3rsity >uthern .ibrary F THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES t RALPH D. REED LIBRARY DEPARTMENT OF GEOLOGY UNIVERSITY of CALIFORNIA LOS ANGELES, CALIF. D. Trace O GEOLOGICAL LIBRARY OF ROBERT DENNY TRACE MAR 8 1941 \frontispiece.] PLATE I. SUKVKYING UNDER DIFFICULTIES. TOPOGRAPHIC SURVEYING. INCLUDING GEOGRAPHIC, EXPLORATORY, AND MILITARY MAPPING, WITH HINTS ON CAMPING, EMERGENCY SURGERY, AND PHOTOGRAPHY. BY HERBERT M. WILSON, Geographer, United States Geological Survey ; Member American Society of Civil Engineers ; Autiior of "Irrigation Engineering" etc. SECOND EDITION, REVISED. FIRST THOUSAND. NEW YORK: JOHN WILEY & SONS. LONDON: CHAPMAN & HALL, LIMITED. 1905. Copyright, 1900, 1905, BY HERBERT M. WILSON. ROBERT DRUMMOND. PRINTER. NEW YORK. Geology Library TA PREFACE. THIS book has been prepared with a view of bringing together in one volume the data essential to a comprehensive knowledge of topographic surveying. It has been my aim to cover the varied phases of all classes of surveys which are made with a view to representing on maps information rela- tive to the features of the earth's surface. The methods elaborated are chiefly those which have been developed in recent years by the great government surveying organiza- tions and by such few private corporations as have kept in touch with the most modern practice; but I have endeavored to go beyond these, and, guided by personal experience, to , adapt them to the most detailed topographic as well as to the crudest exploratory surveys. The hope is entertained, therefore, that the engineer who may be called upon to con- duct an exploratory survey in an unknown region, or to make a detailed topographic map as a preliminary to construction, will find herein descriptions and examples of the methods he should employ, the essential tables for the computation of his results, and hints which will guide in the equipment of his party. I have sought to avoid any detailed description of those instruments or methods which are elaborated in works on general surveying. The volume is devoted practically to higher surveying, and presupposes a knowledge of all the more elementary branches. At the same time, many of the iii 691186 iv PKEFA CE. subjects treated are essentially elementary, and these are briefly described, in order that all the facts which the topog- rapher must know and all the formulas and tables which he must have at hand in the field may be brought together. An effort has been made to present the subject in the most prac- tical form. Accordingly, care has been taken to avoid an elaboration of the mathematical processes by which the vari- ous formulas have been derived, as they are to be found in detail in several well-known treatises to which textual refer- ence is made. To give more immediate aid to the working surveyor, examples of the various computations are pre- sented, as are illustrations of the instruments, methods, and resulting maps from surveys actually executed. The mode of presentation is not that usually followed in such works. Instead of describing the instruments or their uses independently, each is described in that portion of the text in which its employment in field surveying is most prom- inently mentioned. The tables are not brought together at the end of the volume, but each is placed in that portion of the text which relates to its use. The object is to produce a handy reference-book for use in the field, as well as a text-book for guidance in college instruction. It is believed that, by this arrangement, if a topographer in the midst of his field-work desires information on a special point, it can be found, with accompanying examples and tables, gathered together in one chapter or clearly indicated by cross-references. Again, the method of treatment usually followed in works of this class consists in, first, a description of the astronomic methods on which general map surveys must be based, and then a descrip- tion of primary triangulation as a basis for the detailed topographic surveys which are finally described. I have re- versed this order and have adopted the more natural method of commencing with the simplest operations and advancing gradually towards the most complex and refined. Each sub- ject is treated in the same manner. It is believed that the PREFA CE. V work has thus been made especially useful to the inexpert topographer and the student. The volume consists, in fact, of three separate books or treatises: (i) Topographic Surveying, (2) Geodetic Survey- ing, and (3) Practical Astronomy. The first has been sub- divided into three parts: Plane Surveying, Hypsometric Sur- veying, and Map Construction; and these are preceded by a preliminary characterization of the relations existing between topographic, geographic, and exploratory surveys. This latter distinction is essentially arbitrary, as all are of a kind, and differ only in degree of detail and the consequent speed and generalization in procuring the field results. The general subject of Geodetic Surveying has been subdivided into Ter- restrial Geodesy and Astronomic Geodesy, and the treatment of these differs but slightly in method of arrangement from that usually pursued. Part VII is devoted to such practical hints as it is believed will essentially aid those who have the organization and command of camping parties. I am especially indebted to the courtesy of Professors Ira O. Baker, J. B. Johnson, and John F. Hayford for the use of numerous electrotypes and plates from their well- known works on surveying and geodesy; and to the Secre- tary of the American Society of Civil Engineers for electro- types of illustrations in articles by me. I am also indebted to Messrs. W. & L. E. Gurley, Young & Sons, and G. N. Saeg- muller for electrotypes of instruments illustrated in their cata- logues. I have used freely the excellent Manual of Topo- graphic Methods of the U. S. Geological Survey, written by Mr. Henry Gannett; in a few instances I have copied verba- tim examples contained therein, and I desire to express appre- ciation of his courtesy, and of that of the Director of the U. S. Geological Survey in extending this privilege. To the latter I am also indebted for an opportunity to procure the colored illustrations published herewith, which were printed from the admirable copper-plates of the U. S. .Geological Survey. Spe- vi PREfA CE. cifications and several illustrations of tents and other camp equipage were obtained through the courtesy of the Quarter- master-General of the U. S. Army. For much in the chapter on Photography I am indebted to Lieut. Samuel Reber's Manual of Photography and to E. Deville's Photographic Surveying. Finally, I desire to express appreciation of the assistance I have received in editing manuscript and proof from many coworkers on the U. S. Geological Survey, more particularly from Messrs. W. J. Peters, S. S. Gannett, and E. M. Douglas on the subjects of geodesy and astronomy; E. C. Barnard and A. H. Thompson on topographic surveying; C. Willard Hayes and G. K.Gilbert on topographic forms and definitions; N. H. Darton on photography; and to Mr. W. Carvel Hall for assistance in reading proof. Two lists of works of refer- ence are published, on pages 490 and 809, in which are cited the titles of all those works to which the reader is referred for further details. From nearly all of these some example or illustration has been obtained. H. M. W. WASHINGTON, D. C, Feb. 22, 1900. PREFACE TO SECOND EDITION. IN preparing this second edition no radical changes have been made in any chapter. Numerous minor changes and corrections have been made, however, chiefly in the nature of citations of new practices or correction of old. This is par- ticularly true of the subject of Projections, which is better illus- trated, that of Precise Leveling, and the bringing up to date of tables of Polaris Observations. H. M. W. WASHINGTON, D. C., Feb. 20, 1905. CONTENTS. PART I. TOPOGRAPHIC, GEOGRAPHIC, AND EXPLORATORY SURVEYING. CHAPTER I. KINDS OF MAP SURVEYS. ART. PAGE 1. Classes of Surveys i 2. Information Surveys 3 3. Topographic Surveys 4 4. Features Shown on Topographic Maps 5 5. Public Uses of Topographic Maps 6 6. Degree of Accuracy Desirable in Topographic Surveys 8 7. Instructions Relative to Topographic Field-work 12 8. Elements of a Topographic Survey 14 CHAPTER II. SURVEYING FOR SMALL-SCALE OR GENERAL MAPS. 9. Methods of Topographic Surveying 18 10. Geological Survey Method of Topographic Surveying 20 11. Organization of Field Survey 22 12. Surveying Open Country 23 13. Sketching Open Country 28 14. Surveying Woodland or Plains 33 15. Sketching Woodland or Plains 35 16. Control from Public Land Lines 36 17. Sketching Over Public Land Lines 37 18. Cost of Topographic Surveys 40 19. The Art of Topographic Sketching 40 20. Optical Illusions in Sketching Topography 44 vii CONTENTS. CHAPTER III. SURVEYING FOR DETAILED OR SPECIAL MAPS. ART. PACK 21. Topography for Railway Location 47 22. Detailed Topographic Surveys for Railway Location 49 23. Topographic Survey for Canal Location 52 24. Surveys for Reservoirs 57 25. Survey of Dam Site 58 26. City Surveys 62 27. Cadastral and Topographic City Survey 64 28. Cost of Large-scale Topographic Surveys 67 CHAPTER IV. GEOGRAPHIC AND EXPLORATORY SURVEYS. 