Surveying and Levelling (Volume 1) Surveying and Levelling (Volume 1)

S.S. Bhavikatti AICTE Emertitus Fellow, BVBCET, Hubli

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ISBN 978-81-906942-0-9 (Vol 1) 978-81-906942-2-3 (Set)

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Published by Krishan Makhijani for I.K. International Publishing House Pvt. Ltd., S-25, Green Park Extension, Uphaar Cinema Market, New Delhi - 110 016 and Printed by Rekha Printers Pvt. Ltd., Okhla Industrial Area, Phase II, New Delhi - 110 020. Preface

Surveying and Levelling is an important subject for all civil engineers engaged in the field work. They are either called to prepare plans and maps or to use them to prepare the civil engineering projects on to set out the works using the maps. The subject is vast and is taught in two to three courses to undergraduate students. Though many modern techniques have come up still earlier methods like chain survey and compass survey cannot be given up since for all small projects they are commonly used methods. Apart from that the principles lying in these surveys are applicable even in surveying with modern equipment. All common methods of surveying and levelling have been covered in this first volume. The computation of areas and volumes using surveying and levelling is also covered. Various minor instruments used in engineering offices are explained in the last chapter. A sincere effort has been made to present the subject in simple language and with neat sketches so that students can understand it easily. It is hoped that faculty and engineering students will find this book highly useful. Suggestions for im- provements are most welcome. I acknowledge the encouragement and help of the teaching and non-teaching staff of N.I.T.K. Surathkal, B.V.B. C.E.T. Hubli, SDMCEI, Dharwad and RYMEC, Bellary. S.S. Bhavikatti Contents

Preface v

1. Introduction 1 1.1 Plans and Maps 1 1.2 Applications of Surveying 1 1.3 Primary Divisions in Surveying 2 1.4 Classification of Surveying 3 1.5Measurements 5 1.6 Units of Measurements 6 1.7 Scales 6 1.8 Types of Graphical Scales 8 1.9 Vernier Scale 10 1.10 Special Forms of Verniers 13 1.11 Shrunk Scale 14 1.12 Methods of Locating a Point in Plain Survey with Respect to Two Reference Points 15 1.13 Principles of Surveying 16 1.14 Survey of India and Topological Maps 17 1.15 Phases of Works in Surveying 17 Questions 19

2. Errors in Surveying 21 2.1 Types of Errors 21 2.2 Sources of Errors 22 2.3 Most Probable Value of Accidental Error 23 2.4 Errors in the Computed Quantities 26 2.5Accuracy in Measurement 29 2.6 Relative Accuracy between Linear and Angular Measurements 29 2.7 Significant Figures and Rounding off Figures 30 Questions 31 viii Contents

3. Measurement of Horizontal Distances Using Chain and Tape 32 3.1 Approximate Methods of Distance Measurements 32 3.2 Measurements by Chaining 33 3.3 Types of Chains 33 3.4 Advantages and Disadvantages of Chain Over Steel Band 36 3.5Testing and Adjustment of Chains 36 3.6 Tapes 37 3.7 Accessories Required for Horizontal Measurements 39 3.8 Ranging a Survey Line 43 3.9 Chaining a Horizontal Line 45 3.10 Measurement of Distances on Sloping Ground 47 3.11 Precise Measurement/Base Line Measurement 50 3.12 Errors in Chaining 51 3.13 Chain and Tape Corrections 52 Questions 60

4. Chain Surveying 63 4.1 Testing a Triangle for its Condition 64 4.2 Network of Triangles 64 4.3 Selection of Stations 66 4.4 Offsets 66 4.5Setting Out Perpendicular Offsets 67 4.6 Allowable Length of Offset 71 4.7 Equipment Required for Chain Survey 74 4.8 Field Work 74 4.9 Plotting a Chain Survey (Office Work) 78 4.10 Conventional Symbols and Colours 78 4.11 Problems in Chaining 79 4.12 Obstacles in Chaining 84 4.13 Cross Staff Survey 91 4.14 Traversing with Chain and Tape Only 92 Questions 93

5. Angle and Direction Measurements with Compass 95 5.1 Compass 95 5.2 Difference Between Prismatic Compass and Surveyors Compass 99 Contents ix

