PRACTICAL SURVEYING AND ELEMENTARY GEODESY MACMILLAN AND CO., LIMITED LONDON BOMBAY CALCUTTA MELBOURNE THE MACMILLAN COMPANY NEW YORK BOSTON CHICAGO DALLAS SAN FRANCISCO THE MACMILLAN CO. OF CANADA, LTD, TORONTO PRACTICAL SURVEYING AND ELEMENTARY GEODESY INCLUDING LAND SURVEYING, LEVELLING, CONTOURING, COMPASS TRAVERSING, THEODOLITE WORK, TOWN SURVEYING, ENGINEERING FIELD WORK AND SETTING OUT RAILWAY CURVES WITH NOTES ON PLANE TABLING, ASTRONOMICAL SURVEYING AND HELIOGRAPHING BY HENRY ADAMS LATE PROFESSOR OF ENGINEERING AT THE CITY OF LONDON COLLEGE M.INST.C.E., M.I.MECH.E., F.S.I., F.S.E., F.R.SAN.I., M.S.A., ETC. EXAMINER TO THE INSTITUTION OF MUNICIPAL ENGINEERS, THE SOCIETY OF ENGINEERS, THE INSTITUTE OF SANITARY ENGINEERS, THE ROYAL SANITARY INSTITUTE AND THE.SOCIETY OF ARCHITECTS MACMILLAN AND CO., LIMITED ST. MARTIN'S STREET, LONDON 19'S "TA54S COPYRIGHT PREFACE. AN endeavour has been made in this manual to present the elements of practical land surveying in a form suitable for students preparing for examinations in that subject held by various educational and professional bodies, and also for private workers. It is hoped and believed that the volume will be a helpful guide to practical methods whether the intention of the student is to undertake responsible work in the field, or more particularly to qualify for an examination. Many years' experience as a practical surveyor and teacher of land surveying in all its branches has made the author acquainted with the difficulties experienced by beginners ; and although personal effort is necessary to master any subject, progress is facilitated when principles and procedure are stated precisely and concisely. This has been the aim in the pre- paration of the present book. The course of work is so graduated that the careful study of each chapter, together with practical field work and the plotting of the accom- panying surveys should enable the diligent student to become qualified to undertake land surveying in a few months. The questions at the ends of the chapters will serve as exercises to test progress ; while those at the end of the volume should be particularly useful to students preparing for public examination in land surveying. HENRY ADAMS. 60 QUEEN VICTORIA ST., E.G. 29092,3 CONTENTS. CHAPTER I. Scope of subject Definition of land surveying Geometry and men- surationOrigin of the term geometry Distinction between theoretical or pure geometry, and practical or applied geometry Principles upon which land surveying is dependent Difference between old system of surveying and modern systems Objects in view in measuring land Distinction between office and field work Six selected problems in practical geometry Table of linear measures Table of square measures. 1 CHAPTER II. Linear measurement British standard of length Units of measurement Units adopted in measuring land Form of working in calculating area Pointing off Rule for area of rectangular figure Example Rule for area of triangular figure when base and perpendicular are given Example Rule for area of triangular figure when sides only are given Example Rule for area of four-sided figure, having two sides parallel Example Irregular four-sided figure divided into two triangles by a diagonal The same divided into two triangles and a trapezoid Example Method of tabulating the working. 7 CHAPTER III. Drawing to scale or plotting Description and use of chain scales- Decimal system Base line of survey Direction Points of the compass Direction of north obtained by a watch Magnetic meridian Magnetic variation North point. 13 CHAPTER IV. Measuring straight-lined figures Tie and check lines Rule for dis- tance from angle Well-conditioned and ill-conditioned triangles viii CONTENTS Use of box tape Measurements put on sketch plan instead of in field-book Testing tape for shrinkage Gunter's chain General description of its use Tally points Entries in field-book Steel tapes. 20 CHAPTER V. Measurement of straight- sided fields Use of station poles How chain lines and stations are indicated in field-book Conventional signs Offsets, how measured and recorded Examples of offset pieces- Plotting from field notes Drawing in the outlines. - - 26 CHAPTER VI. Nature of boundaries Hedge and ditch Why hedge is on inside of ditch Allowance for width of ditch Owner's side of boundary, how marked Poling out chain line when view of ends obstructed by rising ground Numbering and naming stations. - - 33 CHAPTER VII. Hedges and trees on plans Area of field by equalising lines Area by computing scale Area by planimeter Simpson's rule for area Plotting a survey plan with junctions in boundaries. - - 41 CHAPTER VIII. Cutting-up a plan, or arranging chain-lines, for a survey Complete survey of small field to explain routine Office plans and finished plans Estate in detached portions, how plotted Colouring plans. 