29. Geographic Surveys 68 30. Instrumental Methods Employed in Geographic Surveys 69 31. Geographic Maps 70 32. Features Shown on Geographic Maps 72 33. Geographic Reports 73 34. Scale and Cost of Governmental Geographic Surveys 74 35. Exploratory Surveys 76 36. Exploratory and Geographic Surveys Compared 77 37. Methods and Examples of Exploratory Surveys 82 CHAPTER V. MILITARY AND CADASTRAL SURVEYS. 38. Military -Surveys 52 39. Military Reconnaissance with Guide Map , 95 40. Military Reconnaissance without Guide Map 95 41. Detailed Military Map , , . IO o 42. Military Siege Maps t !Oi 43- Military Sketches and Memoirs IO 2 44- Cadastral Surveys IO< j CHAPTER VI. TOPOGRAPHIC FORMS. 45. Relations of Geology to Topography t> IO 8 46. Origin and Development of Topographic Forms 109 47. Physiographic Processes t> IIO 48. Classification of Physiographic Processes CONTENTS. IX ART. PAGE 49. Erosion, Transportation, and Corrasion 113 50. Topographic Forms 120 51. Classification of Topographic Forms 122 GLOSSARY OF TOPOGRAPHIC FORMS 133 PART II. PLANE AND T ACHY METRIC SURVEYING. CHAPTER VII. PLANE-TABLES AND ALIDADES. 52. Plane and Topographic Surveying 146 53. Plane-table Surveying 147 54. Reconnaissance and Execution of Plane-table Triangulation 149 55. Tertiary Triangulation from Topographic Sketch Points 151 56. Varieties of Plane-tables 152 57. Plane-table Tripods and Boards 153 58. Plane-table Movements 153 59. Telescopic Alidades 157 60. Adjustments of Telescopic Alidade 159 61. Gannett Plane-table 160 62. Sight-alidades 161 63. Folding Exploratory Plane-table 163 64. Cavalry Sketch-board 164 CHAPTER VIII. SCALES, PLANE-TABLE PAPER, AND PENCILS. 65. Special Scales 167 66. Slide-rule : 168 67. Using the Slide-rule 169 68. Plane-table Paper 174 69. Preparation of Field Sheets 175 70. Manipulation of Pencil and Straightedge 178 71. Needle Points, Pencil Holders and Sharpeners 179 CHAPTER IX. PLANE-TABLE TRIANGULATION. 72. Setting up the Plane-table 180 73. Location by Intersection 182 CONTENTS. PAG ART. 74. Location by Resection ........................................ 185 75. Three-point Problem Graphically Solved ...................... 186 76. Tracing-paper Solution of the Three-point Problem ............ 187 77. Bessel's Solution of the Three-point Problem ................. 188 78. Coast Survey Solution of the Three-point Problem ............ 190 79. Ranging-in, Lining-in, and Two-point Problem ............... 192 CHAPTER X. TRAVERSE INSTRUMENTS AND METHODS. 80. Traverse Surveys .............................................. 195 81. Traversing by Plane-table and Magnetic Needle ............... 197 82. Control by Large-scale Magnetic Traverse with Plane-table ____ 199 83. Traversing by Plane-table with Deflection Angles ............. 200 84. Intersection from Traverse .................................... 202 85. Engineers' Transit ............................................. 203 86. Adjustments of the Transit .................................... 204 87. Traversing with Transit ....................................... 207 88. Platting Transit Notes with Protractor and Scale .............. 210 89. Protractors ................................................... 210 90. Platting Transit Notes by Latitudes and Departures .......... 212 91. Prismatic Compass ............................................ 214 92. Magnetic Declination .......................................... 221 93. Secular Variation and Annual Change ........................ 222 94. Local Attraction .............................................. 223 CHAPTER XI. LINEAR MEASUREMENT OF DISTANCES. 95. Methods of Measuring Distances; Pacing ...................... 224 96. Distances by Time ............................................ 226 97. Measuring Distance with Linen Tape ......................... 228 98. Odometer .................................................... 22Q 99. Chaining ..................................................... 234 CHAPTER XII. STADIA TACHYMETRY. 100. Tachymetry ............................... ; ____ f _ g 101. Topography with Stadia ........................ ....... .'237 102. Tachymetry with Stadia ......................... 2 ,g 103. Accuracy and Speed of Stadia Tachymetry ....... ....]. . 240 104. Stadia Formula with Perpendicular Sight .......... ............ 243 105. Stadia Formula with Inclined Sight ............... 246 CONTENTS. XI ART. PAGE 106. Determining Horizontal Distances from Inclined Stadia Meas- ures 249 107. Horizontal Distances and Elevations from Stadia Readings 249 108. Determining Elevations by Stadia 258 109. Diagram for Reducing Stadia Measures 259 1 10. Diagram for Reducing Inclined Stadia Distances to Horizontal.. 264 in. Effects of Refraction on Stadia Measurements 266 112. Stadia-rods 269 CHAPTER XIII. ANGULAR TACHYMETRY. 113. Angular 1'achymetry with Transit or Theodolite 272 114. Measuring Distances with Gradienter 274 115. Wagner-Fennel Tachymeter 280 1 16. Range-finding 282 117. Surveying with Range-finder 283 118. Traversing with Range-finder 284 1 19. Weldon Range-finder 280 120. Accuracy and Difficulties of Range-finding 289 121. Range-finding with Plane-table 290 CHAPTER XIV. PHOTOGRAPHIC SURVEYING. 122. Photo-surveying 29:.* 123. Photo-surveying and Plane-table Surveying Compared 292 124. Principles of Photo-topography 296 125. Camera and Plates 298 126. Field-work of a Photo-topographic Survey 293 127. Projecting the Photo-topographic Map 300 PART III. HYPSOMETRY, OR DETERMINATION OF HEIGHTS. CHAPTER XV. SPIRIT-LEVELING. 128. Hypsometry 305 129. Spirit-leveling 306 130. Engineering Spirit-levels 308 xii CONTENTS. ART. PAGK 131. Adjustments of the Level 308 132. Target Leveling-rods 3 11 133. Speaking-rods 3*3 134. Turning-points 3*5 135. Bench-marks 3 l6 136. Method of Running Single Lines of Levels 317 137. Instructions for Leveling 320 138. Note-books 322 139. Platting Profiles 324 CHAPTER XVI. LEVELING OF PRECISION. 140. Precise Leveling 325 141. Binocular Precise Level 326 142. Precise Spirit-level 327 143. Sequence in Simultaneous Double-rodded Leveling 329 144. Methods of Running 332 145. Precise Rods 332 146. Manipulation of Instrument 336 147. Length of Sight 337 148. Sources of Error 339 149. Divergence of Duplicate Level Lines 343 150. Limit of Precision 344 151. Adjustment of Group of Level Circuits 345 152. Refraction and Curvature 347 153. Speed in Leveling 349 154. Cost of Leveling : 349 155. Long-distance Precise Leveling 352 156. Hand-levels 355 157. Using the Locke Hand-level '. . . 356 158. Abney Clinometer Level 357 CHAPTER XVII. TRIGONOMETRIC LEVELING. 159- Trigonometric Leveling 359 160. Vertical Angulation 361 161. Vertical Angulation, Computation 363 162. Vertical Angulation in Sketching 363 163. Vertical Angulation from Traverse 367 164. Trigonometric Leveling, Computation 368 165. Errors in Vertical Triangulation 370 166. Refraction and Curvature 371 167. Leveling with Gradienter 372 CONTENTS. xiii CHAPTER XVIII. BAROMETRIC LEVELING. ART. PAGE 168. Barometric Leveling 374 169. Methods and Accuracy of Barometric Leveling 375 170. Mercurial Barometer 376 171. Barometric Notes and Computation 378 172. Example of Barometric Computation 381 173. Guyot's Barometric Tables 383 174. Aneroid Barometer 395 175. Errors of Aneroid 395 176. Using the Aneroid 396 177. Thermometric Leveling 402 PART IV. OFFICE WORK OF TOPOGRAPHIC MAPPING. CHAPTER XIX. MAP CONSTRUCTION. 178. Cartography 404 179. Map Projection 405 180. Kinds of Projections 405 181. Perspective Projections 406 182. Cylinder Projections 410 183. Conical Projections 412 184. Constructing a Polyconic Projection 416 185. Projection of Maps upon a Polyconic Development 418 186. Use of Projection Tables 435 187. Areas of Quadrilaterals of Earth's Surface 436 188. Platting Triangulation Stations on Projection 437 189. Scale Equivalents 446 CHAPTER XX. TOPOGRAPHIC DRAWING AND RELIEF MODELING. 190. Methods of Map Construction 449 191. Topographic Drawing 449 192. Contour Lines 455 193. Contour Construction 460 XIV CONTENTS. 