Measurements from Maps (eBook)

Front Cover 1
Measurements from Maps: Principles and Methods of Cartometry 4
Copyright Page 5
Table of Contents 12
Preface 8
Index to Symbols and Characters Used in the Text 14
Chapter 1. The Nature of Cartometry 24
THE USES OF CARTOMETRY 25
MEASUREMENT FOR ROUTE-FINDING 29
CARTOMETRY IN ADMINISTRATION 31
CARTOMETRY AND THE LAW OF THE SEA 32
Chapter 2. The Nature of the Medium 36
THE MAP AS THE MEDIUM 36
THE GEOMETRY OF THE MEDIUM TO BE MEASURED 40
Chapter 3. The Methods of Measuring Distance 53
MEASUREMENT OF DISTANCE 53
MEASUREMENT BY DIVIDERS IN EQUAL STEPS 61
MEASUREMENT BY DIVIDERS IN UNEQUAL STEPS 61
MEASUREMENT OF DISTANCE BY DIGITISER 62
DISTANCE MEASUREMENT BY COMPARISON WITH A PIECE OF THREAD 64
MEASUREMENT BY CHARTWHEEL 65
Chapter 4. Measurement of Area 76
AREA MEASUREMENT BY CALCULATION 77
AREA MEASUREMENT BY COMPARISON WITH STANDARD FIGURES 78
THE METHOD OF SQUARES 79
POINT-COUNTING METHODS OF AREA MEASUREMENT 80
THE INDIRECT METHODS OF AREA MEASUREMENT BY POINT-COUNTING 83
MEASUREMENT OF AREA BY LINEAR MEASUREMENT 83
TRANSECT SAMPLING AS A METHOD OF AREA MEASUREMENT 84
MEASUREMENT OF AREA BY TRACING PARCEL PERIMETERS 85
MISCELLANEOUS METHODS OF AREA MEASUREMENT 87
Chapter 5. The Variability of Cartometric Measurements 89
EXAMPLE 1: THE LENGTH OF THE COASTLINE OF YORKSHIRE 90
EXAMPLE 2: THE LENGTHS OF THE COASTLINES OF THE WORLD 93
EXAMPLE 3: THE LENGTH OF THE COASTLINE OF THE U.S.A. 95
EXAMPLE 4: THE LENGTH OF THE COASTLINE OF THE U.S.S.R. 97
DISCUSSION OF EXAMPLES 1–4 99
Chapter 6. Errors of Measurement and Their Analysis 107
THE NATURE OF AN ERROR 107
THE CAUSES OF ERRORS 108
A CLASSIFICATION OF ERRORS 110
THE NORMAL DISTRIBUTION 116
Chapter 7. Statistical Sampling and Cartometry 128
THE PROPERTIES OF A SAMPLE 129
SIZE OF SAMPLE 138
THE STATISTICS OF SMALL SAMPLES 141
THE SIGNIFICANCE OF THE DIFFERENCE BETWEEN TWO MEANS 143
Chapter 8. Spatial Sampling and Cartometry 146
SAMPLING FRAME, SAMPLING UNITS, SAMPLING STRATEGY 147
SPATIAL SAMPLING METHODS 154
STRATIFIED RANDOM SAMPLING 158
COMPARISON OF SPATIAL SAMPLING METHODS 159
THE SIZE OF SPATIAL SAMPLES 164
Chapter 9. The Concept of the Accurate Map 167
THE COMPONENTS OF MAP ACCURACY 167
MAP ACCURACY STANDARDS 169
TESTING QUANTITATIVE ACCURACY 171
CIRCULAR PROBABILITY 175
HEIGHT ERRORS 176
THE COMPONENTS OF QUANTITATIVE ACCURACY 180
THE TOTAL ROOT MEAN SQUARES ERROR OF A MAP 191
QUALITATIVE ACCURACY 193
SAMPLING STRATEGY IN QUALITATIVE TESTING 196
Chapter 10. Deformations of the Medium 201
REPRESENTATION OF THE CURVED SURFACE OF THE SPHERE AS A MAP 201
THE SCALE OF A GLOBE 203
ANGULAR DEFORMATION 208
THE SPECIAL PROPERTIES OF MAP PROJECTIONS 211
THE CHOICE OF THE MOST SUITABLE PROJECTION FOR CARTOMETRIC WORK 212
AREA MEASUREMENT ON TOPOGRAPHICAL MAPS 214
AREA MEASUREMENT ON AERONAUTICAL CHARTS 216
DEFORMATION OF THE MAP BASE 219
Chapter 11. Correction of Deformation by Measurement Control 231
CORRECTION TO LINEAR MEASUREMENTS 235
DETERMINATION OF AREA BY THE SAVICH METHOD 238
THE FORMAT AND SIZE OF THE UNIT QUADRANGLE 240
CONTROL OF AREA MEASUREMENTS BY MEANS OF ZONES 241
CALCULATION OF THE AREA OF A QUADRANGLE 242
THE CHOICE OF SPHERICAL RADIUS 245
THE AREA OF A SPHEROIDAL QUADRANGLE 248
Chapter 12. Definition of the Feature to be Measured 251
ERRORS IN PRESENTATION 252
THE DEFINITION OF A COASTLINE 255
SOME EXAMPLES OF COASTLINE DEFINITION 257
