Precision Surveying: The Principles and Geomatics Practice

A comprehensive overview of high precision surveying, including recent developments in geomatics and their applications

This book covers advanced precision surveying techniques, their proper use in engineering and geoscience projects, and their importance in the detailed analysis and evaluation of surveying projects. The early chapters review the fundamentals of precision surveying: the types of surveys; survey observations; standards and specifications; and accuracy assessments for angle, distance and position difference measurement systems. The book also covers network design and 3–D coordinating systems before discussing specialized topics such as structural and ground deformation monitoring techniques and analysis, mining surveys, tunneling surveys, and alignment surveys.

Precision Surveying: The Principles and Geomatics Practice:

Covers structural and ground deformation monitoring analysis, advanced techniques in mining and tunneling surveys, and high precision alignment of engineering structures Discusses the standards and specifications available for geomatics projects, including their representations, interpretations, relationships with quality assurance/quality control measures, and their use in geomatics projects Describes network design and simulation, including error analysis and budgeting Explains the main properties of high–precision surveys with regard to basic survey procedures and different traditional measurement techniques Analyzes survey observables such as angle, distance, elevation difference and coordinate difference measurements, and the relevant equipment, including the testing and utilization of the equipment Provides several case studies and real world examples

Precision Surveying: The Principles and Geomatics Practice is written for upper undergraduate students and graduate students in the fields of surveying and geomatics. This textbook is also a resource for geomatics researchers, geomatics software developers, and practicing surveyors and engineers interested in precision surveys.

John O. Ogundare, PhD, has over thirty years of experience in the field of geomatics. He has been working as instructor of geomatics technology for over twenty years at the British Columbia Institute of Technology (BCIT), Canada. Dr. Ogundare has served as a consultant to the Canada Council of Land Surveyors (CCLS) in 2007 and 2009, and is a representative of the Canadian Board of Examiners for Professional Surveyors (CBEPS) Board of Directors and the CBEPS Exemptions and Accreditation Committee. Dr. Ogundare has been a special examiner for CBEPS on Coordinate systems, Map projections, and Cartography for over eight years.

