#Azimuth 252

[thorsenmark]

Blue Ridge Mountains View at the Skyland Lodge (Shenandoah National Park) by Mark Stevens Via Flickr: While taking in views to the west-southwest while at the Skyland Lodge in Shenandoah National Park. The setting is looking down the main ridge in that part of the national park and then beyond to the Shenandoah Valley and Masanutten Mountain off in the distance.

[whatdoesshedotothem]

Saturday 23 November 1839

8

12 25/..

fine morning F62 ½° on my bedroom table at 9 5/.. breakfast at 9 ¼ and about 9 ½  Mr. de Richter came and brought A- the 19 nos. of Demidoffs’ work on South Russia for which paid him 15/. to pay Urbin – could not get to take anything for the 6 lessons he has given 3 Russian to me and 3 botanical to A- and to me – he proposed my subscribing (instead of giving to him) the money to the horticultural society here and becoming a member and having a diploma – to pay (subscribe) 100/. per annum – I fought off this on account of the difficulty of paying annual subscriptions – he mentioned

SH:7/ML/E/23/0133

a young Russian student who, if he had not other views, would be at liberty the end of May next and might suit us as compagnon de voyage – a natural history student – aet. 20 – speaks well French and English and a little German – I said he had best bring him here without saying anything to commit either part d’avance – Mr. de R- staid till 10 ¾ - I then finished breakfast and wrote the above of this morning till now 11 ¼ - then trying on cap got second  pother about it thought of going tonight chez les Goudovich – then give it up on seeing the day promising snow this evening – out at 12 5/.. – walked A- and I 3 turns together and then II one turn alone, she above an hour and I 1 20/.. hour and came in at 1 35/.. – then studying the Russian

Read book Count Panin gave me till now 3 5/.. – vid. St. James’s chronicle of September 12 to 14 p. 3 vol. 4

p. 252 Antarctic expedition quoted from the Literary gazette – the 2 ships seemed to have sailed the very beginning of September – the 2 so much alike, difficult to know one from the other – Erebus [?] 370 tons – Terror about 340 tons – in each the full complement of officers and men = 64 .:. the 2 ships = 128 – each carries 6 guns i.e. four six-pounds and two salute guns – the warming apparatus is ‘a square iron tube, above a foot in diameter, running all round the sides, and distributing a comfortable warmth to every berth in the ship’ – victualler for 3 years with fresh provisions  ‘and pemmican and prepared meats in cases’ ‘the phenomena of terrestrial magnetism will be independently observed throughout the voyage; and also in connection with the new observations about to be established’ (vid. Literary gazette) ‘at St. Helena, the cape, Van Diemens land, etc. the declination, inclination, and intensity of the magnet, will thus form tables of the utmost importance towards solving this great problem. The declination instrument, the horizontal and the vertical force magnetometers, are constructed under the direction of Professor Lloyd of Dublin; and there are besides, dip circles, transits with azimuth circles and chronometers of the most approved construction there are also pendulums for ascertaining the true figure of the earth, thermometers for determining the temperature of the sea at given depths; other blackened thermometers to measure the atmospheric temperature at different latitudes; photometric sensitive paper for experiments on light; barometers to be observed during storms, white squalls, etc; glasses for sidereal observations (particularly on the variable botanical and natural history specimens; actinometers for finding the forces of solar and terrestrial radiation)  hygrometers, Oslers’ anemometers,