5.3 Working and use of Compass 100 5.4 Magnetic Bearing and True Bearing 100 5.5 Whole Circle Bearing and Quadrantal Bearing System 101 5.6 Magnetic Dip 101 5.7 Magnetic Declination 102 5.8 Fore Bearing and Back Bearing 106 5.9 Computation of Angles from Bearings 108 5.10 Computation of Bearings if Bearing of a Line and Included Angles are Given 109 5.11 Local Attraction 111 5.12 Personal Errors 117 5.13 Testing and Adjusting the Compass 119 Questions 120

6. Compass Surveying 124 6.1 Accessories for Compass Survey 124 6.2 Field Work 124 6.3 Checks in Compass Survey 126 6.4 Plotting 128 6.5Closing Error and its Adjustment 131 6.6 Errors in Compass Survey 136 6.7 Limits of Precision 138 6.8 Omitted Measurements 138 Questions 145

7. Plane Table Surveying 147 7.1 Plane Table and its Accessories 147 7.2 Working Operations 151 7.3 Methods of Plane Tabling 153 7.4 Required Accuracy in Centring 163 7.5Errors in Plane Table Surveying 164 7.6 Advantages and Limitations of Plane Table Survey 165 Questions 166

8. Levelling 167 8.1 Definition of Basic Terms used in Levelling 167 8.2 Methods of Levelling 169 8.3 Levelling Instruments 170 8.4 Types of Levels 170 8.5Tripod for the Level 176 8.6 Levelling Staff 177 x Contents

8.7 Relative Merits of Self Reading and Target Staffs 180 8.8 Working Principle of Telescope 180 8.9 Parts of Telescope 181 8.10 Advantages and Disadvantages of Internal Focussing Telescope 184 8.11 Fundamental Axes of a Level 185 8.12 Temporary Adjustments of a Level 185 8.13 Principles of Direct Levelling 187 8.14 Terms used in Levelling 188 8.15T ypes of Levelling 189 8.16 Simple Levelling 189 8.17 Differential Levelling 189 8.18 Fly Levelling 192 8.19 Profile Levelling 193 8.20 Cross-sectioning 199 8.21 Hand Signals During Levelling 201 8.22 Effect of Curvature 201 8.23 Effect of Refraction 202 8.24 Distance of Visible Horizon 203 8.25Bal ancing Backsights and Fore Sights 205 8.26 Reciprocal Levelling 206 8.27 Difficulties in Levelling 209 8.28 Level Tube and its Sensitivity 212 8.29 Errors in Levelling 215 8.30 Degree of Precision 218 8.31 Barometric Levelling 218 8.32 Hypsometry 221 8.33 Additional Problems 222 Questions 224

9. Contouring 227 9.1 Contour Intervals 227 9.2 Characteristics of Contours 229 9.3 Methods of Contouring 232 9.4 Direct Method of Contouring 233 9.5Indirect Contouring 233 9.6 Interpolation of Contours 236 9.7 Drawing Contours 238 9.8 Contour Gradient 238 9.9 Uses of Contour Maps 239 Questions 242 Contents xi

10. Theodolite Surveying 244 10.1 Main Parts of a Vernier Theodolite 244 10.2 Technical Terms Associated with Measurement with Theodolite 248 10.3 Fundamental Axes of Theodolite 249 10.4 Temporary Adjustments of a Theodolite 250 10.5 Measurement of Horizontal Angle 251 10.6 Measurement of Horizontal Angle by Repetition Method 253 10.7 Measurement of Horizontal Angle by Method of Reiteration 254 10.8 Measurement of Vertical Angle 254 10.9 Field Operations with Theodolite 256 10.10 Theodolite Traversing 263 10.11 Plotting and Adjusting Chosing Error 266 10.12 Trigonometric Levelling 266 10.13 Errors in Theodolite Surveying 266 10.14 Good Practices in Theodolite Survey 271 10.15 Additional Problems on Theodolite Survey 272 Questions 280

11. Trigonometric Levelling 281 11.1 Base of the Object Accessible 281 11.2 Base of Object InaccessibleSingle Plane Method Possible 282 11.3 Base of the Object InaccessibleDouble Plane Method is Necessary 284 11.4 Height of an Elevated Object Above the Ground if its Base is also Visible 285 Questions 288

