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. Elementary Surveying, Fourteenth Edition, is updated throughout to reflect the latest advances and technology. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: Emphasize the Theory of Errors in Surveying Work: Common errors and mistakes are listed to remind students to exercise caution in their work. Use Strong Pedagogy Tools to Teach: Numerous worked example problems, figures, illustrations, and end-of-chapter problems help students apply concepts. Reflect the Latest Advances in Technology: To keep your course current and relevant, this edition covers the latest advancements in surveying technology.

1 Introduction1.1 Definition of Surveying 1.2 Geomatics 1.3 History of Surveying 1.4 Geodetic and Plane Surveys 1.5 Importance of Surveying 1.6 Specialized Types of Surveys 1.7 Surveying Safety 1.8 Land and Geographic Information Systems 1.9 Federal Surveying and Mapping Agencies 1.10 The Surveying Profession 1.11 Professional Surveying Organizations 1.12 Surveying on the Internet 1.13 Future Challenges in Surveying Problems Bibliography 2 Units, Significant Figures, and Field Notes Part I Units and Significant Figures 2.1 Introduction 2.2 Units of Measurement 2.3 International System of Units (SI) 2.4 Significant Figures 2.5 Rounding Off Numbers Part II Field Notes 2.6 Field Notes 2.7 General Requirements of Handwritten Field Notes 2.8 Types of Field Books 2.9 Kinds of Notes 2.10 Arrangements of Notes 2.11 Suggestions for Recording Notes 2.12 Introduction to Survey Controllers 2.13 Transfer of Files from Survey Controllers 2.14 Digital Data File Management 2.15 Advantages and Disadvantages of Survey Controllers Problems Bibliography 3 Theory of Errors in Observations 3.1 Introduction 3.2 Direct and Indirect Observations 3.3 Errors in Measurements 3.4 Mistakes 3.5 Sources of Errors in Making Observations 3.6 Types of Errors 3.7 Precision and Accuracy 3.8 Eliminating Mistakes and Systematic Errors 3.9 Probability 3.10 Most Probable Value 3.11 Residuals 3.12 Occurrence of Random Errors 3.13 General Laws of Probability 3.14 Measures of Precision 3.15 Interpretation of Standard Deviation 3.16 The 50, 90, and 95 Percent Errors 3.17 Error Propagation 3.17.1 Error of a Sum 3.17.2 Error of a Series 3.17.3 Error of a Product 3.17.4 Error of the Mean 3.18 Applications 3.19 Conditional Adjustment of Observations 3.20 Weights of Observations 3.21 Least-Squares Adjustment 3.22 Using Software Problems Bibliography 4 Leveling-Theory, Methods, and Equipment Part I Leveling-Theory and Methods 4.1 Introduction 4.2 Definitions 4.3 North American Vertical Datum 4.4 Curvature and Refraction 4.5 Methods for Determining Differences in Elevation 4.5.1 Measuring Vertical Distances by Taping or Electronic Methods 4.5.2 Differential Leveling 4.5.3 Barometric Leveling 4.5.4 Trigonometric Leveling Part II Equipment for Differential Leveling 4.6 Categories of Levels 4.7 Telescopes 4.8 Level Vials 4.9 Tilting Levels 4.10 Automatic Levels 4.11 Digital Levels 4.12 Tripods 4.13 Hand Level 4.14 Level Rods 4.15 Testing and Adjusting Levels 4.15.1 Requirements for Testing and Adjusting Instruments 4.15.2 Adjusting for Parallax 4.15.3 Testing and Adjusting Level Vials 4.15.4 Preliminary Adjustment of the Horizontal Cross Hair 4.15.5 Testing and Adjusting the Line of Sight Problems Bibliography 5 Leveling-Field Procedures and Computations 5.1 Introduction 5.2 Carrying and Setting Up a Level 5.3 Duties of a Rodperson 5.4 Differential Leveling 5.5 Precision 5.6 