 rain gauges, electrometers, skeleton registers of every needful kind; and, in short, such means to employ, and so much to be done, that will be no great leisure for our enterprising countrymen when all these instruments are put in requisition, and their results are regularly chronicled for the information of the world’ ........... they 1st go to ‘St. Helena where Lieutenant Eardley Wilmot, of the Royal Engineers, will be left in charge of the new observatory   Next, at the cape, will be landed for the like purpose, another officer. The vessels then make their way across the ocean, touching at and examining Kerguelens’ land, Amsterdam, and other islands, either known or imperfectly reported in that vast Expanse of waters. Arrived at Van Diemans’ land, the instruments, etc. for the observatory will be sent ashore, and whilst it is [?] they will cruise to various points where the scientific pursuits of the expedition are most likely to be advanced. On their return, they will start de novo in a direct southern course between 120 degrees and 160 degrees east longitude towards the Antarctic pole; and it is a singular and fortunate thing that in this direction, during the present season, a ship of Mr. Enderbys’ has discovered land on both sides of the longitude we have indicated in about 65 and 68 degrees of South latitude (c) these shores have been named Sabrina Lane, seen March 1839, and Balleny Isle, seen February 1839; and between them, as well as upon them, the efforts of the Erebus and Terror will, in the 1st instance, be employed........ they will afterwards circumnavigate the Pole, and try in every quarter to reach the highest point, whether near Enderbys’ land, discovered in 1832, or by Captain Weddells’ furthest reach, about 73 degrees in 1832.

It is between Sabrina Land and Balleney Isle, to the northward, in about latitude 50°, and East longitude 140°, that, it is expected the south magnetic pole will be found............. the vessels on the plan which divides them into 3 compartments; so that either extremity or the middle might be stove in, and yet the remainder be a safe hold for the crew (d)

(c) of these recent discoveries in the Southern Hampshire, Mr. Bates, of the Poultry, has just published an excellent chart, under the superintendence of Captain Beaufort. they appear like the pillars of a gateway, between which the expedition should pass. Editor L.G. i.e. edition of the Literary Gazette –

***

(d) the pumps fitted are those of Massies’ patent. the weather deck is also doubled with 3in. fir-plank, with fear-nought dipped in tallow, laid between them’

SH:7/ML/E/23/0134

had just written so far at 4 20/.. – then till 5 40/.. talking to A- or written a little of rough draft of letter to Mr. P- then dressed – dinner at 6 ¼ in ½ hour – then at Russian grammar till 7 ½ - off at 7 55/.. to the Orousoffs’ – princess R- better tonight – count Kutaitsoff there and prince Michel Orousoff (arrived from St. Petersburg) came and about 9 ½ countess Kutaitsoff with the 2 children from a childs’ ball – the old princess O- always kind asked us to dine there tomorrow her husbands’ birthday – Miss Delamine there as usual – we came away as they all sat down to supper – home at 10 ½ - fine day tho’ a little small crystalline snow as we walked today – R -2° = F28° tonight at 10 40/.. pm – F64 ½° on my bedroom table now at 12 25/.. tonight

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Solution Manual for Elementary Surveying An Introduction to Geomatics 13th Edition by Ghilani Wolf

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Table of Contents

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

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Solution Manual for Elementary Surveying An Introduction to Geomatics 13th Edition by Ghilani

This is Full Solution Manual for Elementary Surveying: An Introduction to Geomatics, 13th Edition Charles D. Ghilani

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Origin Book information:

Charles D. Ghilani

Hardcover: 984 pages

Publisher: Prentice Hall; 13 edition (January 8, 2011)

Language: English

ISBN-10: 0132554348

ISBN-13: 978-0132554343

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Table of Contents

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

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We now know, of course, that at a time when European seafaring was a mostly coast-hugging, tentative affair, loin-clothed “primitives” of Asian origin were braving the long swells of the Pacific. Their craft were probably sennit-lashed vessels of low freeboard (Sinoto 1983) and their navigational feats seemingly uncanny. Thanks to the recent work of such scholars and experimenters as Dodd, Finney, Goodenough, Alkire, Gladwin, and Lewis we now have a good idea of how such long-distance navigation may have taken place. The “discovery” of modern practitioners of the indigenous arts of noninstrumental celestial navigation, especially in Micronesia, has shed much light on the particulars of Pacific wayfinding.

Michael Halpern. “Sidereal Compasses: a Case for Carolinian-arab Links.” The Journal of the Polynesian Society. Volume 95, No. 4, p 441-460.

