kind consists of the following prin- cipal parts : 1 . A telescope to direct the sight, and enable the operator to distinguish objects at a distance. To the telescope is attached a sperit-level, to assist the operator in placing the instrument in a horizontal position. 2. A vertical arc for taking angles of altitude and depression. One side of this arc is graduated to every half degree ; and these are again subdivided to every minute of a degree by the index or nonius. This side is numbered from to 90 decrees towards the eye-end, for angles of altitude ; and from to 50 degrees, towards the object-end, for angles of depression. The other side of the vertical arc contains a line of divisions, showing the number of links to be deducted from each chain's length, in measuring up or down any ascent or descent, in order to reduce it to a true horizontal line, according to the directions given for surveying hilly ground, Method I, Part IV. 3. A horizontal limb and compass, for taking horizontal- angles, and the bearings of objects. Section I.J land-surveying. 375 The horizontal limb consists of two circular plates, one mova- ble on the other ; and the outer edge of the upper plate con- tains an index to the degrees and minutes on the lower plate. The upper plate, together with the compass, vertical arc, tele- scope, and level, are easily turned round upon a centre. The lower plate of the horizontal limb, is divided to half de- grees ; and these are again subdivided, by the scale of the no- nius, to every minute of a degree. This limb is numbered from the right-hand towards the left, with 10, 20, 80, 40, &c. to 3S0 degrees. 4. The whole instrument fits on the conical ferril of a strong, brass-headed staff, with three substantial wooden legs, by which it can be firmly fixed upon the ground. The top or head of the staff, consists of two brass plates, pa- rallel to each other ; and four screws pass through the upper plate, and rest upon the lower plate. By the action of these screws, the situation of the upper plate may be varied, so as to set the horizontal limb truly level, or in a plane parallel to the horizon. Note 1. — The compass is fixed on the tipper plate of the horizontal limb ; and the ring of the compass is divided into 360 degrees, which are numbered in a direction contrary to those on the hox'izontal limb. The bottom of the compass-box is divided into four parts or quadrants, each of which is subdi- vided to every 10 degrees ; and numbered from the meridian, or north and south points, each way, to the east and west points. In the middle of the box is a steel pin, finely pointed, on which is placed the magnetic needle. The box also contains a small sperit-level, fixed at right-angles to that which is attached to the telescope. By the assistance of these two levels, and the four screws before mentioned, the instrument can be placed in a truly hori- zontal position. (See the Description of the Compass, Part II.) 2. — The method of using the theodolite may soon be acquired by a little practice in the field ; but it will be obtained still more easily if the learner be assisted by the instructions of a practical operator. 3. — When trigonometrical calculations are to be made from the angles, they should, if possible, be taken to a minute ; but an instrument that will take an angle to five minutes will answer very well for a practical Surveyor ; as angles cannot be laid down nearer, either by the line of chords or the protractor. 4. — In order to lay down an angle by the protractor, draw a line at plea- sure, for one side of the angle ; apply the diameter of the instrument to this B b 4 376 land-surveying. (Part VII. line, and its centre to the point where the angle is co be made ; mark the point under the given degree, and through this point draw the other side of the angle. 5. — To measure a given angle by the protractor, apply the diameter to one side, and the centre to the angular point ; and the degree of the limb under which the other side passes, is the measure of the angle. (See Problems 19, 20, 21, 22, and 23, Part I.) 6. — The following prices stand in Mr. Jones's Catalogue, for theodolites of different kinds ; viz. a common theodolite, without rack-work, the hori- zontal limb six inches in diameter, eight guineas. Ditto, with rack-work movements, and which will take angles to two minutes of a degree, twelve guineas. Second best 7 or 8-inch theodolites, which will take angles to a minute, sixteen guineas, and =£22 : Is. Very best improved ditto, £33 : 12s, Eight-inch ditto, £37 : 16s. Nine-inch ditto, £42. Directions for Planning