Adjustments of Simple Level Circuits 5.7 Reciprocal Leveling 5.8 Three-Wire Leveling 5.9 Profile Leveling 5.9.1 Staking and Stationing the Reference Line 5.9.2 Field Procedures for Profile Leveling 5.9.3 Drawing and Using the Profile 5.10 Grid, Cross-Section, or Borrow-Pit Leveling 5.11 Use of the Hand Level 5.12 Sources of Error in Leveling 5.12.1 Instrumental Errors 5.12.2 Natural Errors 5.12.3 Personal Errors 5.13 Mistakes 5.14 Reducing Errors and Eliminating Mistakes 5.15 Using Software Problems Bibliography 6 Distance Measurement Part I Methods for Measuring Distances 6.1 Introduction 6.2 Summary of Methods for Making Linear Measurements 6.3 Pacing 6.4 Odometer Readings 6.5 Optical Rangefinders 6.6 Tacheometry 6.7 Subtense Bar Part II Distance Measurements by Taping 6.8 Introduction to Taping 6.9 Taping Equipment and Accessories 6.10 Care of Taping Equipment 6.11 Taping on Level Ground 6.11.1 Lining In 6.11.2 Applying Tension 6.11.3 Plumbing 6.11.4 Marking Tape Lengths 6.11.5 Reading the Tape 6.11.6 Recording the Distance 6.12 Horizontal Measurements on Sloping Ground 6.13 Slope Measurements 6.14 Sources of Error in Taping 6.14.1 Incorrect Length of Tape 6.14.2 Temperature Other Than Standard 6.14.3 Inconsistent Pull 6.14.4 Sag 6.14.5 Tape Not Horizontal and Tape Off-Line 6.14.6 Improper Plumbing 6.14.7 Faulty Marking 6.14.8 Incorrect Reading or Interpolation 6.14.9 Summary of Effects of Taping Errors Part III Electronic Distance Measurement 6.17 Introduction 6.18 Propagation of Electromagnetic Energy 6.19 Principles of Electronic Distance Measurement 6.20 Electro-Optical Instruments 6.21 Total Station Instruments 6.22 EDM Instruments Without Reflectors 6.23 Computing Horizontal Lengths From Slope Distances 6.23.1 Reduction of Short Lines by Elevation Differences 6.23.2 Reduction of Short Lines by Zenith or Altitude Angle 6.24 Errors in Electronic Distance Measurement 6.24.1 Personal Errors 6.24.2 Instrumental Errors 6.24.3 Natural Errors 6.25 Using Software Problems Bibliography 7 Angles, Azimuths, and Bearings 7.1 Introduction 7.2 Units of Angle Measurement 7.3 Kinds of Horizontal Angles 7.4 Direction of a Line 7.5 Azimuths 7.6 Bearings 7.7 Comparison of Azimuths and Bearings 7.8 Computing Azimuths 7.9 Computing Bearings 7.10 The Compass and The Earth's Magnetic Field 7.11 Magnetic Declination 7.12 Variations in Magnetic Declination 7.13 Software for Determining Magnetic Declination 7.14 Local Attraction 7.15 Typical Magnetic Declination Problems 7.16 Mistakes Problems Bibliography 8 Total Station Instruments; Angle Observations Part I Total Station Instruments 8.1 Introduction 8.2 Characteristics of Total Station Instruments 8.3 Functions Performed by Total Station Instruments 8.4 Parts of a Total Station Instrument 8.5 Handling and Setting Up a Total Station Instrument 8.6 Servo-Driven and Remotely Operated Total Station Instruments Part II Angle Observations 8.7 Relationship of Angles and Distances 8.8 Observing Horizontal Angles with Total Station Instruments 8.9 Observing Multiple Horizontal Angles by the Direction Method 8.10 Closing the Horizon 8.11 Observing Deflection Angles 8.12 Observing Azimuths 8.13 Observing Vertical Angles 8.14 Sights and Marks 8.15 Prolonging a Straight Line 8.16 Balancing-In 8.17 Random Traverse 8.18 Total Stations for Determining Elevation Differences 8.19 Adjustment of Total Station Instruments and Their Accessories 8.19.1 Adjustment of Plate-Level Vials 8.19.2 Adjustment of Tripods 8.19.3 Adjustment of Tribrachs 8.19.4 Adjustment of Plummets 