About the Author xvii

Foreword xix

Preface xxi

Acknowledgments xxv

1 Precision Survey Properties and Techniques 1

1.1 Introduction, 1

1.2 Basic Classification of Precision Surveys, 3

1.2.1 Geodetic Control Network Surveys, 3

1.2.2 Monitoring and Deformation Surveys, 4

1.2.3 Geodetic Engineering Surveys, 5

1.2.4 Industrial Metrology, 7

1.2.5 Surveys for Research and Education, 8

1.3 Precision Geodetic Survey Techniques, 8

1.3.1 Positioning using Global Navigation Satellite System, 8

1.3.2 Conventional Horizontal Positioning Techniques, 10

1.3.3 Geodetic Vertical Positioning Techniques, 11

1.4 Review of Some Safety Issues, 12

2 Observables, Measuring Instruments, and Theory of Observation Errors 15

2.1 Observables, Measurements and Measuring Instruments, 15

2.2 Angle and Direction Measuring Instruments, 16

2.2.1 Optical Theodolites, 17

2.2.2 Electronic Digital Theodolites, 19

2.2.3 Gyrotheodolite/Gyro Station Equipment, 20

2.2.4 Global Navigation Satellite System (GNSS) Survey Equipment, 20

2.3 Elevation Difference Measuring Instrument, 20

2.4 Distance Measuring Instrument, 24

2.5 Accuracy Limitations of Modern Survey Instruments, 25

2.5.1 Atmospheric and Target Conditions, 25

2.5.2 Equipment Design and Precision, 26

2.5.3 Instrument Operator Factor, 27

2.6 Error Properties of Measurements, 28

2.6.1 Blunders (or Gross Error), 28

2.6.2 Random and Systematic Errors, 28

2.7 Precision and Accuracy Indicators, 29

2.8 Systematic Error and Random Error Propagation Laws, 30

2.8.1 Systematic Error Propagation Laws, 30

2.8.2 Random Error Propagation Laws, 31

2.8.3 Confidence Regions for One–Dimensional Parameters, 32

2.8.4 Confidence Regions for Two–Dimensional Parameters, 34

2.9 Statistical Test of Hypotheses: The Tools for Data Analysis, 38

2.9.1 Observations of One Observable: Test on the Mean, 39

2.9.2 Observations of Two Observables: Test on the Difference of Their Means, 39

2.9.3 Observations of One Observable: Test on the Variance, 41

2.9.4 Observations of Two Observables: Comparison of Their Standard Deviations, 43

2.10 Need for Equipment Calibration and Testing, 44

3 Standards and Specifications for Precision Surveys 47

3.1 Introduction, 48

3.1.1 Precision Standards, 48

3.1.2 Accuracy Standards, 48

3.1.3 Content Standards, 49

3.1.4 Performance Standards, 49

3.1.5 General Comparison of Standards, 50

3.1.6 Standards and Specifications, 50

3.2 Standards and the Concept of Confidence Regions, 51

3.3 Standards for Traditional Vertical Control Surveys, 52

3.3.1 Accuracy Measure of Vertical Control Surveys, 52

3.3.2 Specifications and Guidelines for Vertical Control Surveys, 55

3.3.3 Typical Field Procedure for Precise Differential Leveling, 58

3.3.3.1 Electronic Leveling, 61

3.3.4 Accuracy of Height Differences, 61

3.3.5 Vertical Control Surveys Examples, 62

3.4 Standards for Horizontal Control Surveys, 66

3.4.1 Accuracy Standards for Traditional Horizontal Control Surveys, 66

3.4.2 Accuracy Standards and Specifications for Traverse Surveys, 68

3.4.3 Accuracy Standards and Specifications for GNSS Surveys, 71

3.5 Unified Standards for Positional Accuracy, 72

3.5.1 Network Accuracy, 73

3.5.2 Local Accuracy, 73

3.5.3 Accuracy Classification, 74

3.6 Map and Geospatial Data Accuracy Standards, 77

3.6.1 Positional Accuracy Determination Based on NSSDA, 78

3.6.2 Relationship between Standards, 81

3.6.2.1 NSSDA and NMAS Horizontal Accuracy Standards, 81

3.6.2.2 NSSDA and NMAS Vertical Accuracy Standards, 82

3.6.2.3 NSSDA and ASPRS Standards, 82

3.7 Quality and Standards, 82

4 Accuracy Analysis and Evaluation of Angle Measurement System 87

4.1 Sources of Errors in Angle Measurements, 87

4.2 Systematic Errors Eliminated by Measurement Process, 88

4.2.1 Horizontal Collimation (Line–of–Sight) Error, 89

