Elementary Surveying, 13e,is ideal for Surveying courses offered in Civil Engineering departments. This highly readable, best-selling text presents basic concepts and practical material in each of the areas fundamental to modern surveying (geomatics) practice. Its depth and breadth are ideal for self-study. The 13th Edition is updated throughout to reflect the latest advances and technology.

Dr. Charles Ghilani is a Professor of Engineering in the B.S. Surveying Engineering and A.S. Surveying Technology programs at Penn State. He holds a Ph.D. and M.S. in Civil and Environmental Engineering from the University of Wisconsin-Madison, and a B.S. degree in mathematics and education from the University of Wisconsin-Milwaukee. He has been involved in education since 1974; teaching at various levels from elementary through graduate school.

Dr. Ghilani has received numerous awards including: a Campus Innovation Award (1991) and Professional Development Award (1994), P.S.L.S. presidential commendation in 1990, Outstanding Club Advisor in 1992, a Distinguished Service Award from the Pennsylvania Society of Land Surveyors in 1995, an American Congress on Surveying and Mapping (ACSM) fellowship (1999), and the Earle J. Fennell Award (2001) for outstanding service in surveying and mapping education from ACSM. He is a member of the graduate faculty at Penn State and University of Maine.

Dr. Ghilani is a member of the American Congress of Surveying and Mapping, the American Society of Photogrammetry and Remote Sensing, the Wisconsin Society of Land Surveyors, and the Pennsylvania Society of Land Surveyors. Dr. Ghilani has authored several professional publications, including **Adjustment Computations: Statistics and Least Squares in Surveying and GIS**, 5th Edition, and **Elementary Surveying: An Introduction to Geomatics,** 13th Edition.