Villages, Toicns, and Cities. All the main-lines must first be laid down ; and the stations upon them marked off. The lines measured along the streets must then he drawn ; and the stations upon them denoted, The bases of the buildings must next be laid down from the offsets, so as to form the streets; and shaded as directed in Part Y., and exhibited in Plate VII, The rough plan must then be transferred to a clean sheet, by some of the methods described in Part Y., in order to make a finished plan. The bases of all public buildings, such as churches, castles, prisons, session-houses, market-places, infirmaries, hospitals, mansion-houses, monuments, &c. &c. should be delineated upon the plan with the utmost correctness ; and most Surveyors draw the bases of the columns which support the roofs of market- crosses, the galleries of churches, &c. &c. as exhibited in the plate to which we last referred. The streets are usually left white ; but some draftsmen pre- fer colouring the causeways, with a tint of blue, to distinguish them from the carriage-roads, which are generally washed with a yellowish brown. The grass-plots, in gardens, public squares, &c. &c. whether they be rectangles, rhombuses, circles, ovals, or regular poly- gons, should be correctly delineated upon the plan; then shaded with Indian ink, and washed with green- *- *he same Section I.) land-surveying. 377 manner as pasture-grounds ; and trees, water, pleasure-grounds gardens, gravel-walks, &c. &c. must be shaded and coloured as directed in Part V. The name of the village, town, or city, should he given in conspicuous characters, in some vacant part of the plan or map ; and the names of all the streets, public squares, churches, colleges, halls, prisons, castles, court-houses, mansion-houses, market-places, lanes, alleys, courts, yards, &c. &c. must be en- tered in their respective situations, in the manner exhibited in Plate VII. Note 1. — If the dimensions be taken and laid down in feet, a scale of feet must be given ; if in yards, a scale of yards must be given ; if in chains and links, a scale of chains and links must be given ; and if the town or city be very large, a scale of miles and furlongs may be given upon the plan, for the purpose of measuring distances ; and as 220 yards make a furlong, the dis- tance of one place from another maybe easily obtained in miles and yards. 2. — Any remarks or explanations that it may be thought necessary to give, may be entered in some vacant corner of the plan. 3. — All plans, ornaments, &c. should first be drawn in pencil ; and it will tend much to the improvement of the learner, if he form all his printing, German text, and large-hand letters by the pencil also, and then finish them with Indian ink. 4. — In forming letters, ornaments, &c. with the pencil, the lines and strokes should be made as fine as possible ; as the ink frequently runs upon the lead, when the pencil has been used too freely ; hence the necessity of applying Indian rubber after the outlines have been finely drawn with Indian ink, in order to remove the lead which is not covered by the ink, before we proceed to finish the letters, ornaments, &c. 5. — If the pupil does not succeed well in his first attempt with the pencil, the letters, ornaments, &c. must be effaced with Indian rubber ; and he must repeat the process until he can form all the letters, devices, &c. correctly. (See Note 6, Page 250.) 6. — Brookman and Langdon's prepared lead pencils, marked F, for fine drawing, will be found to answer well in making letters, ornaments, &c. ; as they are of a middling degree of hardness ; consequently the marks made by them may be easily effaced. (See Note 4, page 209.) 7. — After practice has made the learner a proficient in penmanship, he will be able to print, text, and write more expeditiously, without the use of the pencil. 8. — Here it may not be improper to caution the learner against a very common fault of young draftsmen j namely, that of making their lines and 378 LAND-SURVEYING. (Part VII. letters too strong, both with pencil and ink. The lines, dots, and letters be- longing to wooden cuts should never be imitated by the learner, as they ara mostly too strong and rough ; but he should take for his pattern the specimens exhibited in the different copperplates, given in this Work. 9. — In Part the Second, ivory plotting-scales are recommended, as being the best ; but it may be proper to observe that very good feather-edged plot- ting scales are now made of box, by most mathematical instrument-makers, which will do very well for school-boys. A twelve inch box scale may be had for about four shillings ; but an ivory scale of the same length costs ten or twelve shillings, accordingly as it is finished. 