194. Hachures 4$i 195. Conventional Signs 463 196. Lettering 477 197. Drafting Instruments 477 198. Model and Relief Maps 478 199. Modeling the Map 480 200. Duplicating the Model, Casting 485 WORKS OF REFERENCE ON TOPOGRAPHY 49 PART V. TERRESTRIAL GbODESY. CHAPTER XXI. FIELD-WORK OF BASE MEASUREMENT. 201. Geodesy 495 202. Base Measurement 497 203. Accuracy of Base Measurement 498 204. Base Measurement with Steel Tapes 500 205. Steel Tapes 501 206. Tape-stretchers 501 207. Laying out the Base 505 208. Measuring the Base 507 209. Compensated Base Bars 507 210. Contact-slide Base Apparatus 508 211. Iced-bar Apparatus 511 212. Repsold Base Apparatus 514 213. Base Lines: Cost, Speed, and Accuracy 516 CHAPTER XXII. COMPUTATION OF BASE MEASUREMENT. 214. Reduction of Base Measurement 517 215. Reduction to Standard 517 216. Correction for Temperature 518 217. Record of Base Measurement 518 218. Correction for Inclination of Base 519 219. Correction for Sag 521 220. Reduction of Base to Sea-level 522 221. Summary of Measures of Sections '. 523 CONTENTS. XV ART. PAGE 222. Corrected Length of Base 523 223. Transfer of Ends of Base to Triangulation Signals 524 224. Other Corrections to Base Measurements 526 225. To Reduce Broken Base to Straight Line 526 CHAPTER XXIII. FIELD-WORK OF PRIMARY TRAVERSE. 226. Traverse for Primary Control 527 227. Errors in Primary Traverse 528 228. Instruments Used in Primary Traverse 529 229. Method of Running Primary Traverse 531 230. Record and Reduction of Primary Traverse 532 231. Instructions for Primary Traverse 533 232. Cost, Speed, and Accuracy of Primary Traverse 536 CHAPTER XXIV. COMPUTATION OF PRIMARY TRAVERSE. 233. Computation of Primary Traverse 538 234. Correction for Observed Check Azimuths 539 235. Computation of Latitudes and Longitudes 540 236. Corrected Latitudes and Longitudes 542 CHAPTER XXV. FIELD-WORK OF PRIMARY TRIANGULATION. 237. Primary Triangulation 545 238. Reconnaissance for Primary Triangulation 546 239. Intervisibility of Triangulation Stations 549 240. Accuracy of Triangulation 553 241. Instruments 553 242. Micrometer Microscope 556 243. Triangulation Signals 5591 244. Tripod and Quadripod Signals 561 245. Observing Scaffolds 565 246. Heliotrope 566 247. Night Signals 574 248. Station- and Witness-marks : 575 CHAPTER XXVI. MEASUREMENT OF ANGLES. 249. Precautions in Measuring Horizontal Angles 577 250. Observer's Errors and their Correction 578 XVI CONTENTS. ART. PACK 251.. Instrumental Errors and their Correction 580 252. Methods of Measuring Horizontal Angles 584 253. Record of Triangulation Observations 588 254. Instructions for Field-work of Primary Triangulation 590 255. Primary Triangulation Cost, Speed, and Accuracy 592 CHAPTER XXVII. SOLUTION OF TRIANGLES. 256. Trigonometric Functions 594 257. Fundamental Formulas for Trigonometric Functions 594 258. Formulas for Solution of Right-angled Triangles . ... 594 259. Solution of Plane Triangles 596 260. Given Two Sides and Included Angle, to Solve the Triangle 598 261. Given Certain Functions of a Triangle, to Find Remainder 598 262. Given Three Sides of a Triangle, to Find the Angles 599 263. Three-point Problem 600 CHAPTER XXVIII. ADJUSTMENT OF PRIMARY TRIANGULATION. 264. Method of Least Squares 602 265. Rejection of Doubtful Observations 604 266. Probable Error of Arithmetic Mean 607 267. Reduction to Center 608 268. Station Adjustment 611 269. Routine of Station Adjustment 612 270. Equations of Condition 612 271. Formation of Table of Correlates 614 272. Formation of Normal Equations and Substitution in Table of Correlates 615 273. Figur-e Adjustment 616 274. Routine of Figure Adjustment 617 275. Notation Used in Figure Adjustment 618 276. Angle Equations 619 277. Spherical Excess 619 278. Side Equations .....,.< 623 279. Solution of Angle and Side Equations 625 280. Correlates and Normal Equations 627 281. Algebraic Solution of Normal Equations 628 282. Substitution in Normal Equations 632 283. Substitution in Table of Correlates 632 284. Weighted Observations: 633 CONTENl^S. XV11 CHAPTER XXIX. COMPUTATION OF DISTANCES AND COORDINATES. ART. PACK 285. Geodetic Coordinates 636 286. Computation of Distances 637 287. Formulas for Computing Geodetic Coordinates 638 288. Computation of Geodetic Coordinates: Example 642 289. Knowing Latitudes and Longitudes of Two Points, to Compute Azimuths and Distances 646 CHAPTER XXX. GEODETIC CONSTANTS AND REDUCTION TABLES. 290. Constants Depending on Spheroidal Figure of Earth 672 291. Numerical Constants 672 292. Length of the Meter in Inches 674 293. Interconversion of English and Metric Measures 675 294. Logarithms and Factors for Conversion of English and Metric Measures 676 PART VI. GEODETIC ASTRONOMY. CHAPTER XXXI. ASTRONOMIC METHODS. 295. Method of Treatment ......................................... 678 296. Geodetic Astronomy ........................................... 679 297. Definitions of Astronomic Terms .............................. 679 298. Astronomic Notation .......................................... 683 299. Fundamental Astronomic Formulas ............................ 684 300. Finding the Stars ............................................. 685 301. Parallax ...................................................... 688 302. Refraction ....... ............................................. 689 CHAPTER XXXII. 303. Interconversion of Time ....................................... 695 304. Interconversion of Time and Arc .............................. 698 Xviii CONTENTS. ART. * AGK 305. Determination of Time ?o 306. Time by a Single Observed Altitude of a Star 702 307. Approximate Time from Sun 703 308. Time by Meridian Transits 73 CHAPTER XXXIII. AZIMUTH. 309. Determination of Azimuth 77 310. Observing for Azimuth 707 311. Approximate Solar Azimuth 708 312. Azimuths of Secondary Accuracy 712 313. Primary Azimuths 7 J 9 314. Reduction of Azimuth Observations 720 315. Azimuth at Elongation 721 CHAPTER XXXIV. LATITUDE. 316. Methods of Determining Latitude 723 317. Approximate Solar Latitude 724 318. Latitude from an Observed Altitude 725 319. Astronomic Transit and Zenith Telescope 726 320. Latitude by Differences of Zenith Distances of Two Stars 728 321. Errors and Precision of Latitude Determinations 729 322. Field-work of Observing Latitude 730 323. Determination of Level and Micrometer Constants 732 324. Corrections to Observations for Latitude by Talcott's Method. . 738 325. Reduction of Latitude Observations 743 CHAPTER XXXV. LONGITUDE. 326. Determination of Longitude 744 327. Astronomic Positions: Cost, Speed, and Accuracy 744 328. Longitude by Chronometers 745 329. Longitude by Lunar Distances 746 330. Longitude by Chronograph 748 331. Observing for Time 751 332. Reduction of Time Observations 752 333. Record of Time Observations 754 334. Longitude Computation 757 335. Comparison of Time 774 CONTENTS. XIX CHAPTER XXXVI. SEXTANT AND SOLAR ATTACHMENT. ART. PACK 336. Sextant 777 337. Adjustment of Sextant 778 338. Using the Sextant 780 339. Solar Attachment 781 340. Burt Solar Attachment 781 341. Adjustment of Burt Solar Attachment 782 342. Smith Meridian Attachment 785 343. Adjustment of Smith Meridian Attachment 786 344. Determination of Azimuth and Latitude with Solar Attachment. 789 345. Solar Attachment to Telescopic Alidade 791 CHAPTER XXXVII. PHOTOGRAPHIC LONGITUDES. 346. Field-work of Observing Photographic Longitude 793 347. The Camera and its Adjustments 794 348. Measurement of the Plate 797 349. Computation of the Plate 801 350. Sources of Error 802 351. Precision of Resulting Longitude 806 REFERENCE WORKS ON GEODESY 809 PART VII. CAMPING, EMERGENCY SURGERY, PHOTOGRAPHY. CHAPTER XXXVIII. CAMP EQUIPMENT AND PROPERTY. 352. Attributes of a Skillful Photographer 811 353. Subsistence and Transportation of Party in Field 813 354. Selecting and Preparing the Camp Ground 814 355. Tents 817 356. Specifications for Army Wall Tents 820 357. Specifications for Army Wall-tent Flies 821 358. Specifications for Army Wall-tent Poles 822 359. Specifications for Army Shelter Tents (Halves) 822 360. Specifications for Army Shelter Tents (Poles) 824 361. Erecting the Tent 825 CONTENTS. ART PACK 362. Tent Ditching and Flooring .................................. 825 363. Camp Stoves, Cots, and Tables ............................... 827 364. Specifications for Army Sibley Tent Stoves .................... 829 365. How to , Build Camp-fires ..................................... 830 366. Cooking-fire for a Small Camp ................................. 830 367. Camp Equipment .............................................. 831 368. Provisions .................................................... 833 CHAPTER XXXIX. TRANSPORTATION EQUIPMENT. 369. Camp Transportation: Wagons ................................ 