4.2.2 Vertical Collimation (Index) Error, 90

4.2.3 Tilting (or Horizontal) Axis Error, 92

4.2.4 Compensator Index Error and Circle Graduation Error, 95

4.2.5 Eliminating Systematic Errors by Double–Centering: Example, 96

4.3 Systematic Errors Eliminated by Adjustment Process, 98

4.3.1 Plummet Error, 98

4.3.2 Standing Axis Error, 99

4.3.3 Plate Bubble Error, 101

4.3.4 Atmospheric Refraction, 102

4.4 Summary of Systematic Error Elimination, 106

4.5 Random Error Estimation, 106

4.5.1 Pointing Error, 106

4.5.2 Reading Error, 108

4.5.2.1 Repetition Method, 109

4.5.2.2 Directional Method, 109

4.5.3 Instrument Leveling Error, 110

4.5.4 Instrument and Target Centering Errors, 112

4.5.5 Random Atmospheric Refraction Error, 115

4.5.6 Random Error Propagation for Angle Measurements, 115

4.5.6.1 Horizontal Direction Measurements, 115

4.5.6.2 Horizontal Angle Measurements, 116

4.5.6.3 Zenith (or Vertical) Angle Measurements, 117

4.5.7 Error Analysis of Azimuth Determination, 119

4.5.8 Check of Angular Closure of a Traverse, 121

4.6 Testing Procedure for Precision Theodolites, 123

4.6.1 Precision of Theodolite Based on Horizontal Direction Measurements, 123

4.6.1.1 Precision Determination of Horizontal Direction Measurement, 124

4.6.2 Precision of Theodolite Based on Zenith Angle Measurements, 128

4.6.2.1 Precision Determination of Zenith Angle Measurement, 128

5 Accuracy Analysis and Evaluation of Distance Measurement System 133

5.1 Introduction, 133

5.2 General Properties of Waves, 134

5.2.1 Modulation of EM Waves, 137

5.3 Application of EM Waves to EDM, 138

5.3.1 EDM Pulse Measurement Principle, 138

5.3.2 EDM Phase Difference Measurement Principle, 139

5.3.3 Effects of Atmosphere on EDM Measurements, 143

5.3.3.1 Velocity Corrections to EDM Measurements, 148

5.3.3.2 Geometric Correction: Wave Path to Chord Correction, 151

5.4 EDM Instrumental Errors, 153

5.5 EDM External Errors, 154

5.6 Random Error Propagation of EDM Distance Measurement, 155

5.6.1 Numerical Examples, 158

5.7 Calibration and Testing Procedures for EDM Instruments, 165

5.7.1 Observation and Data–Processing Methodology, 166

5.7.1.1 Temperature Sensor Types, 167

5.7.1.2 Atmospheric Pressure and Relative Humidity Sensor Types, 168

5.7.2 EDM Baseline Designs, 168

5.7.3 EDM Calibration When Length of Baseline Is Known, 170

5.7.4 EDM Calibration When Length of Baseline Is Unknown, 175

5.7.4.1 System Constant Determination: Standard Approach, 175

5.7.4.2 System Constant Determination: Modified Standard Approach, 177

5.7.4.3 System Constant Determination: Approximate Approach, 179

5.7.5 EDM Standardization, 179

5.7.5.1 EDM Standardization: Frequency Method, 180

5.7.6 Use of Calibration Parameters, 180

6 Accuracy Analysis and Evaluation of Elevation and Coordinate Difference Measurement Systems 189

6.1 Introduction, 189

6.2 Pointing Error, 190

6.3 Reading/Rod Plumbing Error, 191

6.4 Leveling Error, 191

6.5 Collimation, Rod Scale, and Rod Index Errors, 192

6.6 Effects of Vertical Atmospheric Refraction and Earth Curvature, 193

6.7 Random Error Propagation for Elevation Difference Measurements, 194

6.8 Testing Procedures for Leveling Equipment, 197

6.8.1 Precision Determination of Leveling Equipment, 199

6.9 Calibration of Coordinate Difference Measurement System (GNSS Equipment), 203

6.9.1 GNSS Measurement Validation, 204

6.9.1.1 Basic Configuration of GNSS Validation Networks, 205

6.9.2 GNSS Zero–Baseline Test, 206

6.9.3 GNSS Antennas Phase Center Variations, 207

6.9.4 Supplementary GNSS Equipment Calibration, 207

6.9.5 General Concerns on GNSS Equipment Calibration, 208

7 Survey Design and Analysis 209

7.1 Introduction, 209

7.2 Network Design, 211

7.2.1 Geodetic Network Design, 212

7.2.2 Design of GNSS Survey, 213

7.2.3 Design of Deformation Monitoring Scheme, 214