**1 • INTRODUCTION 1**

1.1 Definition of Surveying 1

1.2 Geomatics 3

1.3 History of Surveying 4

1.4 Geodetic and Plane Surveys 9

1.5 Importance of Surveying 10

1.6 Specialized Types of Surveys 11

1.7 Surveying Safety 13

1.8 Land and Geographic Information Systems 14

1.9 Federal Surveying and Mapping Agencies 15

1.10 The Surveying Profession 16

1.11 Professional Surveying Organizations 17

1.12 Surveying on the Internet 18

1.13 Future Challenges in Surveying 19

Problems 20

Bibliography 21

**2 • UNITS, SIGNIFICANT FIGURES, AND FIELD NOTES 23**

*PART I UNITS AND SIGNIFICANT FIGURES 23*

2.1 Introduction 23

2.2 Units of Measurement 23

2.3 International System of Units (SI) 25

2.4 Significant Figures 27

2.5 Rounding Off Numbers 29

*PART II FIELD NOTES 30*

2.6 Field Notes 30

2.7 General Requirements of Handwritten Field Notes 31

2.8 Types of Field Books 32

2.9 Kinds of Notes 33

2.10 Arrangements of Notes 33

2.11 Suggestions for Recording Notes 35

2.12 Introduction to Data Collectors 36

2.13 Transfer of Files from Data Collectors 39

2.14 Digital Data File Management 41

2.15 Advantages and Disadvantages of Data Collectors 42

Problems 43

Bibliography 44

**3 • THEORY OF ERRORS IN OBSERVATIONS 45**

3.1 Introduction 45

3.2 Direct and Indirect Observations 45

3.3 Errors in Measurements 46

3.4 Mistakes 46

3.5 Sources of Errors in Making Observations 47

3.6 Types of Errors 47

3.7 Precision and Accuracy 48

3.8 Eliminating Mistakes and Systematic Errors 49

3.9 Probability 49

3.10 Most Probable Value 50

3.11 Residuals 51

3.12 Occurrence of Random Errors 51

3.13 General Laws of Probability 55

3.14 Measures of Precision 55

3.15 Interpretation of Standard Deviation 58

3.16 The 50, 90, and 95 Percent Errors 58

3.17 Error Propagation 60

3.18 Applications 65

3.19 Conditional Adjustment of Observations 65

3.20 Weights of Observations 66

3.21 Least-Squares Adjustment 67

3.22 Using Software 68

Problems 69

Bibliography 71

**4 • LEVELING–THEORY, METHODS, AND EQUIPMENT 73**

*PART I LEVELING–THEORY AND METHODS 73*

4.1 Introduction 73

4.2 Definitions 73

4.3 North American Vertical Datum 75

4.4 Curvature and Refraction 76

4.5 Methods for Determining Differences in Elevation 78

*PART II EQUIPMENT FOR DIFFERENTIAL LEVELING 85*

4.6 Categories of Levels 85

4.7 Telescopes 86

4.8 Level Vials 87

4.9 Tilting Levels 89

4.10 Automatic Levels 90

4.11 Digital Levels 91

4.12 Tripods 93

4.13 Hand Level 93

4.14 Level Rods 94

4.15 Testing and Adjusting Levels 96

Problems 100

Bibliography 102

**5 • LEVELING–FIELD PROCEDURES AND COMPUTATIONS 103**

5.1 Introduction 103

5.2 Carrying and Setting Up a Level 103

5.3 Duties of a Rodperson 105

5.4 Differential Leveling 106

5.5 Precision 112

5.6 Adjustments of Simple Level Circuits 113

5.7 Reciprocal Leveling 114

5.8 Three-Wire Leveling 115

5.9 Profile Leveling 117

5.10 Grid, Cross-Section, or Borrow-Pit Leveling 121

5.11 Use of the Hand Level 122

5.12 Sources of Error in Leveling 122

5.13 Mistakes 124

5.14 Reducing Errors and Eliminating Mistakes 125

5.15 Using Software 125

Problems 127

Bibliography 129

**6 • DISTANCE MEASUREMENT 131**

*PART I METHODS FOR MEASURING DISTANCES 131*

6.1 Introduction 131

6.2 Summary of Methods for Making Linear Measurements 131

6.3 Pacing 132

6.4 Odometer Readings 132

6.5 Optical Rangefinders 133

6.6 Tacheometry 133

6.7 Subtense Bar 133

*PART II DISTANCE MEASUREMENTS BY TAPING 133*

6.8 Introduction to Taping 133

6.9 Taping Equipment and Accessories 134

6.10 Care of Taping Equipment 135

6.11 Taping on Level Ground 136

6.12 Horizontal Measurements on Sloping Ground 138

6.13 Slope Measurements 140

6.14 Sources of Error in Taping 141

6.15 Tape Problems 145

6.16 Combined Corrections in a Taping Problem 147

*PART III ELECTRONIC DISTANCE MEASUREMENT 148*

6.17 Introduction 148

6.18 Propagation of Electromagnetic Energy 149

6.19 Principles of Electronic Distance Measurement 152

6.20 Electro-Optical Instruments 153

6.21 Total Station Instruments 156