836 370. Pack Animals and Saddles .................................... 837 371. Moore Pack-saddles ........................................... 840 372. Throwing the Diamond Hitch ................................. 841 373. Packmen ..................................................... 847 374. Transportation Repairs ......................................... 848 375. Veterinary Surgery ............................................ 849 CHAPTER XL. CARE OF HEALTH. 376. Blankets and Clothing ......................................... 850 377. Care of Health ........................................... . ____ 852 378. Drinking-water ............................................... 855 379. Medical Hints ................................................. 856 380. Diarrhea and Dysentery ....................................... 857 381. Drowning and Suffocation ..................................... 858 382. Serpent- and Insect-bites ...................................... 860 383. Surgical Advice ............................................... 860 384. Medicine-chest ............................................... 861 CHAPTER XLI. PHOTOGRAPHY. 385. Uses of Photography in Surveying ............................ 864 386. Cameras ...................................................... 865 387. Lenses and their Accessories .................................. 867 388. Dry Plates and Films ......................................... 869 389. Exposures .................................................... 872 390. Developing ................................................... 875 391. Fixing ....................................................... 878 392. Printing and Toning .......................................... , 880 393. Blue Prints and Black Prints .................................. 883 TABLES. TABLE PAGE I. Scale and Cost of Detailed Topographic Maps 67 II. Scale, Cost, and Relief of Government Geographic Maps 75 III. Scale and Cost of Cadastral Surveys 107 IV. Error in Horizontal Angle due to Inclination of Plane- table Board 181 V. Logarithms of Numbers to Four Places 215 VI. Logarithms of Trigonometric Functions 217 VII. For Converting Wheel-revolutions into Decimals of a Mile 233 VIII. Reduction of Inclined Stadia Measures to Horizontal Distances 249 IX. Horizontal Distances and Elevations from Stadia Read- ings 250 X. Differences of Elevation from Stadia Measures , 260 XI. Natural Sines and Cosines '.''.'. 275 XII. Natural Tangents and Cotangents 277 XIII. Cost of Leveling per Mile in Various States 350 XIV. Cost and Speed of Government Precise Leveling. 351 XV. Differences of Altitude from Angles of Elevation or De- pression 364 XVI. Logarithms of Radius of Curvature R in Meters 369 XVII. Reduction of Barometric Readings to Feet 384 XVIII. Correction for Differences of Temperature 392 XIX. Correction for Differences of Gravity at Various Latitudes 393 XX. Correction for Decrease of Gravity on a Vertical. . . . 394 XXI. Correction for the Height of the Lower Station. Positive 394 XXII. Altitude by Boiling-point of Water 403 XXIII. Coordinates for Projection of Maps 419 XXIV. Lengths of Degrees of Meridian and Parallel 437 XXV. Arcs of the Parallel 438 XXVI. Meridional Arcs. Coordinates of Curvature 139 xxi XXli TABLES. TABLE PAG * XXVII. Areas of Quadrilaterals of Earth's Surface 445 XXVIII. Scale Equivalents for Various Ratios 447 XXIX. Ratios Equivalent to Inches to One Mile 448 XXX. Convergence of Meridians 54 XXXI. Difference in Height between the Apparent and True Level 549 XXXII. Sizes of Heliotrope Mirrors 569 XXXIII. Solution of Oblique Plane Triangles 597 XXXIV. Pierce's Criterion 606 XXXV. Factors for Computing Probable Error 608 XXXVI. Log m for Determining Spherical Excess 622 XXXVII. Factors for Computation of Geodetic Latitudes, Longi- tudes, and Azimuths 649 XXXVIII. Corrections to Longitude for Difference in Arc and Sine 670 XXXIX. Values of Log * . 671 cos l / 2 d XL. Log F 671 XLI. Interconversion of English Linear Measures 673 XLII. Interconversion of English Square Measures , 674 XLIII. To Convert Metric to English Measures 675 XLIV. To Convert English to Metric Measures 675 XLV. To Convert Meters into Statute and Nautical Miles 676 XLVI. Logarithmic Constants for Interconversion of Metric and Common Measures 676 XLVII. Metric to Common System, with Factors and Log- arithms 677 XLVIII. Miscellaneous Metric Equivalents 677 XLIX. Parallax of Sun (/>) for First Day of Each Month 691 L. Mean Refraction (Rm) 692 LI. Correction (Cb) to Mean Refraction 693 LIT. Correction (Cd) to Mean Refraction 604 LIII. Correction (Co) to Mean Refraction 695 LIV. Conversion of Mean Time into Sidereal Time 696 LV. Conversion of Sidereal Time into Mean Time 697 LVI. Constants for the Interconversion of Time and Arc 698 LVII. Conversion of Time into Arc 699 LVIII. Conversion of Time into Arc (continued) 700 LIX. Conversion of Arc into Time 701 LX. Approximate Local Mean Astronomic Times of the Cul- minations and Elongations of Polaris for the Year 1900 7I5 LXI. Intermediate Times for Above 716 LXII. Azimuths of Polaris at Elongation 717 LXIII. Corrections to Azimuths of Polaris for Each Month... 717 TABLES. TABLE PAGE LXIV. Azimuths of Polaris 718 LXVI. Values of m for Every 5 Declination 737 LXVII. Reduction of Observations on Close Circumpolar Stars.. 738 LXVIII. Correction for Differential Refraction 739 2 sin 2 "i/zT LXIX. Values of ^- 740 sin i LXX. Factors for Reduction of Transit Observations 758 LXXI. Ration List 834 LXXIL Relative Times of Exposure for Different Stops and Subjects 874 LIST OF ILLUSTRATIONS. PLATES PACK I. Surveying Under Difficulties Frontispiece II. Contour Survey of Site for Dam, Snake River, Idaho 58 III. Sand Hills, Bench, Creek, etc., above Albany, N. Y 136 IV. Isogonic Chart of United States for 1900 224 FIGURE 1. Diagram of Plane-table Triangulation, Frostburg, Md 25 2. Roads, Houses, and Locations Resulting from Traverse, Frost- burg, Md 26 3. Adjusted Sketch Sheet, Frostburg, Md 27 4. Completed Topographic Map, Frostburg, Md 31 5. Land Survey Control for Topographic Sketching, North Dakota 38 6. Topographic Map on Land Survey Control, Fargo, N. D 41 7. Optical Illusion as to Relative Heights of Divides 45 8. Contour Topographic Survey for Location of Mexican Central Railway 50 9. Detailed Contour Survey for Canal Location 54 10. Preliminary Map of Canal, Montana 56 11. Contour Survey of a Reservoir Site, Montana 59 12. Portion of Jerome Park Reservoir Survey, New York 60 13. Plan and Profile of Twin Lakes Dam Site, Colorado 61 14. Topographic and Cadastral Map of Baltimore, Md 66 15. Field-sketch Map Made on Plane-table in Alaska 71 16. Geographic Contour Map made from Fig. 15 72 17. Captain Zebulon Pike's Map about Pike's Peak, Colo., 1807 78 18. Captain J. C. Fremont's Map about Pike's Peak, 1845 79 19. Wheeler Map about Pike's Peak, Colo., 1876 80 20. Hayden Map about Pike's Peak, Colo., 1875 81 21. U. S. Geological Survey Sheet about Pike's Peak, Colo., 1892.. 83 22. U. S. Geological Survey Map about Cripple Creek, near Pike's Peak, 1894 85 XXV LIST OF ILLUSTRATIONS. 23. Field Plane-table Sheet, Exploratory Route Survey, Alaska.... 88 24. Exploratory Route Survey, Alaska. Final Drawing 89 25. Exploratory Survey, Seriland, Sonora, Mexico 9 26. Skeleton of Route from Best Available Map 94 27. Sketch Route of Fig. 26, Filled in with Field Notes 96 28. Sketch Route of Fig. 26, Filled out from Field Notes of Fig. 27. . 97 29. Reconnaissance on Nile River from Gordon's Steamer 98 30. Reconnaissance Sketch of Arab Position at Abu Klea 99 31. Military Map of Operations about South Mountain 101 32. Military Siege Map 102 33. Cadastral Map of U. S. Public Land Survey, Indian Territory.. 106 34. Canyon in Homogeneous Rock, Yosemite Park, Cal 115 35. Watergaps and Pirating Streams, Pottsville, Pa 117 36. Erosion in Soft Rock 120 37. Erosion in Hard Rock 120 38. Erosion in Horizontal Beds of Hard and Soft Rock 120 39. Erosion in Alternate Beds of Soft and Hard Rock 120 40. Erosion in Soft Rock Underlain by Hard 120 41. Volcanic Mountain, Mt. Shasta, Cal 123 42. Alluvial Ridge and Flood Plain, Lower Mississippi River 125 43. Sand Dunes, Coos Bay, Ore 127 44. Dissected Plateau, Northern Arizona 129 45. Mountain Range and Amphitheater, Irwin, Col.o 131 46. Drawing Radial Sight Lines 148 47. Intersecting on Radial Lines 149 48. Coast Survey Plane-table 154 49. Telescopic Alidade and Johnson Plane-table 155 50. Johnson Plane-table Movement 156 51. Telescopic Alidade 158 52. Gannett Traverse Plane-table and Sight Alidade 160 53. Vertical Angle Sight Alidade 161 54. Folding Exploratory Plane-table and Small Theodolite 163 55. Cavalry Sketchboard and Straight-edge 165 56. Scales of the Slide Rule 169 57. Double Screw to Hold Plane-table Paper 177 58. Intersections with Plane-table 183 59. Three-point Locations 186 60. Bessel's Graphic Solution of Three-point Problem 189 61. Ranging-in I92 62. Lining-in I93 63. Two-point Problem 194 64. Traversing with Plane-table 198 65. Section of Engineers' Transit 203 66. Collimation Adjustment 206 67. Traversing with .Transit .208 LIST OF ILLUSTRATIONS. XXV'ii FIGURE PAGE 68. Plat of Transit Road Traverse 210 69. Full-circle Vernier Protractor 211 70. Three-arm Protractor 211 71. Signs of Latitudes and Departures 213 72. Prismatic Compass 214 73. Douglas Odometer Attached to Wheel 230 74. Bell Odometer 231 75. Hand Recorder 232 76. Stadia Measurement on Horizontal 244 77. Stadia Measurement on Slope 248 78. Stadia Reduction Diagram 259 79. Stadia Reduction Diagram to Horizontal Distances 265 80. Diagram for Reducing Inclined Stadia Distances to Horizontal.. 