THE ROLE OF THE TIDELINE IN THE CARTOMETRIC DEFINITION OF THE COAST 261
Chapter 13. Measurements on Aerial Photographs 270
THE VARIABLE SCALE OF THE VERTICAL AERIAL PHOTOGRAPH 273
IMAGE DISPLACEMENT RESULTING FROM SURFACE RELIEF 274
THE EFFECT OF CAMERA TILT 276
PRACTICAL CONSIDERATIONS OF MEASUREMENT 279
SPACE IMAGERY AND EARTH CURVATURE 294
Chapter 14. Conventional Linear Measurements and their Reduction 300
THE PRECISION OF CONVENTIONAL LINEAR MEASUREMENTS 300
CORRECTIONS TO DIVIDERS MEASUREMENTS 307
THE INFLUENCE OF MAP SCALE: THE REDUCED LENGTH 322
Chapter 15. Probabilistic Methods of Distance Measurement 327
LAPLACE'S EXTENSION TO THE THEORY OF BUFFON'S NEEDLE 329
CARTOMETRIC APPLICATIONS OF THE THEORIES OF BUFFON AND LAPLACE 331
THE PARADOX OF LENGTH AND THE CONCEPT OF ORDER IN DISTANCE MEASUREMENT 345
Chapter 16. Geometrical Methods of Area Measurement 348
THE AREA FORMULAE OF PLANE GEOMETRY 351
DETERMINATION OF THE AREA OF THE FRAMEWORK OF A PARCEL 353
ERRORS OF THE GEOMETRICAL METHOD 355
DETERMINATION OF AREA FROM COORDINATE DIFFERENCES 358
THE HERRINGBONE METHOD 361
MEASUREMENT OF THE MARGINAL ELEMENTS 364
MEASUREMENT OF AREA FROM OFFSETS 364
THE TOTAL AREA OF THE PARCEL 372
Chapter 17. Area Measurement by Planimeter 374
DESCRIPTION OF THE INSTRUMENTS 375
GEOMETRICAL THEORY OF THE POLAR PLANIMETER 384
CALIBRATION OF POLAR PLANIMETER 391
INDIRECT MEASUREMENT BY PLANIMETER 400
THE ACCURACY OF THE PLANIMETER 401
Chapter 18. Direct Measurement of Area by Point-Counting Methods 417
TREATMENT OF MARGINAL POINTS 421
GROSS ERRORS IN COUNTING, AND SOME INSTRUMENTS TO REDUCE THEM 421
SYSTEMATIC ERRORS AND CALIBRATION OF A DOT GRID 424
THE THEORETICAL ACCURACY OF POINT-COUNTING METHODS 425
THE PRECISION OF POINT-COUNTING 433
THE MAXIMUM ALLOWABLE ERROR AND GRID DENSITY 436
SAMPLING FOR DIRECT MEASUREMENT BY ONE APPLICATION ONLY 438
Chapter 19. Indirect Measurement of Area by Point-Counting Methods 440
AN EXAMPLE OF INDIRECT MEASUREMENT OF LAND-USE CATEGORIES 441
THE THEORY OF INDIRECT MEASUREMENT BY POINT-COUNTING 442
THE NATURE OF THE SAMPLE 447
CHOICE OF METHOD 453
Chapter 20. Area Determined by Linear Measurements 460
THE METHOD OF STRIPS AND ITS APPLICATION IN THE SCALE-AND- TRACE METHOD OF AREA MEASUREMENT 461
AREA MEASUREMENT BY TRANSECT SAMPLING 465
EXAMPLES OF APPLICATIONS 467
YATES' MEASUREMENT OF WOODLAND AREAS FROM THE ONE-INCH MAP 468
THE SPEED OF AREA MEASUREMENT BY TRANSECT SAMPLING 470
THE SPEED OF AREA MEASUREMENT UNDER CONDITIONS OF PRODUCTION CARTOGRAPHY 474
THE ACCURACY OF AREA MEASUREMENT DERIVED FROM LINEAR DISTANCES 476
Chapter 21. Cartometry and the Digital Computer 482
DIGITAL DATA CAPTURE 484
DATA STORAGE 488
AVAILABILITY OF DATA 490
CARTOMETRY IN THE VECTOR MODE 494
CARTOMETRY IN THE RASTER MODE 504
CARTOMETRY AND THE BBC DOMESDAY INTERACTIVE VIDEODISC 518
Chapter 22. Measurement on Mercator's Projection 521
MEASUREMENT OF DIRECTION 522
MEASUREMENT OF DISTANCE 522
MEASUREMENT OF AREA 524
THE GEOMETRY OF MERCATOR'S PROJECTION 525
Chapter 23. The Cartometric Definition, Demarcation and Recovery of Maritime Boundaries 550
MARITIME ZONES 552
BASELINES AND EQUIDISTANCE LINES 554
PRACTICAL LOCATION OF BOUNDARIES AT SEA AND ON THE CHART 558
MEASUREMENT OF BREADTH AND EQUIDISTANCE 561
THE NATURE OF THE LINE USED TO PLOT BOUNDARIES AND MEDIAN LINES 567
BOUNDARY DETERMINATION BY CALCULATION 570
COMPARISON OF DIFFERENT CALCULATED DISTANCES 572
References 577
Index 590