Remnants of star path and star compass navigational systems can be found in both the lore and current usage, as well as Western historical accounts, of other Indo-Pacific peoples. From all across this region comes evidence of long-distance voyaging and indigenous celestial navigation (D. Lewis 1964, 1972, 1978b; Best 1922:28; Dodd 1972:49; Ellis 1831:168; Da Silva and Johnson 1982:313–22; Haddon 1937:93; Sarfert and Damm 1929:187, 195; Liechti et al. 1980:2–4; A. Lewis 1973:252 n.3; Ferrand 1919:160). The present discussion will focus on the best available evidence, that from the Carolines.

All these star systems were made possible by a peculiarity of tropical naked-eye astronomy. In all latitudes stars appear to rise and set at the same point on the horizon throughout the year (Thomas 1982:2). But only relatively close to the equator is their motion vertical as they leave or approach the horizon. Beyond the tropics, stars rise and set obliquely, describing a circle about the celestial pole, the projection of the terrestrial pole on to the “dome” of the heavens (Aveni 1981). This vertical motion allows stars to be used as directional indicators some distance from the tropical horizon. In temperate zones, their oblique motion near the horizon markedly reduces their directional usefulness.

Carolinian navigators still use their sidereal compass to effect voyages often hundreds of kilometres in length (Gladwin 1970:37–39; D. Lewis 1978b:162–3, 177–80). And evidence from Western observers as well as indigenous tradition indicates that such long trips were more common in the past (Parsonson 1963:33; Åkerblom 1968:115; Lewthwaite 1967:76). Meanwhile, a cultural and geographical world away, Arab navigators also used the stars to guide them at sea (Taylor 1957:128). Interestingly, here, too, we find a sidereal rose showing remarkable similarities to the Carolinian (Fig. 2). A diagram of the rose was copied in the early 19th century from an Arab nautical treatise, the Majid Kitab (Prinsep 1836:Plate 48, 788). Its use is described in the Muhit, a 16th century Turkish work (Von Hammer 1834:548, 1838:768–9), though its representational roots probably reach much deeper into history (Ferrand 1928:198; 225; Tibbetts 1971:296). The Arab and Carolinian compasses share 18 points in common. Further, Arab navigators spoke of setting courses on the names of stars rather than in degrees even when the latter were available (Prinsep 1836:788–9). The version of this rose that has come down to us clearly postdates the introduction of the magnetic compass. The azimuths are regularly spaced and accompanied by degree notations. Their names, taken from the rising and setting points of stars, must be mere conventions.

[...]

By calculating the positions of the individual stars and constellations of the Arab rose at various times in the past, it can be seen that their relative positions did, indeed, correspond to those of the currently known representation. 3 This tends to confirm the speculations of both Prinsep (1836:788) and de Saussure (1928:124) that an Arab sidereal rose predated the use of stellar rhumb names on their magnetic compasses. As recently as A.D. 1000, for instance, Canopus was about the same distance from the equator as the prominent stars of the Southern Cross. In ancient times it was farther south, suggesting a cause for its choice as the rose's southern marker. The same precessional change resulted in the shift in the relative positions of Canopus and Alpha/Beta Centauri sometime between 1500 and 2000 years ago. Before that time, their depiction in the Arab rose accurately reflected their actual relationship. The Antares-Pleiades configuration displays a similar pattern. Just before A.D. 1000 Arcturus rose several degrees north of the Pleiades, as in the Arab compass. This gap increases as we recede further into the past, at least to 3500 B.C. The calculations show that at about the beginning of our own era, approximately 2000 years ago, all the stars held relative positions in the sky just as they are found in the representation of the Arab sidereal rose. Several hundred years earlier or later this was not the case.

There is, however, a complicating factor. Some of the gaps between adjacent calculated bearings are very small, on the order of a degree or two (e.g., Capella and Vega). The problem arises, then, of explaining - 447 why a navigator would choose two azimuths in such close proximity. While there is no definitive answer, one need only look to the still-functioning Carolinian compass for instruction. Here, the azimuths denoted by Tarazed (Gamma Aquilae) and Altair, the two closest of the entire compass, show a difference of barely 2° in their rising points along the horizon from the approximate latitude of the Carolines chain. This bunching of points around the east-west line presumably serves the local needs of the navigators since most voyaging was and is along the main axis of the chain (Gladwin 1970:152, 154 but see D. Lewis 1972:67). A similar explanation in the Arab case is plausible, though less readily understandable in light of the scanty information and long, open-water sea routes of the Indian Ocean.