266 81. Speaking Stadia and Level-rods 270 82. Angular Tachymetry 273 83. Wagner- Fennel Theodolite Tachymeter 281 84. Reconnaissance Sketch-map with Cavalry-board and Range- finder 285 85. Range-finding with a Direction-point, D 287 86. Range-finding without Direction-point 287 87. Measuring Long Base with Range-finder 287 88. Weldon Range-finder 288 89. Range-finding with Plane-table 290 90. Photograph by Canadian Survey and used in Map Con- struction 293 91. Bridges-Lee Photo-theodolite 297 92. Projection of Camera-plates from a Station 301 93. Projection of Photograph 302 94. Construction of Map from Four Photographic Stations 303 95. Engineer's Wye Level 309 96. Target-rods 312 97. Speaking Level-rods 314 98. Turning-points 315 99. Illustrated Description of Bench-mark 316 100. Bronze Tablet and Wrought-iron Bench-mark Post... 318 looa. New Coast Survey Binocular Precise Level 326 looft. Section of Binocular Precise Level 327 101. Precise Spirit-level 328 102. Duplicate Direct and Reverse Leveling with Single Rods 330 103. Duplicate Direct and Reverse Leveling with Double Rod 331 104. Single-rodding with Two Rodmen 332 105. Duplicate Rodding, Both Lines Direct Only 332 106. U. S. Geological Survey Double-target Level-rod 334 107. U. S. Geological Survey Precise Speaking-rod 336 108. Level Circuit 346 109. Group of Connected Level Circuits 347 XXV111 LIST OF ILLUSTRATIONS. FIGURE PAGK no. Long-distance Leveling Across Tennessee River 354 in. Locke Hand-level 356 112. Abney Clinometer Hand-level 357 113. Section Through Cistern and Tube of Mercurial Barometer.... 376 1 14. Aneroid Barometer 398 115. Gnomonic and Orthographic Projections 407 116. Stereographic and External Projections 408 117. Orthographic Equatorial Projection 408 118. Orthographic Horizontal Projection 408 119. Stereographic Equatorial Projection 409 1 20. Stereographic Meridional Projection 409 121. Stereographic Horizontal Projection 409 122. Lambert's Surface-true Central Projection 409 123. Cylinder Projections 411 1 24. Equidistant Flat Projection 41 r 125. Mercator's Cylinder Projection 411 126. Van der Grinten's Circular Projection 4I2 127. Babinet's Homalographic Projection of the Whole Sphere 413 128. Tangent Cone Projection 414 129. Intersecting Cone Projection 414 130. Equal-spaced Conical Projection 415 131. Mercator's Conical Projection 415 132. Equivalent Conical Projection 415 133. Bonne's Projection 416 134. Construction of Polyconic Projection 417 135. Contour (>), Shade-line (B), and Hachure Construction (A)... 451 136. Shaded Contour Map 453 137. Sketch Contours. Xalapa, Mexico 455 138. Relief by Crayon-shading 457 139. Contour Sketch 459 140. Contour Projection , 461 141. Hachure Construction 462 142. Shaded Hachures 463 143. Hachured and Contoured Hill on Different Scales 465 144. Conventional Signs; Public and Private Culture 467 145. Conventional Signs; Miscellaneous Symbols and Boundary Lines 469 146. Conventional Signs ; Hydrography 471 147. Conventional Signs ; Relief or Hypsography 473 148. Conventional Signs; Lettering 475 149- Pantograph 4?8 150. Relief Map from Catskill Model 481 151. Relief Map from Contour Model 4^7 152. Coast Survey Tape-stretcher 502 153. Tape-stretcher for Use on Railroads 504 154. Simple Tape-stretcher ^ os 155- Contact-slide Base Apparatus 509 LIST OF ILLUSTRATIONS. XXIX 156. Eimbeck Duplex Base Apparatus 512 157. Cross-section of Iced-bar Apparatus 514 158. Repsold Base Apparatus 515 159. Transfer of Measured Base OO' to Computed and Marked Base AB 525 160. Intervisibility of Objects 551 161. Base Expansion 555 162. Eight-inch Direction Theodolite 557 163. Section of Micrometer through Screw Showing Comb and Cross- hairs in Central Plan 558 164. Quadripod Signal 563 165. Observing Scaffold and Signal 567 166. Telescopic Heliotrope 570 167. Steinheil Heliotrope 572 168. Trigonometric Functions 594 169. Graphic Statement of Formulas for Solution of Right-angled Triangles 595 170. Solution of Triangle Given Two Sides and Included Angle 598 171. Solution of Triangle Given Certain Functions 598 172. Solution of Triangle Given Three Sides 599 173. Three-point Problem 600 174. Reduction to Center 609 175. Station Adjustment 613 176. Angle and Side Notation 618 177. Angle and Side Equations 624 178. Computation of Azimuths 642 179. Latitude, Declination, and Altitude 683 1 80. Conversion of Time 698 i8oa. Aspects of Polaris 713 181. Astronomic Transit and Zenith Telescope 727 182. Chronograph 750 183. Sextant 778 184. Graphic Illustration of the Solar Attachment 783 185. Smith Meridian Attachment 786 186. Where a Pack-mule Can Go '. 813 187. A Pretty Camp Ground, North Carolina 815 188. Wall-tent with Fly 818 189. Ridge and Pole for Wall-tent 822 190. Shelter Tents 823 191. Jointed Shelter-tent Poles 824 192. Sod-cloth and Ditch 826 193. Tent Stove and Pipe 827 194. Folding Camp Table 829 195. Folding Tin Reflecting Baker 832 1 06. Camp Wagon 837 197. Full-rigged Moore Army Pack-saddle 840 XXX LIST OF ILLUSTRATIONS. FIGURE PAGE 198. Pack-saddle Cinches 840 199. Lashing Pack with Diamond Hitch 842 200. Loading Pack-mule with Mess-boxes 843 201. Packing on Men's Backs, Adirondacks 846 202. Pack-basket 847 203. Plane-table Station on Mountain in Alaska 851 204. Inducing Artificial Respiration 859 205. Diagram Showing Relative Exposures at Different Times of Day and Year 873 PART I. TOPOGRAPHIC, GEOGRAPHIC, AND EXPLORATORY SURVEYING. CHAPTER I. KINDS OF MAP SURVEYS. I. Classes of Surveys Surveys may be grouped under three general heads : 1. Those made for general purposes, or information sur- veys. 2. Those made for jurisdictional purposes, or cadastral surveys. 3. Those made for construction purposes, or engineering surveys. Information surveys may be exploratory, geodetic, geo- graphic, topographic, geologic, military, agricultural, mag- netic, or hydrographic. Geodetic surveys are executed for the purpose of determining the form and size of the earth. They do not necessarily cover the entire surface of the country, but only connect points distant from each other 20 to 100 miles. Topographic and geographic surveys are made for military, industrial, and scientific purposes. To be of value they must be based upon trigonometric or tri- angulation surveys, but not necessarily of geodetic accuracy. The mother map, or that from which all others are derived, is the topographic map. This is made from nature in the field 2 KINDS OF MAP SURVEYS. by measures and sketches on the ground. It is the original or base map from which can be constructed any variety of maps for the serving of separate purposes. The historian may desire to make a map which will indicate the places upon which were fought great battles, or on which are located the ancestral estates of historic families. The geologist may desire to indicate the location of certain rock formations. The promoter of railways or other engineering works may desire to represent the route of his projected road or the location of city water-supplies or real-estate subdivisions. For these several purposes the topographic or base map furnishes the original data, or foundation, on which can be indicated, in colors or otherwise, any special class of information. Cadastral surveys define political and private property boundaries and determine the enclosed areas. Such surveys are executed for fiscal and for proprietary purposes, and their value depends upon the degree of accuracy with which they are made. A cadastral survey is not necessarily based upon triangulation and may be only crudely executed with com- pass and chain. To thoroughly serve its purpose, however, it should be based on geodetic work of the greatest refine- ment. It does not necessarily cover the entire area en- closed, but only points and lines which mark the boundaries. Engineering surveys are executed in greater detail than any of the above. They may preferably follow some of them and are preliminary to the construction of engineer- ing works. They are conducted with such detail as to per- mit the computing of quantities of materials to be moved and the exact location of the various elements of the works which are to be constructed. Engineering surveys may be made for the construction and improvement of military works, as forts, navy yards, etc. ; for constructing routes of communication, as roads, electric lines, canals ; for reclama- tion of land, as irrigation and swamp surveys; for the im- provement of natural waterways, as river and harbor sur- INFORMATION SURVEYS. 