8.19.5 Adjustment of Circular Level Bubbles 8.20 Sources of Error in Total Station Work 8.20.1 Instrumental Errors 8.20.2 Natural Errors 8.20.3 Personal Errors 8.21 Propagation of Random Errors in Angle Observations 8.22 Mistakes Problems Bibliography 9 Traversing 9.1 Introduction 9.2 Observation of Traverse Angles or Directions 9.2.1 Traversing by Interior Angles 9.2.2 Traversing by Angles to the Right 9.2.3 Traversing by Deflection Angles 9.2.4 Traversing by Azimuths 9.3 Observation of Traverse Lengths 9.4 Selection of Traverse Stations 9.5 Referencing Traverse Stations 9.6 Traverse Field Notes 9.7 Angle Misclosure 9.8 Traversing with Total Station Instruments 9.9 Radial Traversing 9.10 Sources of Error in Traversing 9.11 Mistakes in Traversing Problems 10 Traverse Computations 10.1 Introduction 10.2 Balancing Angles 10.3 Computation of Preliminary Azimuths or Bearings 10.4 Departures and Latitudes 10.5 Departure and Latitude Closure Conditions 10.6 Traverse Linear Misclosure and Relative Precision 10.7 Traverse Adjustment 10.7.1 Compass (Bowditch) Rule 10.7.2 Least-Squares Method 10.8 Rectangular Coordinates 10.9 Alternative Methods for Making Traverse Computations 10.9.1 Balancing Angles by Adjusting Azimuths or Bearings 10.9.2 Balancing Departures and Latitudes by Adjusting Coordinates 10.10 Inversing 10.11 Computing Final Adjusted Traverse Lengths and Directions 10.12 Coordinate Computations in Boundary Surveys 10.13 Use of Open Traverses 10.14 State Plane Coordinate Systems 10.15 Traverse Computations Using Computers 10.16 Locating Blunders in Traverse Measurements 10.17 Mistakes in Traverse Computations Problems Bibliography 11 Coordinate Geometry in Surveying Calculations 11.1 Introduction 11.2 Coordinate Forms of Equations for Lines and Circles 11.3 Perpendicular Distance from a Point to a Line 11.4 Intersection of Two Lines, Both Having Known Directions 11.5 Intersection of a Line with a Circle 11.6 Intersection of Two Circles 11.7 Three-Point Resection 11.8 Two-Dimensional Conformal Coordinate Transformation 11.9 Inaccessible Point Problem 11.10 Three-Dimensional Two-Point Resection 11.11 Software Problems Bibliography 12 Area 12.1 Introduction 12.2 Methods of Measuring Area 12.3 Area by Division into Simple Figures 12.4 Area by Offsets from Straight Lines 12.4.1 Regularly Spaced Offsets 12.4.2 Irregularly Spaced Offsets 12.5 Area by Coordinates 12.6 Area by Double Meridian Distance Method 12.7 Area of Parcels with Circular Boundaries 12.8 Partitioning of Lands 12.8.1 Trial and Error Method 12.8.2 Use of Simple Geometric Figures 12.8.3 Coordinate Method 12.9 Area by Measurements from Maps 12.9.1 Area by Counting Coordinate Squares 12.9.2 Area by Scaled Lengths 12.9.3 Area by Digitizing Coordinates 12.9.4 Area by Planimeter 12.10 Software 12.11 Sources of Error in Determining Areas 12.12 Mistakes in Determining Areas Problems Bibliography 13 Global Navigation Satellite Systems-Introduction and Principles of Operation 13.1 Introduction 13.2 Overview of GPS 13.3 The GPS Signal 13.4 Reference Coordinate Systems 13.4.1 The Satellite Reference Coordinate System 13.4.2 The Geocentric Coordinate System 13.4.3 The Geodetic Coordinate System 13.4.4 Evolution of WGS84 Reference Frame 13.5 Fundamentals of Satellite Positioning 13.5.1 Code Ranging 13.5.2 Carrier Phase-Shift Measurements 13.6 Errors in Observations 13.6.1 Clock Bias 13.6.2 Refraction 13.6.3 Other Error Sources 13.6.4 Geometry of Observed Satellites 13.7 Differential Positioning 13.8 Kinematic Methods 13.9 Relative