10. — What has been said on the subject of planning villages, towns, and cities, will be further illustrated by examining the plan of some large village, town, or city. The author recommends to those who desire to increase their information on this subject, a small plan of Leeds, neatly engraved ; and sold by J. Heaton, Leeds, price 2s. ; a large, elegant, coloured plan of Leeds, con- taining all the recent improvements ; published by Longman and Co. London, price 21s. ; a small plan of London, neatly engraved, price 2s. 6d. ; also a new coloured plan of London, with its environs, including the surrounding villages. In this plan all the new roads, streets, buildings, bridges, squares, &c. &c. have been accurately inserted from original and actual surveys ; together with the projected improvements not yet-executed. Both these plans are published by Laurie and Whittle, London ; the latter on a large sheet, price 6s. In this plan, the bases of houses are shaded with dots, in imitation of sand, as in the lower part of No. 2 ; but the bases of public buildings are shaded with lines, as in No. 7, Plate VII. The plan is sur- rounded by a border, which is divided into miles ; and each mile is subdi- vided into eight equal parts or furlongs. Besides the above maps, it may be proper to observe that an excellent coloured plan of London and its vicinity, has lately been published by W. Darton, No. 58, Holborn Hill, London, on one large sheet, price 6s. 6d. A plan of Edinburgh might also be consulted with considerable advantage, by the young Surveyor ; as the new town is laid out with remarkable regu- larity and elegance. TO CLEAN PLANS OR MAPS. It has been intimated to the young draftsman, in Note 6, page 250, that every precaution should be taken to keep plans and maps clean, in executing them : but notwithstanding the greatest possible care be exercised, they will generally be some- what soiled, (perhaps in consequence of misfortunes,) either by dust, ink, or colours ; hence it is necessary to give the method of cleaning them after they are finished. Section I.J land-surveying. S79 Note. — Not only the face but also the back of a plan should be cleaned, in order to make it look as well as possible ; and give it the appearance of coming from the hands of a neat and elegant draftsman. To clean Plans or Maps that are soiled with Dust, Indian Ink, or Colours. Take a sharp penknife, with a roundish point, and scrape those parts gently which are besmeared with ink or colours, until you efface the blots ; then use clean Indian rubber freely to those places that are soiled with dust ; and lastly, rub the whole map well with white bread ; taking care to pare the bread as it accumulates the dust. Note 1. — Indian rubber is made from the juice of a large and much branched tree, which grows in Guiana, Cayenne, and other parts of South America. The juice is obtained by making incisions through the bark of the tree, chiefly in wet weather. From the wounds thus formed, the juice, which is of a whitish colour, flows abundantly. It is usually brought to Europe in the form of pear-shaped bottles, which are made by spreading the juice over moulds of clay. These exposed to a dense smoke^ or to a fire, till they become so dry as not to stick to the fingers ; and then by certain instruments of iron or wood, they are ornamented on the outside with various figures. This done, the clay, in the inside, is moistened with water, and then picked out by proper instruments. 2. — When Indian rubber has become foul by frequent use, it may be cleaned by washing it in lukewarm water and soap. To clean Plans or Maps that are blotted with Common Ink. If the blots be light, they may be scraped out with a pen- knife, or effaced by rubbing them repeatedly with clean paper wet in water or saliva ; but when they are deep, acid or salt of lemons must be used in the following manner : Dissolve a small portion of the acid in hot water, and with a clean hair-pencil, dipped in the solution, wash the blots until they are discharged. Note 1. — Recent blots are easily obliterated ; but when they are old, and very deep, it will be found necessary to let the paper dry, and repeat the wash several times. Salt of lemons is sold in small boxes, by druggists. 2. — When you have to write upon those places from which the blots have been removed, the paper will bear the ink better, if you rub a little pounce upon it, with clean paper ; and then smooth it with your folder, or with the -_Lr - Li- r:: 1 SECTION II. MSECTIOXS FOR MZEASTRi: ANL PLAXXIl 3U1LDLSG GSOUXD, AXT> DITLDIXG IT ISTO COXTESTEyT LOTS FOB SALE. L -:r ■ ; J."