3 veys ; or for the improvement of cities, as city water-supply and sewage disposal. 2. Information Surveys. All surveys have a twofold purpose : 1. To acquire certain information relative to the earth; and 2. To spread this among the people. The acquirement of the information is the field survey. The dissemination may be in the form of manuscript, illustra- tions, or sketch maps, as in the case of exploratory surveys; of a map only, as in the case of topographic survey when the map embodies the whole result ; or it may be a combina- tion of the two, as in the case of geographic surveys. In addition to the above primary classes of information surveys are the numerous minor differences in the method of field-work, including the instruments used, the degree of care in obtaining the information, and the mode of recording the results in notes or maps. The instrumental work of explora- tory surveys is usually of the crudest and most haphazard kind, the observations having to be taken and the notes re- corded incidentally and by such means and at such time as the primary necessities of the expedition, those of moving forward over the route traversed, will permit. Moreover, from the necessity of the circumstances such surveys are rarely homogeneous, never covering completely any given area; else they would cease to be exploratory. Being dis- connected, they are fixed from time to time with relation to the earth by such astronomic observations as will fre- quently check the interrupted route surveys in relation one to the other. Topographic- and geographic surveys differ essentially from exploratory surveys, but from each other only in minor details of scale, degree of representation of relief, and the note taken of the sphericity of the earth. Topographic sur- veys are generally executed on so large a scale and with such 4 KINDS OF MAP SURVEYS. care and detail that account need rarely be taken of the sphericity of the earth in plotting the resulting map, and they are therefore based on geodetic data only as they merge into geographic surveys. Moreover, all important natural and artificial features may be represented on the resulting map because of its large scale. Geographic surveys merge imperceptibly, on the one hand, into topographic surveys, as the scale of the latter becomes so small and the area depicted on a given map sheet so large that the shape of the earth must be considered. On the other hand, they may be plotted on so small a scale and the relief be depicted by such approximate methods that they merge imperceptibly into exploratory surveys, being practi- cally of the same nature as the latter excepting that they cover a given area in its entirety. 3. Topographic Surveys. A topographic map is one which shows with practical accuracy all the drainage, culture, and relief features which the scale of representation will per- mit. Such scale may be so large and the area represented on a given map sheet be so small that the control for the field surveys will be procured by means of plane and not of geodetic surveying. On the other hand, the scale may be so small and the area represented on the given map sheet so large as to require control by geodetic methods. The mistake is often made of assuming that a topographic map is special and not general. It is general, as it is not made for the purpose of constructing roads and highways, though it becomes a very valuable aid in their projection ; nor is it made for the purposes of reclaiming swamp-land or irrigating arid land, but it furnishes general information essential to a preliminary study and plan for their improve- ment. The outcome of a topographic survey being a topo- graphic map, it should be judged by the map, and the map should be judged by the manner in which it serves the gen- eral purpose. Above all, of two maps or works of any kind FEATURES ON TOPOGRAPHIC MAPS. 5 made for the same purpose and serving that purpose equally well, that the cheaper one is the better is a well-recognized principle of engineering. In the prosecution of a general topographic survey only such primary points should be determined geodetically as are essential to the making of the map. About one such point per one hundred square miles is a fair average for a one-mile to one-inch map. Such spirit-level bench-marks should be set and recorded as are obtained in carrying bases for levels over the area under survey. On the above scale about one bench to five square miles is a fair average. 4. Features Shown on Topographic Maps. The fea- tures exhibited on topographic maps may be conveniently grouped under the three following heads : 1. The hydrography, or water features, as ponds, streams, lakes. 2. The hypsography, or relief of surface forms, as hills, valleys, plains. 3. The culture, or features constructed by man, as cities, roads, villages, and the names printed upon the map. In order that these various features may be readily dis- tinguishable and thus give legibility to the map, it is usual to represent the hydrography in blue, the relief in brown, and the culture in black. In addition to this, wooded areas may be indicated in a green tint. The object of a topographic survey is the production of a topographic map. Hence the aim of the survey should be to produce only the map ; neither time nor money should be wastefully expended in the erection or refined location of monuments; the demarkation of public or private boundary lines; or the establishment of bench-marks beyond such as are incidental to the work of obtaining field data from which to make the map. The erection, location, and description of boundary marks is the special work of a property or cadastral survey. The erection, description, and determination of 6 KINDS OF MAP SURVEYS. monuments and bench-marks as primary reference points is the work of a geodetic survey. The determination of many unmarked stations for map-making purposes is the work of a topographic survey. 5. Public Uses of Topographic Maps. For the purposes of the Government or State good topographic maps are in- valuable. They furnish the data from which the congressman or the legislator can intelligently discover most of the informa- tion bearing directly upon the problem in hand, and they give committees great assistance in their decisions as to the need of legislation. If a River and Harbor bill is before Congress, or a bill relating to State Canals before the Legislature, by an inspection of such maps the slopes of the country through which the canal is to pass or in which the improvements are to be made may be readily ascertained. The sources of water- supply for a canal or river may be accurately measured on such a map and their relation to the work in hand intelligently ascertained. If the War Department of the Government or the Adjutant- General's Office of the State desires to locate an arsenal, en- campment ground, or other military work, or, above all, if it is to conduct active military operations in the field, such maps serve all the preliminary purposes of the best military maps. With the addition of a very little field-work during war times, such as the indication of ditches, fence lines, outbuildings, etc., on the mother or topographic map, a perfect military map may be obtained. For the Post-office Department or private stage, express, or telephone companies, such maps furnish the basis on which an accurate understanding can be had of contracts submitted for star or other routes for carrying the mails or packages. As these maps show the undulations of the surfaces over which roads pass, their bends and the relative differences in length, the difficulties in travel on competing roads can be readily ascertained from them. PUBLIC USES OF TOPOGRAPHIC MAPS. 7 The Land Departments of the Government and State can discover on such maps not only the outlines of the property under their jurisdiction, but its surface formation. Forestry Boards can see indicated upon these