Positioning 13.9.1 Single Differencing 13.9.2 Double Differencing 13.9.3 Triple Differencing 13.10 Other Satellite Navigation Systems 13.10.1 The GLONASS Constellation 13.10.2 The Galileo System 13.10.3 The Compass System 13.10.4 Summary 13.11 The Future Problems Bibliography 14 Global Navigation Satellite Systems-Static Surveys 14.1 Introduction 14.2 Field Procedures in Satellite Surveys 14.2.1 Static Relative Positioning 14.2.2 Rapid Static Relative Positioning 14.2.3 Pseudokinematic Surveys 14.3 Planning Satellite Surveys 14.3.1 Preliminary Considerations 14.3.2 Selecting the Appropriate Survey Method 14.3.3 Field Reconnaissance 14.3.4 Developing an Observation Scheme 14.3.5 Availability of Reference Stations 14.4 Performing Static Surveys 14.5 Data Processing and Analysis 14.5.1 Specifications for Static Surveys 14.5.2 Analysis of Fixed Baseline Measurements 14.5.3 Analysis of Repeat Baseline Measurements 14.5.4 Analysis of Loop Closures 14.5.5 Baseline Network Adjustment 14.5.6 The Survey Report 14.6 Things to Consider 14.7 Sources of Errors in Satellite Surveys 14.7.1 Instrumental Errors 14.7.2 Natural Errors 378 14.7.3 Personal Errors 378 14.8 Mistakes in Satellite Surveys Problems Bibliography 15 Global Navigation Satellite System-Kinematic Surveys 15.1 Introduction 15.2 Planning of Kinematic Surveys 15.3 Initialization 15.4 Equipment Used in Kinematic Surveys 15.5 Methods Used in Kinematic Surveys 15.6 Performing Post-Processed Kinematic Surveys 15.7 Communication in Real-Time Kinematic Surveys 15.8 Real-Time Networks 15.9 Performing Real-Time Kinematic Surveys 15.10 Machine Guidance and Control 15.11 Errors in Kinematic Surveys 15.12 Mistakes in Kinematic Surveys Problems Bibliography 16 Adjustments by Least Squares 16.1 Introduction 16.2 Fundamental Condition of Least Squares 16.3 Least-Squares Adjustment by the Observation Equation Method 16.4 Matrix Methods in Least-Squares Adjustment 16.5 Matrix Equations for Precisions of Adjusted Quantities 16.6 Least-Squares Adjustment of Leveling Circuits 16.7 Propagation of Errors 16.8 Least-Squares Adjustment of GNSS Baseline Vectors 16.9 Least-Squares Adjustment of Conventional Horizontal Plane Surveys 16.9.1 Linearizing Nonlinear Equations 16.9.2 The Distance Observation Equation 16.9.3 The Azimuth Observation Equation 16.9.4 The Angle Observation Equation 16.9.5 A Traverse Example Using WOLFPACK 16.10 The Error Ellipse 16.11 Adjustment Procedures 16.12 Other Measures of Precision for Horizontal Stations 16.13 Software 16.14 Conclusions Problems Bibliography 17 Mapping Surveys 17.1 Introduction 17.2 Basic Methods for Performing Mapping Surveys 17.3 Map Scale 17.4 Control for Mapping Surveys 17.5 Contours 17.6 Characteristics of Contours 17.7 Method of Locating Contours 17.8 Digital Elevation Models and Automated Contouring Systems 17.9 Basic Field Methods for Locating Topographic Details 17.9.1 Radiation by Total Station 17.9.2 Coordinate Squares or Grid Method 17.9.3 Offsets from a Reference Line 17.9.4 Topographic Detailing with GNSS 17.9.5 Laser Scanning 17.10 Planning a Laser-Scanning Survey 17.11 Three-Dimensional Conformal Coordinate Transformation 17.12 Selection of Field Method 17.13 Working with Survey Controllers and Field-to-Finish Software 17.14 Hydrographic Surveys 17.14.1 Equipment for Making Soundings 17.14.2 Locating Soundings 17.14.3 Hydrographic Mapping 17.15 Sources of Error in Mapping Surveys 17.16 Mistakes in Mapping Surveys Problems Bibliography 18 Mapping 18.1 Introduction 18.2 Availability of Maps and