12. Permanent Adjustment of Dumpy Level and Theodolite 290 12.1 Required Permanent Adjustments in Dumpy Level 290 12.2 First Adjustment of Dumpy Level [Adjustment of Level Tube] 291 12.3 Second Adjustment of Dumpy Level [Adjustment of Cross Hair Ring] 291 12.4 Third Adjustment of Dumpy Level [Adjustment of Line of Sight/Collimation] 292 12.5 Required Permanent Adjustment in Theodolite 297 12.6 First Adjustment of Theodolite [Adjustment of Plate Level] 297 xii Contents

12.7 Second Adjustment of Theodolite [Adjustment of Horizontal Axis] 298 12.8 Third Adjustment [Adjustment of Cross Hairs] 299 12.9 Fourth Adjustment and Fifth Adjustments [Adjustment of Altitude Level and Vertical Index Frame] 300 Questions 302

13. Computation of Areas 303 13.1 Methods of Computation of Areas 303 13.2 Computation Areas from Field Notes 303 13.3 Computation of Areas of Regular Figures 304 13.4 Areas from Offsets at Regular Intervals 305 13.5 Areas from Offsets at Irregular Intervals 310 13.6 Computation of Area from Latitudes and Departures 312 13.7 Area by Coordinates 319 13.8 Computing Areas from Maps 321 13.9 Graphical Methods of Computing Area from Maps 321 13.10 Mechanical Methods for Computing Area of a Plan 322 13.11 Amsler Polar Planimeter 323 13.12 Theory of Planimeter 327 Questions 332

14. Computation of Volumes 335 14.1 Computation of Earthwork from Cross-Sections 335 14.2 Formula for Computing Areas of Cross-Sections 336 14.3 Cross-Sectional Areas in Filling 342 14.4 Equations for Volume of Simple Solids 342 14.5 Computation of Volume by Trapezoidal Rule 343 14.6 Computation of Volume by Prismoidal Rule 344 14.7 Computation of Earthwork from Spot Levels 353 14.8 Computation of Volume from Contours 359 Questions 365

15. Minor Instruments 367 15.1 Hand Level 367 15.2 Burel Hand Level 369 15.3 Clinometers 370 15.4 The Sextants 378 15.5 Pentagraph 382 Questions 384

Index 385 C HAPTER1

Introduction

Surveying is the art of making measurements of objects on, above or be- neath the ground to show their relative positions on paper. The relative position required is either horizontal or vertical. Less precisely, the term ‘Surveying’ is used to the operations directed to the measurements of objects in their horizontal position. Art of measurements to determine their relative vertical positions is known as levelling.

1.1 PLANS AND MAPS

As mentioned in the definition of surveying, the objective of measurements is to show relative position of various objects on paper. Such representations on paper are called plan and map. A plan may be defined as the graphical representation of the features on, near or below the surface of the earth as projected on a horizontal plane to a suitable scale. However, since the surface of the earth is curved and that of paper is plane, no part of the earth can be represented on such maps without distortion. If the area to be represented is small, the distortion is less and large scale can be used. Such representations are called plans. If area to be represented is large, small scales are to be used and distortion is large. Representation of larger areas are called maps. Representation of a locality in a municipal area is a plan while representation of a district/country is a map. There is no exact difference between a plan and a map.

1.2 APPLICATIONS OF SURVEYING

Some of the important applications of surveying are listed below: 1. Astronomical survey helps in the study of astronomical movements of planets and for calculating local and standard times. 2. Maps prepared for countries, states and districts, etc. avoid disputes. 3. Plans prepared record the property boundaries of private, public and gov- ernment which help in avoiding unnecessary controversies. 2 Surveying and Levelling

4. Topographical maps showing natural features like rivers, streams, hills, forests help in planning irrigation projects and flood control measures. 5. Road maps help travellers and tourists to plan their programmes. 6. Locality plans help in identifying location of houses and offices in the area. 7. Maps and plans help in planning and estimating various transportation projects like roads, bridges, railways and airports. 8. For planning and executing water supply and sanitary projects one has to go for surveying first. 9. Marine and hydrographic surveys help in planning navigation routes and harbours. 10. For making final payments in large projects surveying is to be carried out. 11. Military surveys help in strategic planning. 12. For exploring mineral wealth mine surveys are required. 13. Geological surveys are necessary for determining different strata in the earth’s crust so that proper location is found for reservoirs. 14. Archaeological surveys are required for unearthing relics of antiquity.