48 CHAPTER IX. Surveying woods, lakes, marshes, standing crops, etc. Example of survey of a wood and a lake Measuring past obstructions Cross staff, construction and use Optical square, construction and use Setting up perpendiculars by chain only. 55 CHAPTER X. Measuring gaps and detours, view unobstructed Special precautions when view is obstructed Measuring across a lake, quarry or bend in river Measuring across a stream, river or valley Example of survey at Hilly Fields. 63 CONTENTS ix CHAPTER XI. Plans and maps Various systems of projection Curvature of earth not taken into account in ordinary surveys Ordnance survey maps Surveying over hilly ground Correction for inclination, how made Instruments for obtaining angle of slope Indicating hilly ground on maps Hachures Contour lines. 71 CHAPTER XII. Field notes for survey of small farm Sketch of chain lines Secondary lines not falling on previous station Plotting notes and preparation of survey plan. - - - 82 CHAPTER XIII. Instructions of "The Copyhold, Inclosure and Tithe Commission" for the preparation of "First Class Plans" Regulations for testing plans Charges for surveys Errors in chaining. - - 90 CHAPTER XIV. Traversing with chain Traversing with prismatic compass Reducing bearings Circumferentor Definition of terms used in traversing. 96 CHAPTER XV. Examples of open and closed traverses Reducing to a single meridian Tables of sines and cosines Traverse tables Plotting traverse surveys. 105 CHAPTER XVI. Copying plans by tracing and photography Use of triangular compass Pricking through and transfer Enlarging and reducing by pro- portional squares Use of proportional compasses Use and adjust- ment of pantagraph and eidograph Ordnance maps. - - 111 CHAPTER XVII. Definition of levelling Datum line Gravatt's dumpy level Construc- tion of level Construction of level staff Curvature and refraction. 118 CHAPTER XVIII. Simple and compound levelling Parallax and collimation, and adjust- ments therefor Bubble error and its adjustment Setting up a level Holding the staff. - .... 126 CONTENTS CHAPTER XIX. Levelling a section Running or flying levels Check levels Bench marks Ordnance datum Reducing levels Plotting sections Minus readings. 133 CHAPTER XX. Notes for part of a main section Plotting of same Working section of short piece of railway Description of features shown Rise and fall method of keeping level book contrasted with collimation method Telemetry, or optical measurement of distances. - 141 CHAPTER XXI. Levels of building plots Equal vertical and horizontal scales Spot levels Building plot with sections Building plot with sections and contour lines Levelling with barometer Surveyor's compen- sated aneroid barometer and method of using. - - - 148 CHAPTER XXII. Principles of angular measurement Old definition of an angle Trigo- nometrical definition Instruments for setting off or measuring angles Semicircular and rectangular protractors Circular pro- tractor with pricker arm and vernier Scale of chords. - 156 CHAPTER XXIII. Construction and reading of diagonal scale Construction and reading of vernier scale Construction and reading of verniers on the theodolite Construction and adjustment of box sextant Method of using same Construction and use of plane-table The three- point problem. 162 CHAPTER XXIV. Construction of theodolite Primary horizontal circle and verniers Vertical circle and verniers Setting up and adjusting theodolite Reading verniers Repeating an angle. - - - - 170 CHAPTER XXV. Traversing with theodolite, surveying by the back angle Field notes of traverse survey Traversing by angles from magnetic meridian Triangulation or surveying from two stations Field notes of CONTENTS xi survey from two stations Observations required for obtaining heights and distances. 176 CHAPTER XXVI. Principles of town surveying Choice of base lines Chain or steel tape Triangulated offsets Sketching details Field notes of lines and angles with offsets omitted Plotting of same Field notes of one street with measurements Plotting of same Connecting chain lines. - .... 184 CHAPTER XXVII. Difference in lay-out of old and modern towns Available accuracy depending upon scale employed Double chain lines Example of field-book Plotting of same Tape surveys Sketch of back pre- mises with measurements Plotting of same. - - - 192 CHAPTER XXVIII. Principal features of railway surveying Limits of deviation Reference book Railway gauges Engineering field work Location field- book Permanent stakes Level pegs Earthwork terms Batters and slopes Earthwork formulae. - . - - - 201 CHAPTER XXIX. Railway curves Nomenclature of curves Minimum radius Curve " elements " and formulae Simple and compound curves Reverse curves. - - 207 CHAPTER XXX. Difference in length of inner and outer rails Centrifugal force and super-elevation of outer rail Widening of gauge on curves Transi- tion curves. 220 CHAPTER XXXI. Ranging a curve By chain and offsets By one theodolite By two theodolites Practical example Points and crossings Sidings. 