Related Information 18.3 National Mapping Program 18.4 Accuracy Standards for Mapping 18.5 Manual and Computer-Aided Drafting Procedures 18.6 Map Design 18.7 Map Layout 18.8 Basic Map Plotting Procedures 18.8.1 Manually Plotting by Coordinates 18.8.2 Plotting Using CADD 18.9 Contour Interval 18.10 Plotting Contours 18.11 Lettering 18.12 Cartographic Map Elements 18.13 Drafting Materials 18.14 Automated Mapping and Computer-Aided Drafting Systems 18.15 Migrating Maps between Software Packages 18.16 Impacts of Modern Land and Geographic Information Systems on Mapping 18.17 Sources of Error in Mapping 18.18 Mistakes in Mapping Problems Bibliography 19 Control Surveys and Geodetic Reductions 19.1 Introduction 19.2 The Ellipsoid and Geoid 19.3 The Conventional Terrestrial Pole 19.4 Geodetic Position and Ellipsoidal Radii of Curvature 19.5 Geoid Undulation and Deflection of the Vertical 19.6 U.S. Reference Frames 19.6.1 North American Horizontal Datum of 1927 (NAD27) 19.6.2 North American Horizontal Datum of 1983 (NAD83) 19.6.3 Later Versions of NAD83 19.6.4 National Geodetic Vertical Datum of 1929 (NGVD29) 19.6.5 North American Vertical Datum of 1988 (NAVD88) 19.6.6 Future Reference Frames in the United States 19.7 Transforming Coordinates between Reference Frames 19.7.1 Helmert Transformation and Its Variant 19.7.2 The Two plus One Approach 19.8 Accuracy Standards and Specifications for Control Surveys 19.9 The National Spatial Reference System 19.10 Hierarchy of the National Horizontal Control Network 19.11 Hierarchy of the National Vertical Control Network 19.12 Control Point Descriptions 19.13 Field Procedures for Conventional Horizontal Control Surveys 19.13.1 Triangulation 19.13.2 Precise Traverse 19.13.3 Trilateration 19.13.4 Combined Networks 19.14 Field Procedures for Vertical-Control Surveys 19.15 Reduction of Field Observations to Their Geodetic Values 19.15.1 Reduction of Distance Observations Using Elevations 19.15.2 Reduction of Distance Observations Using Vertical Angles 19.15.3 Reduction of Directions and Angles 19.15.4 Leveling and Orthometric Heights 19.16 Geodetic Position Computations 19.16.1 Direct Geodetic Problem 19.16.2 Inverse Geodetic Problem 19.17 The Local Geodetic Coordinate System 19.18 Three-Dimensional Coordinate Computations 19.19 Software Problems Bibliography 20 State Plane Coordinates and Other Map Projections 20.1 Introduction 20.2 Projections Used In State Plane Coordinate Systems 20.3 Lambert Conformal Conic Projection 20.4 Transverse Mercator Projection 20.5 State Plane Coordinates in NAD27 and NAD83 20.6 Computing SPCS83 Coordinates in the Lambert Conformal Conic System 20.6.1 Zone Constants 20.6.2 The Direct Problem 20.6.3 The Inverse Problem 20.7 Computing SPCS83 Coordinates in the Transverse Mercator System 20.7.1 Zone Constants 20.7.2 The Direct Problem 20.7.2 The Inverse Problem 20.8 Reduction of Distances and Angles to State Plane Coordinate Grids 20.8.1 Grid Reduction of Distances 20.8.2 Grid Reduction of Azimuths and Angles 20.9 Computing State Plane Coordinates of Traverse Stations 20.10 Surveys Extending from One Zone to Another 20.11 The Universal Transverse Mercator Projection 20.12 Other Map Projections 20.12.1 Oblique Stereographic Map Projection 20.12.2 Oblique Mercator Map Projection 20.13 Map Projection Software Problems Bibliography 21 Boundary Surveys 21.1 Introduction 21.2 Categories of Land Surveys 21.3 Historical Perspectives 21.4 Property Description by Metes and Bounds 21.5 Property Description by Block and Lot System 21.6 