6.22 EDM Instruments Without Reflectors 157

6.23 Computing Horizontal Lengths from Slope Distances 158

6.24 Errors in Electronic Distance Measurement 160

6.25 Using Software 165

Problems 165

Bibliography 168

**7 • ANGLES, AZIMUTHS, AND BEARINGS 169**

7.1 Introduction 169

7.2 Units of Angle Measurement 169

7.3 Kinds of Horizontal Angles 170

7.4 Direction of a Line 171

7.5 Azimuths 172

7.6 Bearings 173

7.7 Comparison of Azimuths and Bearings 174

7.8 Computing Azimuths 175

7.9 Computing Bearings 177

7.10 The Compass and the Earth’s Magnetic Field 179

7.11 Magnetic Declination 180

7.12 Variations in Magnetic Declination 181

7.13 Software for Determining Magnetic Declination 183

7.14 Local Attraction 184

7.15 Typical Magnetic Declination Problems 185

7.16 Mistakes 187

Problems 187

Bibliography 189

**8 • TOTAL STATION INSTRUMENTS; ANGLE OBSERVATIONS 191**

*PART I TOTAL STATION INSTRUMENTS 191*

8.1 Introduction 191

8.2 Characteristics of Total Station Instruments 191

8.3 Functions Performed by Total Station Instruments 194

8.4 Parts of a Total Station Instrument 195

8.5 Handling and Setting Up a Total Station Instrument 199

8.6 Servo-Driven and Remotely Operated Total Station Instruments 201

*PART II ANGLE OBSERVATIONS 203*

8.7 Relationship of Angles and Distances 203

8.8 Observing Horizontal Angles with Total Station Instruments 204

8.9 Observing Horizontal Angles by the Direction Method 206

8.10 Closing the Horizon 207

8.11 Observing Deflection Angles 209

8.12 Observing Azimuths 211

8.13 Observing Vertical Angles 211

8.14 Sights and Marks 213

8.15 Prolonging a Straight Line 214

8.16 Balancing-In 216

8.17 Random Traverse 217

8.18 Total Stations for Determining Elevation Differences 218

8.19 Adjustment of Total Station Instruments and Their Accessories 219

8.20 Sources of Error in Total Station Work 222

8.21 Propagation of Random Errors in Angle Observations 228

8.22 Mistakes 228

Problems 229

Bibliography 230

**9 • TRAVERSING 231**

9.1 Introduction 231

9.2 Observation of Traverse Angles or Directions 233

9.3 Observation of Traverse Lengths 234

9.4 Selection of Traverse Stations 235

9.5 Referencing Traverse Stations 235

9.6 Traverse Field Notes 237

9.7 Angle Misclosure 238

9.8 Traversing with Total Station Instruments 239

9.9 Radial Traversing 240

9.10 Sources of Error in Traversing 241

9.11 Mistakes in Traversing 242

Problems 242

**10 • TRAVERSE COMPUTATIONS 245**

10.1 Introduction 245

10.2 Balancing Angles 246

10.3 Computation of Preliminary Azimuths or Bearings 248

10.4 Departures and Latitudes 249

10.5 Departure and Latitude Closure Conditions 251

10.6 Traverse Linear Misclosure and Relative Precision 251

10.7 Traverse Adjustment 252

10.8 Rectangular Coordinates 255

10.9 Alternative Methods for Making Traverse Computations 256

10.10 Inversing 260

10.11 Computing Final Adjusted Traverse Lengths and Directions 261

10.12 Coordinate Computations in Boundary Surveys 263

10.13 Use of Open Traverses 265

10.14 State Plane Coordinate Systems 268

10.15 Traverse Computations Using Computers 269

10.16 Locating Blunders in Traverse Observations 269

10.17 Mistakes in Traverse Computations 272

Problems 272

Bibliography 275

**11 • COORDINATE GEOMETRY IN SURVEYING CALCULATIONS 277**

11.1 Introduction 277

11.2 Coordinate Forms of Equations for Lines and Circles 278

11.3 Perpendicular Distance from a Point to a Line 280

11.4 Intersection of Two Lines, Both Having Known Directions 282

11.5 Intersection of a Line with a Circle 284

11.6 Intersection of Two Circles 287

11.7 Three-Point Resection 289

11.8 Two-Dimensional Conformal Coordinate Transformation 292

11.9 Inaccessible Point Problem 297

11.10 Three-Dimensional Two-Point Resection 299

11.11 Software 302

Problems 303

Bibliography 307

**12 • AREA 309**

12.1 Introduction 309

12.2 Methods of Measuring Area 309

12.3 Area by Division Into Simple Figures 310

12.4 Area by Offsets from Straight Lines 311

12.5 Area by Coordinates 313