1.3 PRIMARY DIVISIONS IN SURVEYING

The earth is an oblate spheroid, the length of equatorial axis being 12756.75 km and polar axis being 12713.80 km. Since the difference between these two axes and irregularities on the earth surfaces are very small compared to these two axes, the plane passing through any point and the centre of the earth may be treated as circular. Figure 1.1 shows such a circular plate, passing through the point A. The gravitational force is always directed towards the centre of the earth. Hence, a plumb line is shown in the figure, known as a vertical line. Line perpendicular to vertical line (tangential to earth surface is known as horizontal line. In surveying all measurements at any point are in the direction of these two lines.

Horizontal line at A Vertical B lines

Centre of Horizontal line at B earth

Fig. 1.1 Vertical and horizontal lines Introduction 3

If we take another point on the surface of the earth, (say point B), obviously the vertical and horizontal lines here are not parallel to the vertical and horizontal lines respectively at A. Hence, in surveying earth’s curvature is to be considered. It should be noted that all lines lying on the earth’s surface are curved lines and all triangles are spherical triangles as shown in Fig. 1.2. Surveying involves spherical trigonometry.

A B

Fig. 1.2 Plane and spherical triangles

If the area to be surveyed is small, the curvatures of earth may be neglected and all plumb lines treated as the same vertical. Hence, the lines normal to plumb lines at any point in the area are treated as the same horizontal. All triangles in the area may be treated as plane triangles. The survey in which earth’s curvature is considered is called Geodetic Survey- ing and the survey in which earth’s curvature is neglected is called Plane Sur- veying. No definite limit can be assigned to the area upto which a survey may be treated as plane, since the degree of accuracy required forms the controlling factor. However, a surveyor should note the following two points: 1. The length of an arc of 1.2 km on earth’s mean surface is only 1 mm more than the straight line connecting those two points. 2. The sum of the interior angles of a geometrical figure laid on the surface of the earth differs from that of the corresponding figure only to the extent of one second for about every 200 square kilometres of area. Hence, plane surveying is used in most of engineering projects. The geodetic surveying is used to determine the precise positions of control stations on the surface of the earth to which plane survey details are connected in works of larger magnitude like preparing maps. Thus, in surveying there are two primary divisions viz: Geodetic Surveying and Plane Surveying.

1.4 CLASSIFICATION OF SURVEYING

Surveying may be classified based on the following three points: 1. Nature of the field of survey 4 Surveying and Levelling

2. Object of survey 3. Instruments used. 4. The methods employed

1.4.1 Classification Based on Nature of the Field of Survey

On this basis field of survey may be classified as land survey, marine or hydraulic survey and astronomical survey. Land Survey: It involves measurement of various objects on land. This type of survey may be further classified as given below: (i) Topographic Surveys: They consist of measurement of various points to plot natural features such as rivers, streams, lakes, hills and forests as well as man-made features like roads, railways, towns, villages and canals. (ii) Cadestal Surveys: These surveys are for marking boundaries of munici- palities, states, etc. The surveys made to mark properties of individuals also come under this category. (iii) City Surveys: The surveys made in connection with the construction of streets, water supply and sewage lines fall under this category. Marine or Hydrographic Surveys: The survey conducted to find depth of water at various points in bodies of water like sea, river and lakes fall under this category of surveying. Finding depth of water at specified points is known as soundings. Astronomical Surveys: Observations made to heavenly bodies like sun and stars to locate absolute position of points on the earth and for the purpose of calculating local times is known as astronomical survey.

1.4.2 Classification Based on Object of Surveying

On the basis of objective of surveying, the classification can be as engineering survey, military survey, mines survey, geological survey and archaeological survey. 1. Engineering Survey: The objective of this type of surveying is to collect data for designing roads, railways, irrigation, water supply and sewage disposal projects. These surveys may be further subdivided into: (i) Reconnaissance survey for determining feasibility and estimation of the scheme. (ii) Preliminary survey for collecting more information to estimate the cost of the project selected, and (iii) Location survey to set the work on the ground. 2. Military Survey: This survey is meant for working out points of strategic importance. 3. Mine Survey: This is used for exploring mineral wealth. Introduction 5

4. Geological Survey: This survey is for finding different strata in the earth’s crust. 5. Archaeological Survey: This survey is for unearthing relics of antiquity.