7.2.3.1 Accuracy Requirement, 215

7.2.3.2 Reliability Requirement, 217

7.2.3.3 Separability or Discriminability Requirement, 217

7.2.3.4 Cost–Effectiveness Requirement, 217

7.3 Solution Approaches to Design Problems, 218

7.3.1 Simulation Steps for Network Design, 218

7.4 Network Adjustment and Analysis, 223

7.5 Angular Measurement Design Example, 223

7.6 Distance Measurement Design Example, 226

7.7 Traverse Measurement Design Examples, 227

7.8 Elevation Difference Measurement Design Example, 235

8 Three–Dimensional Coordinating Systems 237

8.1 Introduction, 238

8.1.1 Two–Dimensional Coordinate Reference Systems, 239

8.1.2 Three–Dimensional Coordinate Reference Systems, 240

8.1.2.1 Topographic Coordinate System, 242

8.2 Coordinate System for Three–Dimensional Coordinating Systems, 243

8.3 Three–Dimensional Coordination with Global Navigation Satellite System, 244

8.4 Three–Dimensional Coordination with Electronic Theodolites, 244

8.4.1 Coordinating Techniques, 244

8.4.2 Field Data Reductions, 246

8.4.3 Three–Dimensional Coordinate Determination, 248

8.4.4 Factors Influencing the Accuracy of Electronic Coordinating Systems, 251

8.4.4.1 Effect of Equipment and Target Design, 252

8.4.4.2 Effect of Geometry of Measurement Scheme, 253

8.4.4.3 Effect of the Environment, 253

8.4.5 Analysis of Three–Dimensional Traverse Surveys, 253

8.4.5.1 Observables in Three–Dimensional Traverse Surveys, 254

8.4.5.2 Data Processing and Analysis, 256

8.4.5.3 Effect of Correlation on Traverse Closure, 257

8.5 Three–Dimensional Coordination with Laser Systems, 258

8.5.1 Coordination with Airborne Laser Scanning System, 258

8.5.1.1 Accuracy Analysis of Airborne Laser Scanning System, 259

8.5.2 Coordination with Terrestrial Laser Scanning System, 261

8.5.2.1 Georeferencing Problem, 262

8.5.2.2 Accuracy Analysis of Terrestrial Laser Scanning System, 263

9 Deformation Monitoring and Analysis: Geodetic Techniques 267

9.1 Introduction, 268

9.1.1 Characteristics of Geodetic Monitoring Techniques, 270

9.1.2 Deformation Monitoring and Control Surveys, 272

9.1.3 Geodetic Monitoring Measurements and Error Sources, 272

9.2 Geodetic Deformation Monitoring Schemes and the Design Approach, 273

9.3 Monumentation and Targeting, 278

9.3.1 Dam Slope and Crest Monuments and Targets, 282

9.3.2 Monuments for Subsidence Monitoring in Mining Area, 282

9.4 Horizontal Deformation Monitoring and Analysis, 284

9.4.1 Monitoring Techniques, 284

9.4.2 Observables and Data Preprocessing, 287

9.4.3 Monitoring–Data Processing Techniques, 291

9.4.3.1 Least Squares Adjustment of Single–Epoch Measurements, 291

9.4.3.2 Free Network Adjustment Model, 293

9.4.3.3 Statistical Analysis of Single–Epoch Measurements, 297

9.4.3.4 Deformation Estimation from Two–Epoch Measurements, 299

9.4.3.5 Iterative Weighted Similarity Transformation, 302

9.4.4 Observation Differencing Adjustment Approach, 304

9.4.5 Geometrical Analysis of Deformation Measurements, 305

9.4.5.1 Statistical Trend Analysis of Deformations, 307

9.4.5.2 Graphical Trend Analysis of Deformations, 308

9.4.6 Examples: Deformation Monitoring and Analysis of Hydroelectric Dams, 309

9.4.6.1 Simulated Dam Deformation Monitoring and Analysis, 311

9.4.6.2 Dam Deformation Monitoring and Analysis in Practice, 315

9.4.7 Deformation Monitoring of Slope Walls, 317

9.4.8 Deformation Monitoring of Tunnels, 321

9.5 Vertical Deformation Monitoring and Analysis, 322

9.5.1 Tilt, Strain, and Curvature Determination from Geodetic Leveling, 324

10 Deformation Monitoring and Analysis: High–Definition Survey and Remote Sensing Techniques 329

10.1 Introduction, 330

10.2 Laser Systems, 330

10.2.1 Properties of Laser, 330

10.2.1.1 Monochromatic Property of Laser, 331

10.2.1.2 Directional Property of Laser, 331

10.2.1.3 Coherency Property of Laser, 332