Property Description by Coordinates 21.7 Retracement Surveys 21.8 Subdivision Surveys 21.9 Partitioning Land 21.10 Registration of Title 21.11 Adverse Possession and Easements 21.12 Condominium Surveys 21.13 Geographic and Land Information Systems 21.14 Sources of Error in Boundary Surveys 21.15 Mistakes Problems Bibliography 22 Surveys of the Public Lands 22.1 Introduction 22.2 Instructions For Surveys Of The Public Lands 22.3 Initial Point 22.4 Principal Meridian 22.5 Baseline 22.6 Standard Parallels (Correction Lines) 22.7 Guide Meridians 22.8 Township Exteriors, Meridional (Range) Lines, and Latitudinal (Township) Lines 22.9 Designation of Townships 22.10 Subdivision of a Quadrangle into Townships 22.11 Subdivision of a Township into Sections 22.12 Subdivision of Sections 22.13 Fractional Sections 22.14 Notes 22.15 Outline of Subdivision Steps 22.16 Marking Corners 22.17 Witness Corners 22.18 Meander Corners 22.19 Lost and Obliterated Corners 22.20 Accuracy of Public Lands Surveys 22.21 Descriptions by Township Section and Smaller Subdivision 22.22 BLM Land Information System 22.23 Sources of Error 22.24 Mistakes Problems Bibliography 23 Construction Surveys 23.1 Introduction 23.2 Specialized Equipment for Construction Surveys 23.2.1 Visible Laser-Beam Instruments 23.2.2 Reflectorless Total Stations 23.2.3 Laser Scanners 23.3 Horizontal and Vertical Control 23.4 Staking Out a Pipeline 23.5 Staking Pipeline Grades 23.6 Staking Out a Building 23.7 Staking Out Highways 23.8 Other Construction Surveys 23.9 Construction Surveys Using Total Station Instruments 23.10 Construction Surveys Using GNSS Equipment 23.11 Machine Guidance and Control 23.12 As-Built Surveys with Laser Scanning 23.13 Sources of Error in Construction Surveys 23.14 Mistakes Problems Bibliography 24 Horizontal Curves 24.1 Introduction 24.2 Degree of Circular Curve 24.3 Definitions and Derivation of Circular Curve Formulas 24.4 Circular Curve Stationing 24.5 General Procedure of Circular Curve Layout by Deflection Angles 24.6 Computing Deflection Angles and Chords 24.7 Notes for Circular Curve Layout by Deflection Angles and Incremental Chords 24.8 Detailed Procedures for Circular Curve Layout by Deflection Angles and Incremental Chords 24.9 Setups on Curve 24.10 Metric Circular Curves by Deflection Angles and Incremental Chords 24.11 Circular Curve Layout by Deflection Angles and Total Chords 24.12 Computation of Coordinates on a Circular Curve 24.13 Circular Curve Layout by Coordinates 24.14 Curve Stakeout Using GNSS Receivers and Robotic Total Stations 24.15 Circular Curve Layout by Offsets 24.16 Special Circular Curve Problems 24.16.1 Passing a Circular Curve through a Fixed Point 24.16.2 Intersection of a Circular Curve and a Straight Line 24.16.3 Intersection of Two Circular Curves 24.17 Compound and Reverse Curves 24.18 Sight Distance on Horizontal Curves 24.19 Spirals 24.19.1 Spiral Geometry 24.19.2 Spiral Calculation and Layout 24.20 Computation of As-Built Circular Alignments 24.21 Sources of Error in Laying Out Circular Curves 24.22 Mistakes Problems Bibliography 25 Vertical Curves 25.1 Introduction 25.2 General Equation of a Vertical Parabolic Curve 25.3 Equation of an Equal Tangent Vertical Parabolic Curve 25.4 High or Low Point on a Vertical Curve 25.5 Vertical Curve Computations Using the Tangent Offset Equation 25.5.1 Example Computations Using the English System of Units 25.5.2 Example Computations Using the Metric System 25.6 Equal Tangent Property of a Parabola 25.7 Curve Computations by