1.4.3 Classification Based on Instruments Used

Based on the instruments used, surveying may be classified into the following: 1. Chain Survey 2. Compass Survey 3. Plane Table Survey 4. Theodolite Survey 5. Tacheometric Survey 6. Modern Survey using electronic equipment like distance metres and total stations 7. Photographic and Aerial Survey. The engineering students are taught surveying mainly based on this classification.

1.4.4 Classification Based on the Methods Employed

Based on the methods employed, surveying may be classified as triangulation and traversing. 1. Triangulation: In this method control points are established through a network of triangles. 2. Traversing: In this scheme of control points consist of a series of connected points established through linear and angular measurements. If last line meets the starting point it is called as closed traverse. If it does not meet, it is known as open traverse.

1.5 MEASUREMENTS

In surveying linear as well as angular measurements are involved. Linear measurements are horizontal or vertical only. Even if inclined measurements are made they B

B1 Fig. 1.3 6 Surveying and Levelling should be converted into equivalent horizontal and vertical distances to be shown in the maps. In Fig. 1.3, AB is a inclined line. Horizontal distance of AB is AB1 which is shown in plans and vertical distance BB1 is shown in elevations. Angular measurements are also in a horizontal plane or in a vertical plane.

1.6 UNITS OF MEASUREMENTS

In 1956 according to standards of Weights and Measurement Act, India switched over to MKS units giving up FPS units used earlier. In 1960 System International of units (SI units), i.e. International System of units was approved by the Con- ference of Weights and Measures. It is an international organization of which most of the countries are the members. In this system also unit of linear measurement is metre. However, main difference in MKS and SI units in linear measurement is centimetre (cm) is commonly used in MKS while its use in SI is discouraged. The recommended multipliers in SI units are given below. Giga metre = 1 ¥ 109 metre Mega metre = 1 ¥ 106 metre Kilometres = 1 ¥ 103 metre Metre = 1 ¥ 100 metre Millimetre = 1 ¥ 10–3 metre Micrometre = 1 ¥ 10–6 metre Commonly used linear units in surveying are kilometre, metre and millimetres. For measurement of angles sexagesimal system is used. In this 1 circumference = 360° (degrees) 1 degree = 60¢ (minutes of arc) 1 minute = 60≤ (seconds of arc).

1.7 SCALES

It is not possible and also not desirable to make maps to full scale. All distances are reduced by fixed proportion and drawings are made. The scale of a map or the drawing is the fixed proportion which every distance on the map bears to the corresponding distance on the ground. Thus, if 1mm on the paper represents 1m on the ground, then the scale is 1 mm = 1 m (or 1 cm = 10 m) or 1:1000. To make scale independent of units it is preferable to use representative factor, which is defined as the ratio of distance of one unit on paper to one unit on ground. Thus, 1 mm = 1 m is equivalent to 1 RF = 1000 Apart from writing scale/representative factor, it is desirable to show it graphi- cally on all drawings. The reason is, over the time, the paper may shrink and scale/ Introduction 7

RF written may mislead the reader. The graphical scale should be sufficiently long (180 mm to 270 mm) and the main divisions should represent one, ten or hundred units so that it can be easily read. The scale of a map is considered as (i) large if greater than 1 cm = 10 m (RF > 1/1000) (1:1000) (ii) Intermediate if between 1 cm = 10 m and 1 cm = 100 m (1:1000) (1:10000) (iii) Small if less than 1 cm = 100 m. (1:10000) In general, scale selected should be as small as possible, since it is not possible to read the map accurately for less than 0.25 mm distance. The recommended scales for various types of surveys are shown in Table 1.1.