10.2.1.4 Output Intensity Property of Laser, 332

10.2.1.5 Degradation of Laser Properties, 332

10.2.1.6 Application of Laser, 333

10.2.2 Terrestrial Laser Scanners, 333

10.2.2.1 Measuring Techniques of Terrestrial Laser Scanners, 333

10.2.2.2 Georeferencing Principles of Scanner Data, 334

10.2.2.3 Classification of Terrestrial Laser Scanners, 336

10.2.2.4 Procedures for Terrestrial Laser Scanning Project, 336

10.2.2.5 Sources of Error in Terrestrial Laser Scanners, 340

10.2.2.6 Advantages and Limitations of Terrestrial Laser Scanners, 342

10.2.2.7 Application of Terrestrial Laser Scanners in Deformation Monitoring, 344

10.2.2.8 Propagated Error for Computed Deformations, 350

10.3 Interferometric Synthetic Aperture Radar Technologies, 350

10.3.1 Concepts of Synthetic Aperture Radar, 350

10.3.2 Basic Principles of Interferometric Synthetic Aperture Radar, 353

10.3.3 InSAR Data Processing Overview, 358

10.3.4 Persistent or Permanent Scatterer InSAR Technique, 364

10.3.5 Artificial Scatterer or Corner Reflector InSAR Technique, 365

10.3.6 Limitations of InSAR Techniques, 366

10.3.7 Applications of InSAR Techniques, 367

10.3.8 Ground–Based InSAR (GB–InSAR) Techniques, 368

10.3.8.1 Examples of SAR Systems: IBIS–L and IBIS–FS, 371

10.3.8.2 Examples of Real–Beam Aperture Radar Systems: SSR and MSR 300, 373

10.3.8.3 Example: Fast Ground–Based Synthetic Aperture Radar (FastGBSAR), 373

10.3.8.4 Advantages and Disadvantages of GB–InSAR Techniques, 374

10.4 Comparison of Laser (LiDAR) and Radar (InSAR) Technologies, 376

11 Deformation Monitoring and Analysis: Geotechnical and Structural Techniques 377

11.1 Introduction, 378

11.2 Overview of Geotechnical and Structural Instrumentation, 380

11.2.1 Extensometers, 380

11.2.1.1 Rod Extensometers, 383

11.2.1.2 Tape Extensometers, 387

11.2.2 Four–Pin Gauges, 389

11.2.3 Joint Meters, 390

11.2.4 Plumb Lines, 390

11.2.4.1 Suspended (or Weighted) Plumb Lines, 393

11.2.4.2 Inverted Plumblines, 396

11.2.5 Inclinometers, 399

11.2.6 Tiltmeters, 405

11.2.7 Fiber–Optic Sensors, 406

11.2.7.1 Basic Principle, 407

11.2.7.2 Partially Distributed Fiber–Optic Sensors, 407

11.2.7.3 Long–Base Fiber–Optic Sensors, 409

11.2.7.4 Fully Distributed Fiber–Optic Sensors, 411

11.2.8 Micro–Electro–Mechanical System (MEMS) Sensors, 412

11.2.8.1 Example of MEMS Sensor: ShapeAccelArray (SAA) Sensor, 413

11.3 Design of Geotechnical and Structural Monitoring Schemes, 419

11.4 Analysis of Geotechnical Measurements, 422

11.4.1 Analysis of Extensometer Measurements, 424

11.4.1.1 Calibration Aspects of Rod and Tape Extensometers, 428

11.4.1.2 Borehole Rod Extensometer Measurements, 429

11.4.1.3 Tape Extensometer Measurements, 430

11.4.2 Analysis of Joint Meter Measurements, 431

11.4.3 Analysis of Plumbline Measurements, 432

11.4.4 Analysis of Tiltmeter Measurements, 433

11.4.5 Numerical Examples, 435

11.5 Integrated Deformation Monitoring System, 437

12 Mining Surveying 441

12.1 Introduction, 442

12.1.1 Survey Standards and Procedures for Mine Surveys, 444

12.1.1.1 Typical Survey Markers in the Mines, 445

12.2 Mining Terminology, 445

12.3 Horizontal Mine Orientation Surveys, 446

12.3.1 Direct Traversing Technique, 447

12.3.2 Mechanical Technique, 448

12.3.2.1 Orientation Transfer with Two Wires in a Single Vertical Shaft, 449

12.3.2.2 Orientation Transfer with Two or More Vertical Shafts, 462

12.3.3 Orientation Transfer Using Optical Method, 463

12.3.3.1 Using Laser Plummet, 464

12.3.3.2 Using Zenith Plummet, 465

12.3.3.3 Using Theodolite and Plummet, 466

12.3.4 Orientation Transfer by Gyro Azimuth, 467

12.3.4.1 Gyrotheodolite/Gyro Station Equipment, 467

12.3.4.2 Preorientation of Gyrotheodolite, 469

12.3.4.3 Precise Methods of Gyro Orientation, 470

12.3.4.4 Azimuth Determination with the Gyro Station GP3X Equipment, 475