227 CHAPTER XXXII. Finding true merii mean time Astrono time Finding the latitude of a place. - - - - - 236 Astronomical surveying Finding true meridian Celestial sphere- Longitude and local mean time Astronomical, civil and nautical xii CONTENTS CHAPTER XXXIII. Signalling at a distance The Morse alphabet and Universal code Flag signalling Flashing signals Heliographing. - - - 242 APPENDIX. 300 Examination questions. - 245 INDEX. - - - 272 CHAPTER I. Scope of subject Definition of land surveying Geometry and men- suration Origin of the term Geometry Distinction between theoretical or pure geometry and practical or applied geometry Principles upon which land surveying is dependent Difference between old system of surveying and modern systems Objects in view in 'measuring land Distinction between office and field work Six selected problems in practical geometry Table of linear measures Table of square measures. Scope of the subject. Geodesy comprises several branches of work that will perhaps be better recognised under their ordinary titles of chain surveying, levelling, theodolite work, compass traversing, town surveying, engineering field work, etc. It is proposed to deal with these in the order named. Land surveying, as it is usually called, consists of accu- rately measuring and recording the lengths and positions of carefully selected lines, indicated by temporary poles placed in the ground adjacent to the boundaries of the various pro- perties. Land is measured usually for one or both of two purposes, either to find the area or to enable a plan or map of the place to be prepared ; in either case equal care must be taken in the measurements to produce correct results. Many text-books commence with a chapter on Practical Geometry, and rightly so, because this forms the ground-work of the method of recording upon paper the plans of any surveys of which the measurements may have been obtained, while Mensuration is the art of determining the areas of the various plots or surveys by calculation, the two branches forming together that part of surveying which may be called office work, as distinguished from outdoor or field work. Geometry. The word Geometry is derived from two Greek words, signifying earth-measure or land-measure, and from this it may readily be assumed that Geometry had its origin in p.s. A < PRACTICAL SURVEYING attempts to measure exactly certain portions of the earth's surface. The science of Geometry is supposed to have had its birthplace in Egypt some 3000 years ago, and to have been necessitated by the annual overflow of the Nile obscur- ing any minor landmarks which might have been set up by the respective owners of property adjacent to its course. The theoretical investigations of Geometry have, however, far outstripped the direct practical use of the science. Theoretical or Pure Geometry, of which Euclid, who lived in the third century before the Christain era, is the well-known exponent, teaches us, by reasoning, what are the properties of lines, surfaces, and solids, irrespective of matter or substance. Practical or Applied Geometry shows us in what way the properties may be made subservient to our various handicrafts. Before use can be made of any of these properties, it is essential to know (1) the meaning of the different names or terms employed, (2) their fundamental relationships, and (3) what may be possible in the way of employing them. These are the (1) definitions, (2) axioms, (3) postulates given by Euclid. A definition is simply a strict description of what is meant by a certain name. An axiom is something intuitively known to be true or self-evident, and is so simple that it cannot be proved by any- thing simpler. A postulate is something which it is admittedly possible to do. Six simple and useful constructions in Practical Geometry are given below. From a given point in a straight line to erect a perpendicular. Let AB be the given line in any direction, and C the given point. Then from C, with any radius Cd, describe the arc defg, and from points d and g, with the same radius, cut the arc at e and /. From points e and / de- scribe arcs intersecting in h, and FIQ. 1. To erect a perpendicular from . . 7 i i n t a given point in a straight line. ]Oin AC, which Will be dicular to AB. GEOMETRICAL PROBLEMS 3 It will be observed that the given lines are shown thin, the construction lines dotted, and the lines found by construction thick. They are also lettered in the order of construction, the given parts with capital letters and the construction lines with small letters, so that what may be called the " life- history " of the problem is presented at a glance, and does not really require any description to enable anyone to work it out. To let fall a perpendicular from a given point on to a given straight line. Let AB be the given line and C the given point. From C, with any radius greater than the distance from the line, draw arcs cutting the line at d and e. From points d and e, with a radius less than the distance to C, describe arcs intersecting at /, and draw line from C through / to meet the base line in g. required perpendicular to AB. FIG. 2. To let fall a perpendicular from a given point on to a given straight line. Then Cg will be the To copy a given angle. Let ABC be the given angle. With any radius ~Bd describe arcs cutting BA and BC at d and e. Then draw line fg indefinitely, or the same length as BC, and from / strike the arc ih with radius equal to Ed, then from point h with radius de cut hi in, point i, and through i draw fj equal in length to BA. If BC is at any given angle with the horizontal, this angle may be first copied to give an identical position for the lines forming the angle. 