maps the outlines of the various wooded areas, besides the slopes of the lands on which these woods are situated, their relation to highways of trans- portation, railways, or streams, and the slopes to be encoun- tered in passing through the woods on these highways. The Legal department of the Government or State finds these maps of service in discussing political or property bound- ary lines, in ascertaining within what political division crimes are committed, or individuals reside with whom the officers of the law desire to communicate. It is difficult to see how any systematic or economical plan of road improvement can be advantageously made without the knowledge of existing grades, the physiography of the district through which the roads pass, and the location of quarries, which such maps present. The whole system of making successive special surveys or maps for every new need is one of the most wasteful in our present public practice, nor can it be otherwise until one survey shall be made that answers all important official uses. The amount of money that has been expended in making small maps of numerous cities and villages would have mapped, on a general scale, many times the area of the country. Even when we have these special maps they do not fully answer the purpose for which they were intended, as they only show the small area included within the immediate plan of operations. The value of a stream for economic purposes cannot be fully ascertained by an examination of the stream at the point from which it is to be used, but the drainage basin from which it derives its supply should be surveyed, and its area and slopes be known. A good topographic map not only shows the re- lations between the natural and artificial features in the im- mediate neighborhood under consideration, but it shows the relations of these to the surrounding country. 8 KINDS OF MAP SURVEYS. 6. Degree of Accuracy Desirable in Topographic Sur- veys. It is difficult to set any standard for the amount of de- tail which the topographer must sketch on his map, or the amount of control which must be obtained for the checking of this detail. A topographic map may be so made as to serve many useful purposes and yet be almost wholly a sketch, scarcely controlled by mathematical locations. The same territory may be mapped on the same scale with little improve- ment in the quality of representation of topographic form and yet the work be done with such detail and accuracy and such amount of control as to make it useful for all practical pur- poses to which its scale adapts it. With these facts clearly in view, it is evident that explicit instructions to the topographer are a practical necessity. Un- like any other surveyor the topographer must use his own judgment or be guided by instructions regarding the amount of time and money to be spent in obtaining detail and control, since the latitude permissible in mapping the same territory on the same scale varies greatly according to the uses to which the map is to be put. Such instructions should in- terpret the significance of scale and contour interval, and should cover the technical details of operations as found ap- plicable to conditions and locality (Art. 7). They should also fix the method of making and preserving field-notes. There are a variety of methods of survey, of instruments, and of records which are generally applicable to any case, yet to the expert topographer there is practically only one best way for each, and this can be decided only after he has inspected the country or has otherwise acquired knowledge of its characteristics. The scale and mode of expressing relief (Art. 191) must be fixed as well as the contour interval, if contours are em- ployed, in order that all the data necessary for the construc- tion of the map on this scale may be obtained. The methods and instruments should be stated in order that those best ACCURACY DESIRABLE. 9 suited to the conditions may be selected in the beginning. The mode of record should be fixed in order that there may be uniformity in the results brought into the office, provided there are various topographers working on the same area. Such instructions are to the topographer what specifications are to the contractor, yet they cannot quite carry the force of law because of the unforeseen exigencies which may arise and which require departure from fixed instructions in ac- cordance with the best judgment of the topographer. In topographic mapping it is sometimes desirable to make hasty preliminary or reconnaissance maps of a region in order that some information of the area may be immediately ob- tained. Such maps are practically sketches covering an ex- tensive area and without adequate framework of control, yet they contain most of the information required in the early de- velopment of the region. The error has too frequently been made of giving such maps the ear-marks of accuracy by rep- resenting the relief by numbered contours. In this they are misleading. Contours indicate precision and should justly be taken as accurate within the limits of the map scale. As has been aptly stated by Mr. J. L. Van Ornum, " accuracy is ex- pected where exactitude is shown, and the conclusion is just that inaccuracy in representation is inexcusable." Where for any reason the desired accuracy cannot be attained for lack of the proper control, the resulting map is merely a sketch-map, and relief should be indicated not by contours but by hachures or by sketched contours ; that is, lines in contour form, but disconnected and unnumbered. Such sketch-maps are useful as representations of topographic form, but are valueless as base-maps on which to plan great public improve- ments, the inception of which is so closely connected with topographic surveys. A topographic map well executed is, to quote Captain George M. Wheeler, "the indispensable, all-important sur- vey, being general and not special in character, which under- 10 KINDS OF MAP SURVEYS. lies every other, including also the graphic basis of the eco- nomic and scientific examination of the country. This has been the main or principal general survey in all civilized coun- tries. The results of such a survey become the mother source or map whence all other fiscal examinations may draw their graphic sustenance." Such a characterization of a topographic survey can apply only to one accurately made and on which every feature represented is as accurately shown as the scale of map warrants. In planning a topographic survey the controlling factor of the scale must always be kept clearly in mind, as this is the ul- timate criterion which decides the method of survey and the amount of time and money to be expended in its execution. The underlying law of topographic mapping is that applied to other engineering works, namely, no part of the construction, nor any part of the survey, should be executed with greater detail or at greater expense than will permit it to safely per- form the duties for which it is intended. Thus, in mapping an extended area, traverse methods alone for horizontal con- trol are insufficient unless performed with the greatest exacti- tude. The primary triangulation on which such a survey is based should be no more accurate than will permit of plotting the points with such precision that they shall not be in error by a hair's breadth at the extreme limit to which the triangu- lation is extended. The secondary triangulation should be executed with only such care as will permit of plotting with- out perceptible error on the scale selected and within the lim- its controlled by the nearest primary triangulation points. Sim- pler methods of securing horizontal control may be adopted for the minor points within the secondary triangulation, and these methods, be they by plane-table triangulation (Chap. IX) or by traverse (Chap. X), need be nothing better than will assure the plotting of the result without perceptible error and within distances controlled by the nearest secondary tri- angulation points. Finally, minor details may be obtained by AMOUNT OF CONTROL REQUIRED. II the crudest methods of traverse, range-finding, pacing, or sketch-board (Arts. Si, 116, 95, and 61), providing that the distances on the map over which such methods are propagated shall be so small as to warrant their not being perceptibly in error within the limits of the controlling points ^ the next higher order. As with the horizontal control so with the vertical control, no more time should be expended or precision attempted in determining elevations than are necessary to obtain the data essential to the mapping of the relief accurately to the scale limit. Where relief is to