12.3.4.5 Use of Gyro Equipment in Underground Mines, 480

12.4 Transferring Levels or Heights Underground, 483

12.4.1 Height Transfer with EDM, 483

12.4.2 Height Transfer with Measuring Tape, 485

12.4.3 Height Transfer in Shallow Shafts, 486

12.4.4 Typical Corrections Applied to Measurements in Height Transfer, 486

12.5 Volume Determination in Mines, 491

13 Tunneling Surveys 495

13.1 Introduction, 495

13.2 Basic Elements and Methods of Tunneling Surveys, 496

13.3 Main Sources of Error in Tunneling Surveys, 500

13.4 Horizontal Design and Simulation of Tunneling Surveys, 503

13.5 Vertical Design and Simulation of Tunneling Surveys, 508

13.5.1 Design of Surface Vertical Control Network, 509

13.5.2 Design of Underground Vertical Control Network, 510

13.5.3 Vertical Breakthrough Analysis, 510

13.6 Numerical Example: Horizontal Breakthrough Analysis, 512

13.6.1 Surface Network Analysis, 513

13.6.1.1 Results of the Surface Survey Analysis, 514

13.6.2 Underground Network Analysis, 515

13.6.2.1 Results of the Underground Survey Analysis, 516

13.7 Examples of Tunneling Surveys, 516

13.7.1 Transportation Tunneling Surveys: Rogers Pass Tunnel in Canada, 516

13.7.2 Transportation Tunneling Surveys: The Channel Tunnel in Europe, 517

13.7.3 Tunneling Surveys for Scientific Research: SSC Project in Texas, USA, 519

13.8 Analysis of Underground Traverse Surveys, 520

13.8.1 Analysis of Underground Traverse Surveys: Numerical Example, 522

13.8.2 Gyro Orientation of Underground Surveys: Numerical Example, 523

14 Precision Alignment Surveys 527

14.1 Introduction, 527

14.2 Direct Laser Alignment Technique, 530

14.3 Conventional Surveying Techniques of Alignment, 530

14.3.1 Traversing Method of Alignment, 531

14.3.1.1 Closed Traverse, 531

14.3.1.2 Fitted (or Open) Traverse, 532

14.3.1.3 Separate–Point–Included–Angle Traverse, 532

14.3.2 Alignment with Three–Dimensional Electronic Coordinating System, 533

14.3.2.1 Measurement of Reference Micro–Network, 535

14.3.2.2 Measurement of Object Micro–Network, 535

14.3.2.3 Notes on Alignment of Underground Nuclear Accelerators, 537

14.4 Optical–Tooling Techniques, 538

14.4.1 Optical–Tooling Instruments, 540

14.4.1.1 Special Instrument Stand and Precision Lateral Adjuster, 540

14.4.1.2 Alignment Telescope, 540

14.4.1.3 Jig Transit, 542

14.4.1.4 Optical Micrometer and Optical–Tooling Scale, 545

14.4.1.5 Precise Leveling Instrument, 547

14.4.1.6 Optical–Tooling Targets, 548

14.4.1.7 Other Optical–Tooling Equipment, 549

14.4.2 Collimation, Autocollimation, and Auto–Reflection, 550

14.4.2.1 Collimation and Autocollimation, 550

14.4.2.2 Auto–Reflection, 551

14.4.3 Basic Optical–Tooling Operations, 553

14.4.4 Optical–Tooling Example, 555

14.4.4.1 Horizontal Alignment, 555

14.4.4.2 Vertical Alignment, 558

14.5 Metrology by Laser Interferometer Systems, 559

14.5.1 Doppler Effects and Interferometer Systems, 559

14.5.2 Interferometry Principle, 560

14.5.2.1 Accuracy Limitation Factors, 561

14.5.3 Interferometer Systems and Alignment Principles, 562

14.5.3.1 Angular Measurement with Interferometer, 563

14.5.3.2 Straightness Measurement with Interferometer, 564

14.6 Alignment by Polar Measurement Systems, 565

14.6.1 Laser Trackers, 565

14.6.1.1 Tracker Measurement Head, 566

14.6.1.2 Tracker Controller with System Software, 566

14.6.1.3 Remote Power Unit and Other Accessories, 567

14.6.1.4 Tracker Observables and Measurements, 568

14.6.2 High–Precision Industrial Total Stations, 570

14.6.3 Coherent Laser Radar System, 572

14.7 Main Sources of Error in Alignment Surveys, 573

Appendix I: Extracts From Baarda s Nomogram 575

Appendix II: Commonly used Statistical Tables 577

Appendix III: Tau Distribution Table for Significance Level 581

Appendix IV: Important Units 587

References 589

Index 607