[...]

But what of the Arab compass? Altair appears to rise even farther from true east, though only marginally, from the slightly higher latitudes frequented by Arab seafarers. Here too, then, it could not have been chosen because of some past correspondence with the celestial equator. Both Ibn Majid, the famous 15th century navigator and his 16th century Turkish translator, Admiral Sidi Ali Çelebi, were aware of the Altair discrepancy and the latter, at least, knew of precessional changes (Grosset-Grange 1972:39; Ferrand 1919:500–01). Tibbetts (1971:150) states that, while the “ancients” were aware of Altair's true position, early mariners used it anyway because their measurements were only approximate and because “the seamen of the Indian Ocean and others relied on it and so described it to each other.” If true, this would be a strong indication that early Arab navigators learned the use of the sidereal rose from other seafarers plying the Indian Ocean. These “others” were, perhaps, Austronesian cousins of the Carolinians.

Celestial longitude is usually designated by right ascension, a temporal measure based on the equivalence of 360° of longitude and 24 sidereal hours. It is measured in hours and minutes east from the vernal equinox. For example, a star found 60° east of the zero point has a right ascension of four hours (Jastrow and Thompson 1972:I–21 — I–23). Though the rising times of the Carolinian compass stars are generally spread out over a given 24-hour period, gaps do occur. This is not a serious problem for the navigator since the companion stars, those of similar declination but different right ascension, serve during these periods. Conveniently, the Carolinian compass calculated for 2000 years ago displays one large gap which falls entirely in daylight hours during the voyaging season. The differing conditions of Indian Ocean monsoon sailing eliminates this correspondence, though the voyaging season was much more flexible in these seas (Grosset-Grange 1970:236–38, 1978:18, Fig. 6). The companion stars would, of course, have permitted use of the compass at any time. This is one more indication, however, that the Arabs were working with a borrowed system.

The Arab rose of 2000 years ago (calculated) shows a bunching of azimuths around due north. This fact, plus the Arabs' well-known skill at latitude sailing by the height of Polaris and circumpolar stars (Prinsep 1836; Ferrand 1928; Tolmacheva 1980) might argue for a more northerly origin of their compass. But as we have seen, the astronomical requisites of navigation by rising and setting azimuths are particular to tropic regions. The Arabs' facility at latitude sailing carried them at least as far as India (and later to China and the East Indies) where they could have met Tibbetts' “seamen of the Indian Ocean and others,” possibly from or in contact with tropical Indo-Pacific lands, who taught them to key their compass to Altair. Such contact may have also led to the Arabs' use of the height of al-Murabba', the Southern Cross, for latitude determination south of the equator (Tibbetts 1971:340), though they may have discovered it themselves on voyages to the east or south to Madagascar.

There is, however, important evidence of former star compass use elsewhere in the Pacific. On Tonga, an elder of a traditional clan of navigators named “eight star points indicating directions rather than the positions of islands...” (D. Lewis 1978b:76). These had been learned from his father who reportedly knew more than he. In Tahiti Andia y Varela found a 16-point compass rose in use near the end of the 18th century, east being the principal direction (D. Lewis 1964:365). And David Malo reported that in Hawaii the stars were used as a compass (Hornell 1936:25). From the island of Madura off Java's north coast comes the report that there were 25 stars basic to navigational science, their rising and setting points constituting the bintang pedoman or star compass. Here, Altair was considered of primary importance, though not all the azimuths were remembered by the informants (Liechti et al. 1980:2–4). Though there is some question as to the accuracy of the star names reported (Horridge 1984; D. Lewis 1984; Frake 1984), the compass suggested by the researchers may have been a system of star path navigation used in conjunction with a cognitive directional system based on wind or other names. Support for the validity of this rose comes from an unusual quarter: Ibn Majid, the 16th-century Arab pilot. He claimed that, while most seafaring peoples of the Indian Ocean used a 32-point compass, the Chinese and Javanese roses contained only 24 stations (Ferrand 1924:216). It is not difficult to imagine that Majid's 24-point Javanese compass and the 25 stars of the Madurese informants refer to the same construct.