Table 1.1 Recommended Scales for Various Types of Surveys

Type of Survey Scale RF 1 1. Building sites 1 cm = 10 m or less or less 1000 (1: 1000 or less) 1 1 2. Town planning schemes 1 cm = 50 m to 100 m to 5000 10000 and reservoirs (1:5000 to 1:10000) 1 1 3. Cadastral maps 1 cm = 5 m to 500 m to 500 50000 (1: 500 to 1:50000) 1 1 4. Location Surveys 1 cm = 50 m to 200 m to 5000 20000 (1:5000 to 1:20000) 1 1 5. Topographic Surveys 1 cm = 250 m to 2500 m to 25000 250000 (1:25000 to 1:250000) 1 1 6. Geographic maps 1 cm = 5000 m to 160000 m to 500000 16000000 (1:500000 to 1:16000000) 1 7. Route Surveys 1 cm = 100 m 10000 (1:10000) 8. Longitudinal Sections 1 1 (i) Horizontal scale 1 cm = 10 m to 200 m to 1000 20000 (1:1000 to 1:20000) 1 1 (ii) Vertical scale 1 cm = 1 m to 2 m to 100 200 (1:100 to 1:200) 1 1 9. Cross-sections 1 cm = 1 m to 2 m to 100 200 (Both horizontal and (1:100 to 1:200) vertical scales same) 8 Surveying and Levelling

1.8 TYPES OF GRAPHICAL SCALES

Any one of the following two graphical scales should be drawn on survey drawings: (i) Plain scale (ii) Diagonal scale.

1.8.1 Plain Scale

It is not drawn like a foot-rule (30 cm rule) scale. If a scale of 1:40 is to be drawn, the markings are not like 4 m, 8 m, 12 m at every cm distances. On a plain scale it is possible to read two dimensions directly such as unit and tenths. Construction of such a scale is illustrated with the example below:

1 Example 1.1 Construct a plain scale of RF = and indicate 53 m on it. 400 Solution: If total length of the scale on paper is selected as 20 cm, it represents a total length of 40 ¥ 20 = 8000 cm = 80 m. Hence, draw a line of 20 cm and divide it into eight equal parts. Hence, each part corresponds to 10 m on the ground. First part on extreme left is further subdivided into 10 parts, each subdivision representing 1 m on the field. Then they are numbered as shown in Fig. 1.4. If any distance on the map is between 50 m and 60 m, it is picked up with a divider and one leg of divider is placed at 50 m marking. The other leg of the divider falls in the first division, from which one can read field distance directly. Reading of 53 m is shown in the figure.

53 m

10 5 0 10 20 30 40 50 60 70

1 Fig. 1.4 Plain Scale 1:400 LRF = O NM 400 QP

IS 1491-1959 recommends requirements of metric plain scales designated as A, B, C, D, E and F as shown in Table 1.2. They are commonly available in market. They are made of either varnished cardboard or of plastic materials. Such scales are commonly used by architects, engineers and surveyors.

Table 1.2 Recommended Plain Scales

Designation Scale RF A Full size 1/1 (1:1) 50 cm to a metre 1/2 (1:2) B 40 cm to a metre 1/2.5 (1:25) 20 cm to a metre 1/5 (1:5) Contd. Introduction 9

C 10 cm to a metre 1/10 (1:10) 5 cm to a metre 1/20 (1:20) D 2 cm to a metre 1/50 (1:50) 1 cm to a metre 1/100 (1:100) E 5 mm to a metre 1/200 (1:200) 2 mm to a metre 1/500 (1:500) F 1 mm to a metre 1/1000 (1:1000) 0.5 mm to a metre 1/2000 (1:2000)

1.8.2 Diagonal Scale

In plain scale only units and tenths could be shown whereas in diagonal scales it is possible to show units, tenths and hundredths. Units and tenths are shown as in plain scale. To show hundredths, principle of similar triangles is used. If AB is a small length and its tenths are to be shown, it can be done as shown below in Fig. 1.5. Draw the line AC of convenient length at right angles to AB. Divide it into 10 parts.

C 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 AB Fig. 1.5

From each tenth line on AC draw lines parallel to AB. Then line 1-1 represents 1 4 th of AB, 4-4 represents th of AB, 8-8 represents 8/10 of AB. 10 10 Using this principle construction and use of diagonal scale is illustrated with example 1.2.

1 Example 1.2 Construct a diagonal scale with RF = and indicate 53.6 m 400 on it. Solution: Plain scale as explained in example 1.1 is first drawn. Then a rectangle of suitable size is made as shown in Fig. 1.6. The ordinate of this rectangular block is divided into 10 equal parts and horizontal lines are drawn. In the first part lines Surveying & Levelling Volume-I

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