12.6 Area by Double-Meridian Distance Method 317

12.7 Area of Parcels with Circular Boundaries 320

12.8 Partitioning of Lands 321

12.9 Area by Measurements from Maps 325

12.10 Software 327

12.11 Sources of Error in Determining Areas 328

12.12 Mistakes in Determining Areas 328

Problems 328

Bibliography 330

**13 • GLOBAL NAVIGATION SATELLITE SYSTEMS—INTRODUCTION AND PRINCIPLES OF OPERATION 331**

13.1 Introduction 331

13.2 Overview of GPS 332

13.3 The GPS Signal 335

13.4 Reference Coordinate Systems 337

13.5 Fundamentals of Satellite Positioning 345

13.6 Errors in Observations 348

13.7 Differential Positioning 356

13.8 Kinematic Methods 358

13.9 Relative Positioning 359

13.10 Other Satellite Navigation Systems 362

13.11 The Future 364

Problems 365

Bibliography 366

**14 • GLOBAL NAVIGATION SATELLITE SYSTEMS—STATIC SURVEYS 367**

14.1 Introduction 367

14.2 Field Procedures in Satellite Surveys 369

14.3 Planning Satellite Surveys 372

14.4 Performing Static Surveys 384

14.5 Data Processing and Analysis 386

14.6 Sources of Errors in Satellite Surveys 393

14.7 Mistakes in Satellite Surveys 395

Problems 395

Bibliography 397

**15 • GLOBAL NAVIGATION SATELLITE SYSTEMS—KINEMATIC SURVEYS 399**

15.1 Introduction 399

15.2 Planning of Kinematic Surveys 400

15.3 Initialization 402

15.4 Equipment Used in Kinematic Surveys 403

15.5 Methods Used in Kinematic Surveys 405

15.6 Performing Post-Processed Kinematic Surveys 408

15.7 Communication in Real-Time Kinematic Surveys 411

15.8 Real-Time Networks 412

15.9 Performing Real-Time Kinematic Surveys 413

15.10 Machine Control 414

15.11 Errors in Kinematic Surveys 418

15.12 Mistakes in Kinematic Surveys 418

Problems 418

Bibliography 419

**16 • ADJUSTMENTS BY LEAST SQUARES 421**

16.1 Introduction 421

16.2 Fundamental Condition of Least Squares 423

16.3 Least-Squares Adjustment by the Observation Equation Method 424

16.4 Matrix Methods in Least-Squares Adjustment 428

16.5 Matrix Equations for Precisions of Adjusted Quantities 430

16.6 Least-Squares Adjustment of Leveling Circuits 432

16.7 Propagation of Errors 436

16.8 Least-Squares Adjustment of GNSS Baseline Vectors 437

16.9 Least-Squares Adjustment of Conventional Horizontal Plane Surveys 443

16.10 The Error Ellipse 452

16.11 Adjustment Procedures 457

16.12 Other Measures of Precision for Horizontal Stations 458

16.13 Software 460

16.14 Conclusions 460

Problems 461

Bibliography 466

**17 • MAPPING SURVEYS 467**

17.1 Introduction 467

17.2 Basic Methods for Performing Mapping Surveys 468

17.3 Map Scale 468

17.4 Control for Mapping Surveys 470

17.5 Contours 471

17.6 Characteristics of Contours 474

17.7 Direct and Indirect Methods of Locating Contours 474

17.8 Digital Elevation Models and Automated Contouring Systems 477

17.9 Basic Field Methods for Locating Topographic Details 479

17.10 Three-Dimensional Conformal Coordinate Transformation 488

17.11 Selection of Field Method 489

17.12 Working with Data Collectors and Field-to-Finish Software 490

17.13 Hydrographic Surveys 493

17.14 Sources of Error in Mapping Surveys 497

17.15 Mistakes in Mapping Surveys 498

Problems 498

Bibliography 500

**18 • MAPPING 503**

18.1 Introduction 503

18.2 Availability of Maps and Related Information 504

18.3 National Mapping Program 505

18.4 Accuracy Standards for Mapping 505

18.5 Manual and Computer-Aided Drafting Procedures 507

18.6 Map Design 508

18.7 Map Layout 510

18.8 Basic Map Plotting Procedures 512

18.9 Contour Interval 514

18.10 Plotting Contours 514

18.11 Lettering 515

18.12 Cartographic Map Elements 516

18.13 Drafting Materials 519

18.14 Automated Mapping and Computer-Aided Drafting Systems 519

18.15 Impacts of Modern Land and Geographic Information Systems on Mapping 525

18.16 Sources of Error in Mapping 526

18.17 Mistakes in Mapping 526

Problems 526

Bibliography 528

**19 • CONTROL SURVEYS AND GEODETIC REDUCTIONS 529**

19.1 Introduction 529

19.2 The Ellipsoid and Geoid 530

19.3 The Conventional Terrestrial Pole 532