..:: - . - ■ ':' .: - L-lxd lying in dbe TkEnrj of large tonus, is frequently sold ' - -'i- : .n:t 71J:. : : ' _ Liz^-r: : — - :-- - 1= -- --~^ ": -~~ a h%ft pice when ike saiadon is e%£Ue. k is of ike greatest tan to die toner and aeflo. to ascertain is Section II.) land-surveying. 381 In order to accomplish this desirable object, the dimensions should be very correctly taken, with a measuring-tape, divided into yards, tenths, and hundredths ; or with a tape divided into feet and tenths, or feet and inches. When the dimensions are taken in feet and inches, the inches must be reduced to the decimal parts of a foot ; and the area found from such dimensions, must be divided by 9, to bring it into square yards. Whatever be the shape of the ground to be measured, it must be divided into such squares, rectangles, trapezoids, trapeziums, or triangles, as will give the true content of the whole ; and if the sides be crooked, offsets must be taken as directed in Pro- blem 6, Part III. Narrow pieces of building-ground must be measured by Pro- blem 7 ; and if they be very irregular, their areas may be cor- rectly found by the method of equidistant ordinates described in Problem 9, Part III. Note 1. — As a measuring-tape is not so convenient in taking the dimen- sions of land as a chain, it is more eligible to use the latter when the land to he measured is extensive ; the greatest care, however, must be used in order to obtain the dimensions correctly, which should be taken to a quarter of a link, 2. — The chain must be completely stretched, and held at the bottom of the arrows, in measuring ; and if it be an inch or two over long, an allowance must be made in the dimensions : thus, if a line of 650 links be measured by a chain that is 2} 2 inches above 66 feet, we shall have 6^x2^ = 161 inches i= 2 links nearly ; hence the true length of the line will be 652 links. 3. — The above method may also be adopted in measuring land, when it is found necessary to correct the dimensions taken by a chain that exceeds the proper length. (See the Description of the Chain, Part II.) 4.— As 4840 square yards make 1 acre, 1210 square yards 1 rood, and 30 i square yards 1 perch, we can easily reduce acres, roods, and perches to square yards, in the following manner : Multiply 4840 by the number of acres ; 1210 by the number of roods ; and 30.25 by the number of perches ; then the sum of these three products will be the square yards required. 5. — When the area is in square links, divide it by 20.6611, the number of square links in a square yard ; and the quotient will be the area in square yards. (See the Table of Square Measures in Tart III.) 382 land-surveying. (Part VII fi. — Building-ground is generally sold in small parcels. Sometimes, how- ever, it is sold by whole fields together, which are afterwards divided by the buyer, and retailed out in small lots. EXAMPLES. 1. The length of a rectangular piece of building -ground is 65.8 yards, and its breadth 32.6 yards ; "what is its area in square yards, and its value at .5s. 9d. per square yard ? Yds. 65. S •32.6 3948 1316 1974 2145.08 Area. yd. s. vds. £. s. d. As"l : 5.75 :: 2145.08 : 616 14 2 J the value. 2. The length of a rectangle measures £5.36, and its breadth 43.28 yards ; what is its area in square yards, and its value at 6s. 3d. per square yard ? Ans. The area is 3694.3808 square yards ; and the value of the land £1154. 9s. 10id. 3. The parallel sides of a piece of ground in the form of a trapezoid, measure 84.63, and 72.78 yards, and the perpendi- cular distance between them 56.59 yards ; what is its area in square yards ? Ans. 4453.91595 square yards. 4. The diagonal of a trapezium measures 236.5 feet, one of the perpendiculars 189.3 feet, and the other 127.9 feet; what is its area in square yards ; and its value at £l. 6s. 6d. per square yard ? Ans. The area is 4167.655 square yards; and the value of the ground £5522. 2s. lOjd. 5. The base of a triangle measures 369.9 feet, and the per- pendicular 234.7 feet ; what is its area in square yards, and its value at 2s. 6d. per square yard ? Ans. The area is 4823.085 square yards; and the value «£602. 17s. 8|d. Section II.) land-suuveying. 383 6. The three sides of a triangle measure 362 feet 3 inches, 316 feet 6 inches, and 284 feet 9 inches respectively; what is its area in square } r ards ? Ans. By Note 4, Part IV., you will find the area to be 4810 square yards. 