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Chief Mountain Hidden in Clouds by Mark Stevens Via Flickr: From a roadside pullout along Chef Mountain Highway in Montana just outside of Glacier National Park. The view is looking to the west-southeast across some prairies with rolling hillsides and forest leading up to the mountain. My thought on composing this image was to capture a leveled-on view and center the mountain, even though hidden in clouds, in the image center. I later worked with control points in DxO PhotoLab 6 and then made some adjustments to bring out the contrast, saturation and brightness I wanted for the final image.

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A 5-Star Day in Pinnacles National Park (Black & White) by Mark Stevens Via Flickr: A conversion to black & white using DxO PhotoLab 6 where I made some adjustments to color filters to bring out a much richer tonal contrast for the final image.

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Taking in Resurrection Wall and The Fingers While Hiking the Juniper Canyon Loop (Pinnacles National Park) by Mark Stevens Via Flickr: A setting looking to the west-southwest while taking in views across eroded volcanic formations present in this part of Pinnacles National Park. I captured this image while I was hiking the Juniper Canyon Loop. The view is looking to Resurrection Wall and The Fingers.

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I’d Rather Spend a Sunset with a Bestest of Friend and Dog (Shenandoah National Park) by Mark Stevens Via Flickr: A setting looking to the southwest while taking in views across this grassy meadow at the Spitler Knoll Overlook. This is in Shenandoah National Park along the Skyline Drive. My thought in composing this image was to find a balance in the focal length so that much of the image would be with the girl and her dog while still having a backdrop of some of the Blue Ridge Mountains. I liked the warm colors present from the sun setting off in the distance.

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Creosote Bushes and Rock Formations (Joshua Tree National Park) by Mark Stevens Via Flickr: A setting looking to the southwest while taking in views across some nearby creosote bushes to more distant rock formations in Joshua Tree National Park. With this image, I decided to take advantage of some nearby creosote bushes and capture a view with a look beyond. Kind of like filling up the foreground with something interesting and having a backdrop equally as interesting.

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Distant Mountains Hidden in the Clouds (Pinnacles National Park) by Mark Stevens Via Flickr: While walking the Juniper Canyon Loop with a view looking southwest to other pinnacle formations in this part of Pinnacles National Park. My thought on composing this image was to take advantage of the layer look that, I felt, was present in the nearby ridge with the volcanic formations, and then more distant ridge, and finally mountains and peaks somewhat hidden in the clouds off in the distance.

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A Deer Crossing the Trail (Capitol Reef National Park) by Mark Stevens Via Flickr: While walking along the Fremont River Trail in the Fruita area of Capitol Reef National Park. The view is looking to the southwest. With this image, I decided to use the trail ahead as a leading line to the deer crossing, having that centered, more or less, in the image.

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Casa Grande While Hiking the Lost Mine Trail (Big Bend National Park) by Mark Stevens Via Flickr: The view is looking to the west while walking the Lost Mine Trail in Big Bend National Park.

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Reflections of White Sands in Remaining Rain Waters (White Sands National Park) by Mark Stevens Via Flickr: While in the parking area around the Alkali Flat Trailhead in White Sands National Park. The view is looking to the west and includes a small area of remaining rain water that had reflections of both the nearby dune ridge, as well as blue skies and clouds from above.

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A 5-Star Day in Pinnacles National Park by Mark Stevens Via Flickr: While walking the Juniper Canyon Loop with a view looking west-northwest to other pinnacle formations in this part of Pinnacles National Park. What I wanted to capture with this image was the formation with Resurrection Wall and The Fingers. My thought was to keep that more or less in the image center and pull back on the focal length to include some of the nearby landscape to add to this national park setting. There was almost, you could say, a layered look with some nearby foreground with the trees in the canyon below and then more distant ridges.