19.4 Geodetic Position and Ellipsoidal Radii of Curvature 534

19.5 Geoid Undulation and Deflection of the Vertical 536

19.6 U.S. Reference Frames 538

19.7 Accuracy Standards and Specifications for Control Surveys 547

19.8 The National Spatial Reference System 550

19.9 Hierarchy of the National Horizontal Control Network 550

19.10 Hierarchy of the National Vertical Control Network 551

19.11 Control Point Descriptions 551

19.12 Field Procedures for Traditional Horizontal Control Surveys 554

19.13 Field Procedures for Vertical Control Surveys 559

19.14 Reduction of Field Observations to Their Geodetic Values 564

19.15 Geodetic Position Computations 577

19.16 The Local Geodetic Coordinate System 580

19.17 Three-Dimensional Coordinate Computations 581

19.18 Software 584

Problems 584

Bibliography 587

**20 • STATE PLANE COORDINATES AND OTHER MAP PROJECTIONS 589**

20.1 Introduction 589

20.2 Projections Used in State Plane Coordinate Systems 590

20.3 Lambert Conformal Conic Projection 593

20.4 Transverse Mercator Projection 594

20.5 State Plane Coordinates in NAD27 and NAD83 595

20.6 Computing SPCS83 Coordinates in the Lambert Conformal Conic System 596

20.7 Computing SPCS83 Coordinates in the Transverse Mercator System 601

20.8 Reduction of Distances and Angles to State Plane Coordinate Grids 608

20.9 Computing State Plane Coordinates of Traverse Stations 617

20.10 Surveys Extending from One Zone to Another 620

20.11 Conversions Between SPCS27 and SPCS83 621

20.12 The Universal Transverse Mercator Projection 622

20.13 Other Map Projections 623

20.14 Map Projection Software 627

Problems 628

Bibliography 631

**21 • BOUNDARY SURVEYS 633**

21.1 Introduction 633

21.2 Categories of Land Surveys 634

21.3 Historical Perspectives 635

21.4 Property Description by Metes and Bounds 636

21.5 Property Description by Block-and-Lot System 639

21.6 Property Description by Coordinates 641

21.7 Retracement Surveys 641

21.8 Subdivision Surveys 644

21.9 Partitioning Land 646

21.10 Registration of Title 647

21.11 Adverse Possession and Easements 648

21.12 Condominium Surveys 648

21.13 Geographic and Land Information Systems 655

21.14 Sources of Error in Boundary Surveys 655

21.15 Mistakes 655

Problems 656

Bibliography 658

**22 • SURVEYS OF THE PUBLIC LANDS 659**

22.1 Introduction 659

22.2 Instructions for Surveys of the Public Lands 660

22.3 Initial Point 663

22.4 Principal Meridian 664

22.5 Baseline 665

22.6 Standard Parallels (Correction Lines) 666

22.7 Guide Meridians 666

22.8 Township Exteriors, Meridional (Range) Lines, and Latitudinal (Township) Lines 667

22.9 Designation of Townships 668

22.10 Subdivision of a Quadrangle into Townships 668

22.11 Subdivision of a Township into Sections 670

22.12 Subdivision of Sections 671

22.13 Fractional Sections 672

22.14 Notes 672

22.15 Outline of Subdivision Steps 672

22.16 Marking Corners 674

22.17 Witness Corners 674

22.18 Meander Corners 675

22.19 Lost and Obliterated Corners 675

22.20 Accuracy of Public Lands Surveys 678

22.21 Descriptions by Township Section and Smaller Subdivision 678

22.22 BLM Land Information System 679

22.23 Sources of Error 680

22.24 Mistakes 680

Problems 681

Bibliography 683

**23 • CONSTRUCTION SURVEYS 685**

23.1 Introduction 685

23.2 Specialized Equipment for Construction Surveys 686

23.3 Horizontal and Vertical Control 689

23.4 Staking Out a Pipeline 691

23.5 Staking Pipeline Grades 692

23.6 Staking Out a Building 694

23.7 Staking Out Highways 698

23.8 Other Construction Surveys 703

23.9 Construction Surveys Using Total Station Instruments 704

23.10 Construction Surveys Using GNSS Equipment 706

23.11 Machine Guidance and Control 709

23.12 As-Built Surveys with Laser Scanning 710

23.13 Sources of Error in Construction Surveys 711

23.14 Mistakes 712

Problems 712

Bibliography 714

**24 • HORIZONTAL CURVES 715**

24.1 Introduction 715

24.2 Degree of Circular Curve 716

24.3 Definitions and Derivation of Circular Curve Formulas 718