7 FIG. 3. To copy a given angle. PRACTICAL SURVEYING To construct a e whose sides shall be equal to three given 4 Pro. 4. To construct a triangle haying sides equal to three given straight lines. Let A, B and C be the three given lines any two of which must be greater than the third. Draw de equal to A, from point d with radius equal to B describe an arc, and from point e with radius equal to C describe another arc to intersect the previous one in point /; join fd and fe, then dfe is the required triangle. To construct a triangle on a given line length of its perpendicular given. Let AB be the given line (Fig. 5), C the position of the perpendicular and CD the length of perpendicular. Draw line AB and mark position C, then from C with any radius cut AB with arcs e and /, and from points e and / with any radius draw arcs intersecting in g. Then from point C through g draw CD equal to the given length CD, and join AD and BD. the position and FIG. 5. To construct a triangle on a given line having the position and length of its perpendicular given. To make a triangle equal to a given trapezium. Let ABCD be the given trapezium (Fig. 6). Join CA. Pro- duce DA to e, meeting Be, drawn parallel to CA. Join Ce. Then the triangle CeD is equal to the trapezium ABCD, as the piece cut off the trapezium at B is equal to the piece added on to the triangle at Ac. The solution really depends upon the proposition of Euclid, " Triangles upon the same base and between the same parallels are equal." The triangles are ABC and AeC, and the parallels SYSTEMS OF SURVEYING Fio. 6. To make a triangle equal to a given trapezium. AC and eE ; the triangle ACD is common to both the trapezium and the equivalent triangle. We need not trouble at present with anything relat- ing to angles or angular mea- surement, as in chain surveying we are only concerned with the length of the sides of the triangles, and from these lengths the work can be plot- ted and the areas calculated without knowing what the angles are. Old and modern systems of surveying. In the old system of land surveying, each field was measured separately, often by the village schoolmaster, and added on to the bulk already measured, large estates being sometimes checked by the theodolite used round its boundary. In the modern system, if there are several fields, a base line or two main lines are laid out, running to each extreme of the survey, and triangles are set out from these following the irregularities of the various boundaries, so that the whole is tied into a network of triangles with the fewest possible lines. In large surveys the theodolite is used to measure the angles of the main lines, in order that the distances may be checked by calculation, as will be shown later. Inches. TABLE OF LINEAR MEASURE. Links. 7'92 12 36 198 792 7,920 63,360 1 1-515 4-545 25 100 1,000 8,000 Feet. Yards. Poles. Chains. Furlongs. 1 3 16-5 66 660 5,280 1 5-5 22 220 1,760 1 4 40 320 1 10 80 I Miles. 8 1 PRACTICAL SURVEYING Sq. Links. TABLE OF SQUARE MEASURE. Sq. Feet. 2-296 20-661 625 10,000 25,000 100,000 64,000,000 1 9 272-25 4,356 10,890 43,560 27,878,400 Sq. Yards. Perches. Sq. Chains 1 30-25 484 1,210 4,840 3,097,600 1 16 40 160 102,400 1 2-5 10 6,400 Roods. Acres. 1 4 2,560 Sq I Mil 640 1 QUESTIONS ON CHAPTER I. 1. Give a brief description of land surveying under the two heads of field work and office work. 2. Draw two lines at right angles to each other by a rule and set square, and test them by geometrical construction. 3. Draw the outline of one of your set squares, and by con- struction drop a perpendicular from the largest angle to the opposite side. 4. Measure the length of the sides of a set square, and draw a similar triangle whose sides are half the length. 