Proportion 25.8 Staking a Vertical Parabolic Curve 25.9 Machine Control in Grading Operations 25.10 Computations for an Unequal Tangent Vertical Curve 25.11 Designing a Curve to Pass through a Fixed Point 25.12 Sight Distance 25.13 Sources of Error in Laying Out Vertical Curves 25.14 Mistakes Problems Bibliography 26 Volumes 26.1 Introduction 26.2 Methods of Volume Measurement 26.3 The Cross-Section Method 26.4 Types of Cross Sections 26.5 Average End Area Formula 26.6 Determining End Areas 26.6.1 End Areas by Simple Figures 26.6.2 End Areas by Coordinates 26.7 Computing Slope Intercepts 26.8 Prismoidal Formula 26.9 Volume Computations 26.10 Unit-Area or Borrow-Pit Method 26.11 Contour-Area Method 26.12 Measuring Volumes of Water Discharge 26.13 Software 26.14 Sources of Error in Determining Volumes 26.15 Mistakes Problems Bibliography 27 Photogrammetry 27.1 Introduction 27.2 Uses of Photogrammetry 27.3 Aerial Cameras 27.4 Types of Aerial Photographs 27.5 Vertical Aerial Photographs 27.6 Scale of a Vertical Photograph 27.7 Ground Coordinates from a Single Vertical Photograph 27.8 Relief Displacement on a Vertical Photograph 27.9 Flying Height of a Vertical Photograph 27.10 Stereoscopic Parallax 27.11 Stereoscopic Viewing 27.12 Stereoscopic Measurement of Parallax 27.13 Analytical Photogrammetry 27.14 Stereoscopic Plotting Instruments 27.14.1 Basic Concepts in Stereoplotters 27.14.2 Analytical Stereoplotters 27.14.3 Softcopy Stereoplotters 27.15 Orthophotos 27.16 Ground Control for Photogrammetry 27.17 Flight Planning 27.18 Airborne Laser-Mapping Systems 27.19 Remote Sensing 27.20 Software 27.21 Sources of Error in Photogrammetry 27.22 Mistakes Problems Bibliography 28 Introduction to Geographic Information Systems 28.1 Introduction 28.2 Land Information Systems 28.3 GIS Data Sources and Classifications 28.4 Spatial Data 28.4.1 Simple Spatial Objects 28.4.2 Vector and Raster Formats 28.4.3 Topology 28.5 Nonspatial Data 28.6 Data Format Conversions 28.6.1 Vector-to-Raster Conversion 28.6.2 Raster-to-Vector Conversion 28.7 Creating GIS Databases 28.7.1 Generating Digital Data from Field Surveys 28.7.2 Digitizing from Aerial Photos with Stereoplotters 28.7.3 Digitizing Existing Graphic Materials 28.7.4 Keyboard Entry 28.7.5 Existing Digital Data Sets 28.7.6 Scanning 28.8 Metadata 28.9 GIS Analytical Functions 28.9.1 Proximity Analysis 28.9.2 Boundary Operations 28.9.3 Spatial Joins 28.9.4 Logical Operations 28.9.5 Other GIS Functions 28.10 GIS Applications 28.11 Data Sources Problems Bibliography A Tape Correction Problems A.1 Correcting Systematic Errors in Taping B Example Noteforms C Astronomical Observations C.1 Introduction C.2 Overview of Usual Procedures for Astronomical Azimuth Determination C.3 Ephemerides C.4 Definitions C.5 Time C.6 Timing Observations C.7 Computations for Azimuth from Polaris Observations by the Hour Angle Method C.8 Azimuth from Solar Observations C.9 Importance of Precise Leveling D Using the Worksheets on the Companion Disk D.1 Introduction D.2 Using the Files D.3 Worksheets as an Aid in Learning E Introduction to Matrices E.1 Introduction E.2 Definition of a Matrix E.3 The Dimensions of a Marix E.4 The Transpose of a Matrix E.5 Matrix Addition E.6 Matrix Multiplication E.7 Matrix Inverse F U.S. State Plane Coordinate System Defining Parameters F.1 Introduction F.2 Defining Parameters for States Using the Lambert Conformal Conic Map Projection F.3 Defining Parameters for States Using the Transverse Mercator Map Projection G Answers to Selected Problems Index