7. Draw a plan of an irregular piece of land, and find its area in square yards, from the following dimensions, taken in feet. AB 1286 247.6 1015 987 790 317.6 720 560 223.5 465 346 345.2 268 372.4 000 Begin at A, and 145.6 5Q.8 136.5 164.2 124.8 245.3 go West, Answer. Dcuhle Areas. 359147.3 Offsets on the right. 676164.8 Ditto on the left. 2)1035312.1 Sum. 9)517656.05 Area in square feet. 57517.33 Ditto in square yards. 8. Required the plan of a piece of building-ground, and also its area in square yards, from the following equidistant ordi- nates, taken in feet. — L->UKTtYI ft VII A z :■:■:? ~ i < _ :•« * :-.■ - ; ■*•" ?■':.'* ■ :: : - ; '•" . : "•'-: - ; • ' :. • : I • : ; : vr - -r"- i- A_ I" . 1 ~ -~-' : : : : ; -- ----- z z li r : _ — _' 15- 7 Section II) land-surveying, 385 Answer. Double Areas. 658576.8 Triangle ABC. 81307.2 Offsets on B C. 2)739884.0 9)369942.0 Area in square feet 41104.6 Ditto in square yards. 10. Required the plan of a portion of building-ground, and also its area in square yards, from the following dimensions, taken by Gunter's chain ; likewise its value, supposing it to have been sold by auction, at 14s. 9d, per square yard. BD 1235 1075 4741 A C482I 270 R. off B. AB 221 1175 25 \ 1100 45| 1000 m 900 54| 800 681 700 701 600 65| 500 60i 400 55\ 300 40f 200 321 100 000 Begin at A, and go Wesi Note. — In calculating the area, the 'quarter-links must be treated decimals. Answer, Double Areas. 1181895.00 Trapezium ABCD. 112881.25 Offsets on A B. 2)12917 76^25 Sum. 647388.125 Area square links. c c 386 LAND-SURVEYING. (Tori VII By note 5. we have 647388,125 -r 20.6611 = 31333.67. the area in square yards; then, as 1 yd. : 14.75s. :: 31333.67 yds. : 462171. 6325s. = 23M $£. lis. 7§. 4. The area of a rectangular field is l±a. 2r. lip. ; what is its length, its breadth being 925 links ? Ans. 1575 links. 5. A rectangular allotment upon a common, cost 78/. 1.?. lO^d. digging and levelling, at 11. 10s. per acre ; what will be the expense of fencing it half round, at 5s. 6d. per rood ; its length being 122.5 links ? Ans. 171. 18s. 8d. 6. Measuring along the base of a field in the form of a rhoni- boides, I found the perpendicular to rise at 678, and its length 1264 links ; the remainder of the base measured 2435 links; what is the area of the field ? Ans. 39a. Ir. 15£p. 7. A grass-plot, in a gentleman's pleasure-ground, cost Si. 14.?. Id. making, at 4<7. per square yard; what is the length of the base, the perpendicular being 40 feet, and the figure a rhombus? Ans. 50 feet. 8. What is the area of a triangular field, the base of which measures 3568 links, the perpendicular 1589 links, and the distance between one end of the base and the place of the per- pendicular 1495 links 1 Ans. 28a. Ir. 15lp. 9. After measuring along the base of a triangle -895 links. I found the place of the perpendicular, and the perpendicular itself =994 links ; the whole base measured 1958 links ; what is the area of the triangle \ Ans. 9m. 2v\ 37//. Section III. J miscellaneous questions. 389 10. The area of a triangle is 6 acres, 2 roods, and 8 perches, and its perpendicular measures 826 links ; what will be the expense of making a ditch, the whole length of its base, at 2s. 6d. per rood? Ans. 61. 4s. 7^/. 11. What is the area of a triangle whose 3 sides measure 15, 20, and 25 chains respectively? Ans. 15 Acres. 12. Required the area of a grass-plot in the form of an equi- lateral triangle, whose sidels 36 feet. Ans. 561. 18446 / I //c /A00 /000 /000 &'J0 +4 f ^r /. 1 e^tf/aw dsj/a/es FlULB-BOOIC. J>!r?'&jfi>?t &&?z eyfon z//?^ A & v£u&ii JflZ/s;/.,. y ,v +/ 3r&& ,;vvv %&0l tA0& /2* i ?£0- M0P S0j0 fog 3p0 Y& c/^.y' '/A/is: +; V I < _./'/(>/ 11 T-~- /5 '*- 24 I KA ^ ^ SWA 600 200 /oo OOP gale. V ?;■ vy. i 3\ /y /// d4A<5 /, + / '■> //. 2JZ s s . t — — / 8$ Sfhziifa?? Y >//<'/// 7, pW^S) 7 I '//. //>r„y/+/^ s?te>o. 6; ' - w. I \0 T- y V/i Ml — / /. y ^-\-J0v,J<>. ' /// ,/ SM >/) *7^ 000 ■<-: N T7T7 1 \ 0' + - V • >/ _i/x cMwri/-\-£J, /SO /JO • /Vf>//z +■/?, aoo^ Wo 'tne- z , <6> +/ &?ie> .0 £ 'JL #000 2000- 2000 /0S0 2000 ^40 24-00 2000 /000 0*00 200?v??Z/-V4s #^0k2J&?&e/ 2. 2^+4. 4000 4000 2/00 2000 0200 2000 £ 20^- J. \S& 10 6 /4. <220&&' /J S&. 2/ J /a2<> 42.-J22. 1^0.jyv4^c .j^aJ2 22a*?e'$e/sz22&7?v&?z/, CI./0, -22?. e&2>za20~e>, FlMLJ)~B$22K. ■v; Finis. /// / __-■ s, // /•/ // / ■ / ,/ /? " '//,// .;/',- s>, ////,////■// s,// /,-///r// //////■ //rr j/s/ ///'■- > - Syr*//? -\-//, ^^ A - M Z#??z -ir^ ^/' ; g^§ /////.;. 3/04 3000 2//0 2000 /Jp0 /#&3 S000 & + 2. /?63 /0tf#~ 2000 77* 2060 2000 /320 20/3 /000 fr+3. ^ ' £. 2300 2000 /S00 /3e?3 /000 7A0