5. Repeat the last triangle on both sides of the longest line as a common base, and draw a single triangle equal to the combined area of the two. 6. Describe the general principles upon which a survey is made. CHAPTEE II. Linear measurement British standard of length Units of measurement Units adopted in measuring land Form of working in calcu- lating area Pointing off Rule for area of rectangular figure Example Rule for area of triangular figure when base and perpendicular are given Example Rule for area of triangular figure when sides only are given Example Rule for area of four- sided figure, having two sides parallel Example Irregular four- sided figure divided into two triangles by a diagonal The same divided into two triangles and a trapezoid Example Method of tabulating the working. Linear measurement. Linear measurement is the mea- surement of straight lines referred to some known length called a unit, or standard, of length. This length is purely arbitrary, and differs in different countries. The yard is the British standard of length. It is subdivided into feet and inches, and multiplied into chains of 66 feet, and into furlongs and miles. The fifi x 19 chain again is subdivided into 100 links, each = 7 92 inches long, so that the apparently odd length of 7 '92 inches is strictly derived from the British yard. In linear measurement, when the total length of any measured distance is given, it may be stated in different ways. As a general rule, long distances are given in miles and fur- longs, or miles and chains, or miles and yards ; and short distances in chains and links, or feet and inches. Square measure is called also superficial measure, because it is the measure of surfaces. A square foot is a space that measures a foot each way ; or a surface measuring half a foot one way and two feet the other way will likewise be a square foot. The term " square feet " must not be confused with the term "feet square." Thus, 9 square feet make 1 square yard, but the expression 9 feet square means a square each 8 PRACTICAL SURVEYING side of which is 9 feet long, arid therefore has an area of 81 square feet. There is as much difference between square feet and feet square as between a horse chestnut and a chest- nut horse* In square measure the denominations most used by land surveyors are acres, roods and perches, any small amount over being put as the fraction of a perch, J, * or j, whichever is nearest to the true result. Decimal fractions of a perch, such as are recorded in the Ordnance Survey, give the appear- ance of minute accuracy which, however, the facts of the case do not warrant. It may be taken as a rule that no field survey can be relied upon for accuracy within less than one perch per acre (five-eighths of 1 per cent.), but straight-sided building plots measured with a steel tape may be accurate within a tenth of 1 per cent. The tables at the end of the last chapter (pp. 5 and 6) give a concise view of the common linear and square measures. In some tables of square measure, areas are stated as acres, roods and poles, instead of acres, roods and perches, as here given. The reason is that the length of 1 6 J yards is known as a rod, pole, or perch, and the corresponding square with that length of side as a square rod, pole or perch. In order to avoid confusion, surveyors have generally adopted the term pole for linear measure and perch for square measure, and it is well to bear in mind this distinction. Areas Of regular figures. We are now in a position to consider the methods of finding the areas of any regular figures or those bounded by straight lines. The area of any rectangular figure is found by multi- plying together its length and breadth. Ex. 1. In a field 7 chains long and 3 chains wide (Fig. 7) how many acres, roods and perches ? 7 3 2,1 8 4 "^ 4 7-00 40 160 Ans. : 2 a. Or. 16 p. FIG. 7. Rectangular field. AREAS OF PLANE FIGURES 9 Explanation. 1 square chains make 1 acre, therefore divide 21 square chains by 10, or, what is the same thing, point off one figure. Then multiply the remainder by 4 to bring to roods and point off. Then multiply the remainder by 40 to bring it to perches and point off. The figures to the left of the pointing show the acres, roods and perches. The area of a triangle is found by multiplying together its base and perpendicular height and dividing by 2. There is a special reason for not saying multiply the base by half the height, which will be seen later. Ex. 2. In a triangular field (Fig. 8), one side of which is 13 clmins long, and the perpendicular to the opposite angle 9 chains long, how many acres, roods and perches ? FIG. 8. Triangular field Ans. : 5 a. 3r. 16 p. When the length of the three sides only of a triangle is given, the calculation is a little more complicated. The rule is : From half the sum of the three sides subtract each side severally, and multiply it and the three remainders together and take the square root for the area. This is usually expressed by the formula, Area = >Js(s-a)(s-b) (s-c), where a, b and c are the three sides respectively, and s = half a + b + c their sum, or - . O 10 PRACTICAL SURVEYING Ex. 3. In a triangular field (Fig. 9) the three sides are 3, 4 and 5 chains long. What is the area ? 6-4 = 2 6x3x2x1=36, .736 = 680. ch. 6 5=1. _4 24 40 160 Ans. : a. 2 r. 1 6 p. With a four sided figure having two sides parallel and perpendicular to the base, called by surveyors a trapezium, the rule is : Multiply the sum of the two parallel sides by the base, and divide by 2. Ex. 4. In a field (Fig. 10) with two parallel sides whose 8 *>. FIG. 10. Four-aided field having two sides parallel, and perpendicular to the FIG. 9. Triangular field. base, called a trapezium. lengths are respectively 3 and 5 chains long, and their distance apart 7 chains, what is the area ? 