24.4 Circular Curve Stationing 720

24.5 General Procedure of Circular Curve Layout by Deflection Angles 721

24.6 Computing Deflection Angles and Chords 723

24.7 Notes for Circular Curve Layout by Deflection Angles and Incremental Chords 725

24.8 Detailed Procedures for Circular Curve Layout by Deflection Angles and Incremental Chords 726

24.9 Setups on Curve 727

24.10 Metric Circular Curves by Deflection Angles and Incremental Chords 728

24.11 Circular Curve Layout by Deflection Angles and Total Chords 730

24.12 Computation of Coordinates on a Circular Curve 731

24.13 Circular Curve Layout by Coordinates 733

24.14 Curve Stakeout Using GNSS Receivers and Robotic Total Stations 738

24.15 Circular Curve Layout by Offsets 739

24.16 Special Circular Curve Problems 742

24.17 Compound and Reverse Curves 743

24.18 Sight Distance on Horizontal Curves 743

24.19 Spirals 744

24.20 Computation of “As-Built” Circular Alignments 749

24.21 Sources of Error in Laying Out Circular Curves 752

24.22 Mistakes 752

Problems 753

Bibliography 755

**25 • VERTICAL CURVES 757**

25.1 Introduction 757

25.2 General Equation of a Vertical Parabolic Curve 758

25.3 Equation of an Equal Tangent Vertical Parabolic Curve 759

25.4 High or Low Point on a Vertical Curve 761

25.5 Vertical Curve Computations Using the Tangent Offset Equation 761

25.6 Equal Tangent Property of a Parabola 765

25.7 Curve Computations by Proportion 766

25.8 Staking a Vertical Parabolic Curve 766

25.9 Machine Control in Grading Operations 767

25.10 Computations for an Unequal Tangent Vertical Curve 767

25.11 Designing a Curve to Pass Through a Fixed Point 770

25.12 Sight Distance 771

25.13 Sources of Error in Laying Out Vertical Curves 773

25.14 Mistakes 774

Problems 774

Bibliography 776

**26 • VOLUMES 777**

26.1 Introduction 777

26.2 Methods of Volume Measurement 777

26.3 The Cross-Section Method 778

26.4 Types of Cross Sections 779

26.5 Average-End-Area Formula 780

26.6 Determining End Areas 781

26.7 Computing Slope Intercepts 784

26.8 Prismoidal Formula 786

26.9 Volume Computations 788

26.10 Unit-Area, or Borrow-Pit, Method 790

26.11 Contour-Area Method 791

26.12 Measuring Volumes of Water Discharge 793

26.13 Software 794

26.14 Sources of Error in Determining Volumes 795

26.15 Mistakes 795

Problems 795

Bibliography 798

**27 • PHOTOGRAMMETRY 799**

27.1 Introduction 799

27.2 Uses of Photogrammetry 800

27.3 Aerial Cameras 801

27.4 Types of Aerial Photographs 803

27.5 Vertical Aerial Photographs 804

27.6 Scale of a Vertical Photograph 806

27.7 Ground Coordinates from a Single Vertical Photograph 810

27.8 Relief Displacement on a Vertical Photograph 811

27.9 Flying Height of a Vertical Photograph 813

27.10 Stereoscopic Parallax 814

27.11 Stereoscopic Viewing 817

27.12 Stereoscopic Measurement of Parallax 819

27.13 Analytical Photogrammetry 820

27.14 Stereoscopic Plotting Instruments 821

27.15 Orthophotos 826

27.16 Ground Control for Photogrammetry 827

27.17 Flight Planning 828

27.18 Airborne Laser-Mapping Systems 830

27.19 Remote Sensing 831

27.20 Software 837

27.21 Sources of Error in Photogrammetry 838

27.22 Mistakes 838

Problems 839

Bibliography 842

**28 • INTRODUCTION TO GEOGRAPHIC INFORMATION SYSTEMS 843**

28.1 Introduction 843

28.2 Land Information Systems 846

28.3 GIS Data Sources and Classifications 846

28.4 Spatial Data 846

28.5 Nonspatial Data 852

28.6 Data Format Conversions 853

28.7 Creating GIS Databases 856

28.8 Metadata 862

28.9 GIS Analytical Functions 862

28.10 GIS Applications 867

28.11 Data Sources 867

Problems 869

Bibliography 871

APPENDIX A • DUMPY LEVELS, TRANSITS, AND THEODOLITES 873

APPENDIX B • EXAMPLE NOTEFORMS 888

APPENDIX C • ASTRONOMICAL OBSERVATIONS 895

APPENDIX D • USING THE WORKSHEETS FROM THE COMPANION WEBSITE 911

APPENDIX E • INTRODUCTION TO MATRICES 917

APPENDIX F • U.S. STATE PLANE COORDINATE SYSTEM DEFINING PARAMETERS 923

APPENDIX G • ANSWERS TO SELECTED PROBLEMS 927

INDEX 933