28 ^ \ X. *. > CO N \ V *^ s *O ^ ^ V 1 1 V) t Jan Feb. March dpnL May June JuLy dug. Sept. Octr Norr Deer Fio. 20. Monthly variation of compass. P.S. B 18 PRACTICAL SURVEYING Fig. 21. In London the mean annual position is now about 15J degrees west of true north, and is reducing at the rate of about 7 minutes per annum. The exact variation will be found in the Nautical Almanac for the current year. The north point. In the field-book the bearing of the '/V5' FIG. 21. Mean annual variation of compass. base line with regard to tha magnetic north is generally entered as so many degrees east or west of north or south ; thus, N. 20 W. would mean a direction of 20 degrees west of north, but on all plans, whether manuscript or lithographed, both the true north and the magnetic variation should be shown, in order to make quite clear what the bearing of the plot really is. This is generally done by means of a north NORTH POINT 19 point, as Fig. 22, but which may be very much more elaborate. In maps and Ordnance sheets it is customary to make the top of the sheet north, but in detached surveys, if the shape of FIG. 22. North point. the plot should render it desirable, the plan may be placed in any position, provided the north point is placed accordingly. QUESTIONS ON CHAPTER III. 1. What will be the length in inches of a line representing 19 chains 12| links to a scale of 3 chains to 1 inch ? (Ans. : 6.) 2. Make a scale of 40 feet to 1 inch to represent chains and tens of links. 3. Find the area in square yards of a rectangular plot of land, two adjacent sides of which measure 4 chains 34 links and 2 chains 15 links. (Ans. : 4516-204.) 4. In 395,590 square links how many acres, roods and perches ? (Ans.: 3 a. 2r. 33 p.) 5. A line measures 6 chains 13 links ; what is its length in feet and inches? (Ans. : 404ft. Tin. nearly.) 6. With a magnetic variation of 16 degrees west, what will be the true bearing of a line whose compass direction is N. 82 W. ? (Ans. : 262 or S. 82 W.) CHAPTER IV. Measuring straight-lined figures Tie and check lines Rule for distance from angle Well-conditioned and ill-conditioned triangles Use of box tape Measurements put on sketch plan instead of in field- book Testing tape for shrinkage Gunter's chain General description of its use Tally points Entries in field-book Steel tapes. Measurement of straight-lined figures. In the rules laid down for the mensuration of areas it was assumed that the outlines were more or less regular, and that, for instance, in a rectangular four-sided figure it was only necessary to multiply the length by the breadth. In practice, it must not be assumed that there are any regular figures. If it were desired to obtain the plan of a single room it would not be sufficient to measure the length and the breadth, and assume the angles all to be right angles, although they might appear to be so ; some method must be adopted by which measured lines representing the four sides can be trans- ferred to paper in their true relative positions. It might be divided into two triangles by means of a diagonal across two opposite corners, but in a large room there might be obstruc- tions in the way, and there is another method of which constant use is made in surveying. It is founded upon the method of copying an angle shown among the selected pro- blems in Practical Geometry. Suppose distances are marked from one of the corners on each of the walls meeting there, and then the distance is measured between the two marks, these three measure- ments will give the sides of a small triangle, two of which produced to a sufficient length give two of the walls, and the third one is a tie between them, deciding their relative positions. TIE AND CHECK LINES 21 Tie and check lines. In a four-sided figure (Fig. 23) the measurement of the sides a, b, c and d, and one angle e, enables it to be put down to scale ; but in that case the accu- racy of the result depends solely upon the carefulness with which the work has been done, as there is no check upon it. If, however, a second angle be measured, /, there is a perfect check upon the work, as it would be found impossible to close the figure entirely if a mistake is made in either measuring or plotting any one of the lines. The rule in surveying for a Fm. 23. Measuring sides and angles of a room. these tie and check lines is that the points should be taken not less than one-fourth of the length of each main line from the angle, and not necessarily at equal distances, so long as the triangles formed are welt-conditioned, i.e. having no angle less than 30 degrees nor more than 120 degrees. An ill- conditioned triangle is one that would not conform to these conditions. The rule only applies to ordinary surveys ; for important work the complete diagonals should be taken. Use of box tape. The box tape (Fig. 24) is commonly employed for all measurements about buildings and yards, where the general distances are under one chain in length. It is marked off to a total length of 66 feet, one side being divided into feet and inches, and the other into poles and 22 PRACTICAL SURVEYING links, so that either denomination can be used for the measurements. In using a tape line the starting point is always the furthest extremity of the brass ring. There must be no twist in the tape, and it must be pulled sufficiently tight to prevent the sagging from affecting the measurements. As the surveyor cannot be at both ends of the tape, he takes the box and gives the ring end to an assistant, and, unless the assistant is experienced,, care must be taken that he does not take a turn of the tape round his wrist to keep his hold firm. About buildings and yards the tape is much simpler than the chain, and handier to carry about, and the measurements being short and intricate are generally entered upon a sketch plan instead of in the columns of a field-book. Testing tape for shrinkage. Although the 66-feet Chesterman metallic tape has wires woven in to prevent on one sio/e and inches potes and FIG. 24. Box tape. stretching, it is worthy of notice that one of these tapes used on wet grass and wound up again was found, when tested two days later at the Guildhall, to have shrunk to 65 feet 4 inches, and when tested three weeks later it had recovered so far as to measure 65 feet 9 inches long. It is useful to practise pacing as a rough check upon distances ; a long step is 3 feet or 1 yard, and a natural step or pace about 2| feet ; therefore multiply the number of paces by 4 and point oft' two figures ; the result is chains and links. Gunter'S chain. For land surveying the chain is always used, but the tape sometimes comes in as an accessory for measuring long offsets. The surveyors' chain is called a Gunter's chain, after its inventor, Rev. Edward Gunter, who was a professor of astronomy about the year 1640 at Gresham College. It is sometimes called a 4-pole chain, to distinguish GUNTER'S CHAIN 23 it from the 1 00-feet chain used by civil engineers. The 4-pole chain is more useful for land measure, as it is an exact decimal of a mile, one-eightieth, and the square formed by it is exactly one-tenth of an acre. It consists of a series of links and rings (Fig. 25), measuring altogether 66 feet, and is always used on the ground, as its weight would cause it to sag if held up, as the tape often is. It requires at least two operators, the sur- veyor and his assistant, or surveyor and chainman, or driver and leader. Use of Gunter's chain. The chain is accompanied by ten galvanised iron arrows or pins, to indicate the various Brass tatty M 3O or 70 FIG. 25. Gunter's chain and arrows. chain lengths as they are reached in a measurement. These are inserted in the ground by the leader and withdrawn by the driver, an exchange taking place at every ten chains which is entered in the field-book. In using the chain the driver passes his fingers through the end ring, holding it vertically on the ground at the starting point ; the leader holds the other end leg high, with his fingers through the ring and an arrow held against it by his thumb through the loop ; he sees that it is straight, and then watches the signals made by the surveyor with his free hand, the palm of the hand facing the side the leader must go to to put himself in line, and the fingers moved to show it, reversing the palm and movement of fingers when the leader goes too far, and putting the palm 24 PRACTICAL SURVEYING downwards and moving the fingers in the same direction when the leader is in the right spot. As he nears the right spot he will, of course, be stooping down, with the point of the arrow just clearing the ground. To get the chain to lie straight on the ground, the leader gives the end held by him a few sharp vertical jerks, which causes a wave-like motion to pass along the length of the chain. The jerks must not be too vigorous, or the pull on the chain too tight, as that would cause it to stretch by opening the links. As soon as the arrow is fixed the two operators walk on for another chain length, unless there are any interim measure- ments to be made for offsets, or notes to be entered. In the old days there was an eleventh arrow made of brass to insert in the ground when the tenth was withdrawn by the surveyor, but the writer has not seen one for many years, and the custom now is for the surveyor to put his toe on the spot, count the ten arrows at every change, and hand them over to the leader again. The divisions of the chain are indicated by brass tallies at each tenth link -one point stands for 10 or 90 links, being the same from each end, two points for 20 or 80, three points for 30 or 70, four points for 40 or 60, and a round tally with the maker's name for 50 links. No confusion arises from the number of points being the same for two readings, as it is easy to see which is the nearer end. Entries in the field-book. In the field-book there is one column only, down the centre. This is for entering any measurement obtained by the chain in a direct line, all the measurements being reckoned from the starting point. The left-hand space is for recording anything occurring to the left of the chain line, and the right for anything occurring on the right. An important and curious point in connection with the field-book is that the surveyor begins at the end and finishes at the beginning, working backwards all the way. He begins at the bottom of the last page and makes his entries consecutively upwards, so that he stands with regard to the book exactly in the same position as he stands with regard to the chain line. Steel Tape. In modern work a 66-feet or 100-feet steel tape is often used instead of a chain, consisting of a ribbon of USING THE CHAIN 25 steel | inch wide, with brass plugs riveted in to mark the links. It is more accurate than a chain, but requires more care in handling. A 100-feet standard steel tape is a very delicate instrument, marked in feet, inches and eighths, needing as much care as an infant, difficult to keep free from corrosion and consequent indistinctness of divisions, and only used for building surveys. QUESTIONS ON CHAPTER IV. 1. A chain is one link short, next to the 50 tally, a line measured by it is given as 13'47 ; what is the true length ? (Ans. : 13'34.) 2. A triangular plot of land has its sides 4'32, 3'51 and 2'17 ; plot this to a scale of 1 chain to 1 inch, and find the distance along the base line, from the shortest side, where a perpendicular from the apex would fall. (Ans. : V28 nearly.) 3. What will be the area in acres, roods and perches of 10 square inches on a map drawn to a scale of 3 chains to 1 inch ? (Ans. : 9 a. r. p.) 4. Describe the instruments used for measuring distances in the field. 5. Describe the operation of poling out and chaining a line in the field. 6. Explain, by a sketch, the reason for measuring check lines as well as tie lines in a survey. CHAPTER V. Measurement of straight-sided fields Use of station poles How chain lines and stations are indicated in field-book Conventional signs Offsets, how measured and recorded Examples of offset pieces- Plotting from field notes Drawing in the outlines. Measurement of straight-sided fields. In surveying a field with straight sides it is, in theory, only necessary to divide it into triangles and measure the base and perpen- dicular of each, but in practice very few straight- sided fields occur, and the only spaces of the sort likely to be found are building plots. Generally, the chain lines cannot be laid along the boundaries, but must be some little distance inside them, so that the position of the boundary must be measured by perpendicular offsets from the chain line. These offset measurements are put in the right or left-hand column of the field-book according as they occur to the right or left-hand side of the chain line when facing forwards from the starting point. Use of Station poles. The positions of the chain lines are marked out on the ground by light poles, painted in red, white and black bands (Fig. 26), with a small red and white e'o' Scac/on poie FIG. 26. Station pole. flag about 12 in. square nailed on the top, to distinguish them at a distance, a pole being placed at each junction of the CONVENTIONAL SIGNS 27 lines and at one or two intermediate points when the line is a long one. Conventional signs. In measuring the lines, whenever a station pole is reached, the measurement is recorded and the pole indicated in the field-book by a small circle with a dot in the centre (Fig. 27). There are other conventional signs used MARKS (3) Number of (.tne Q Ordinary scat/on TnqoriomeCricaL station Direction marks 1H- * IN FIELD BOOK D = Broty of of/tch H = Centre of hedge F " Face of fence rp. - Footpath R - Road & = Brick buiictinq W = Wood. FIG. 27. Marks in field-book. by surveyors for indicating in the field-book and on plans the various details of a survey, as roads, fences, footpaths, etc., which are here given. In chain surveying the lines are numbered in the order in which they are measured. It is useful to record the chain lines on the plan and show the direction in which they were measured, as in Fig. 28. of Line t'n circLe than '/*' oJtam Direction of measurement tatton c/rcte not mo re th&n Me" a/iometer Fia. 28. Drawing chain lines on plan. When the offsets are short they are measured by an offset- staff, which is simply a ten or fifteen-link rod, divided into 28 PRACTICAL SURVEYING links, painted alternately black and white, the fifth link having a red ring painted round its end, as in Fig. 29. The end K - Offset staff - - /O Links - Reef nnq FIG. 29. Offset-staff. of the offset-staff is finished with a flush hook for pulling the chain through a hedge. In a well-arranged survey no offset should exceed one chain in length. Sometimes it may happen that there is a strip of grass, a footpath, and a roadway occurring between the chain line and the boundary ; with an offset-staff the measurements would be recorded as in Fig. 30, 1 23 12 20 5 8 1 2 J 3 5- ^15 76 c ^ V I I O I 1 ^ / 1 | I 1