be represented by contours of a small interval and on a large scale, or where the slopes of the country are gently undulating or comparatively level, the leveling must be of a high order that the contours may be ac- curately placed in plan. In country having slopes as gentle as 5 to 10 feet to the mile, a difference of a few feet in elevation may mean that distance in error in the horizontal location of the contour if the elevations are not determined with accuracy. On the other hand, in precipitous mountain country much less care is necessary in the quality of the level- ing, since a large error in vertical elevation may be represented in plotting by the merest fraction in horizontal plan. For a large contour interval in country of moderate slopes less ac- curacy is essential in the determination of the elevation. For contours of 20 feet inte'rval errors of elevation varying from 5 to 20 feet or more may be made, depending upon the steepness of the slope and the consequent nearness in hori- zontal plan of one contour to the next. The same ratio applies to greater contour intervals. Therefore the methods pursued in determining the elevations should begin with a careful framework of spirit-leveling (Art. 129), and the amount of this should be only so great as to insure that the dependent levels of less accuracy shall not be so far in error as to be appreciable for the scale and contour interval selected and for a given slope of country. Based on these spirit-levels 12 KINDS OF MAP SURVEYS. rougher elevations by vertical angulation with stadia (Art. 102) or by trigonometric methods (Art. 1 59) may be employed, and tied in between these may be elevations by aneroid (Art. 174), the latter being checked at intervals sufficiently frequent to assure that the resulting elevations shall not introduce ap- preciable errors in the location of contours. The same rules should apply to the frequency with which vertical control points are determined. These should be so close together for the scale of the map and for the contour interval selected that in connecting them by eye in the course of the sketching no error appreciable on the scale shall be introduced. Any map, the best obtainable, is but a sketch controlled by locations. No one would undertake to determine the elevation and horizontal plan of every point on a contour line. Control positions on contours are only deter- mined with sufficient frequency to insure comparative accu- racy in connecting them. Bearing on this same point is the fact that such connection by sketching can undoubtedly be done with greater accuracy on the plane-table board with the terrane in view than from notes platted up in office or from photographs or profile drawings. Where relief is to be represented by hachures or broken sketch contours, precision in absolutely fixing the vertical ele- ment is of the least moment. It is generally desirable in making such maps to write approximate altitudes at promi- nent points, as stream junctions, villages, or mountain sum- mits, but the chief desideratum is relative differences in eleva- tion in order that the number of the sketched contours and their frequency, or the degree of density of the hachuring, may give an index to the amount of relief. 7. Instructions Relative to Topographic Field-work. The following instructions are those issued by the Director of the United States Geological Survey for the guidance of topographers in the field : I. At least two primary triangulation points or a primary control line INSTRUC7^IONS TO TOPOGRAPHERS. 13 1. All primary triangulatipn points and primary control lines should be platted on each atlas sheet previous to commencing field-work. 2. All existing map material should be diligently sought for; such of this as may be of value, as public-land plats, railroad, water-supply, city, Coast Survey, Army Engineer, or other public or private material, should be carefully compiled. If on field inspection this proves adequate, it should be brought up to date and incorporated in the field sheets. 3. On each atlas sheet, in addition to primary levels, such other eleva- tions should be obtained instrumentally that aneroids when used need never be left without a check elevation for distances exceeding z\ to 3 miles. These control elevations may come from profiles of railroads, from spirit-levels or from vertical angulation. 4. Plane-table triangulation must be conducted on the large sheets, and it is desired that as fast as intersections are obtained by the topog- rapher the vertical heights of stations and intersected points should be computed. 5. In conducting plane-table triangulation, as many prominent features as possible, including hilltops, churches, and houses, should be intersected in order to furnish connections with the traverse work, while gaps or passes and salients on ridges should also have their positions and elevations deter- mined from the plane-table stations. 6. Secondary topographic control must precede topographic sketching and the filling in of minor details of the map. 7. Field sheets must be as few in number and as large as the character of the topography will permit, and all main control must be adjusted thereon; this to be done before the filling in of minor detailed sketching is commenced. These minor details may be obtained by traverse on separate sheets, but must at once be transferred to and adjusted on main field sheets, so that no uncompleted spaces shall be left on them in the field. 8. The stage of water in rivers to be shown on the topographic maps is to be that which exists during the greater portion of the year and represents the normal condition of the stream. When any other condition is represented an explanatory note giving stage and date should be inserted in the legend. 9. The topographer in charge will be held responsible not only for the quality of the topographic work but also for the quality and management of the spirit-leveling done under his direction, and for the location and mark- ing of the bench marks, each of which he should endeavor to examine person- ally. Standard bench marks should be indicated on field sheet. 10. Only so much of the field sheets should be inked in the field as can be done with sufficient care to permit of their being accepted as final draw- ings and of their being directly photographed or photolithographed (except where land-survey plats are used as field sheets). Accordingly, only such 14 KINDS OF MAP SURVEYS. inks should be used as will photograph readily mixed burnt sienna for contours, black for culture, and mixed Prussian blue for drainage. 11. A full record must be made on the title-page of each notebook, stating character of work, locality, atlas sheet, and date of record; also name of topographer and maker of notes. 12. Plats, on a large scale, should be made or obtained of all large cities, showing the streets and houses in detail. 13. The determination and spelling of names of streams, mountain peaks, villages, and other places of note should receive particular attention. 14. Plane-table stations must be numbered consecutively with Roman numerals. If the station has been sighted before occupation, the station number must be followed by the number of the sight to it. Sights or points must be numbered by Arabic numerals consecutively; and a point once numbered must always be given the same number whenever recognized. If the points sighted exceed one thousand in number, a capital M shall be written at the head of the number column of the notebook. This rule must be followed by all members of the topographic branch. 15. The standard conventional signs must be used on all plane-table and traverse sheets. 1 6. The sheets must be inked clearly and carefully, with uniformity throughout, and in such manner as to adapt them for one-third reduction to publication scale. Only such ink should be used as will photograph readily. (See par. 10, above.) Culture should be inked first, and standard conven- tional signs used. 17. In drawing streams care should be taken that the lines shall not become faint and uncertain near the sources of the streams, and the placing of drainage in every little gully simply to indicate that it may be a water- course should be avoided. Use the symbol dash and three dots for intermittent streams. 1 8. In lettering, names parallel to the east or west sides of the sheet should read from the south side. Names of minor importance and figures of eleva- tion should be placed close to the object, on the right and horizontally. The letters, figures, and cross pertaining to a bench mark should be arranged with the letters above and to the left of the cross, and the figures below and to the right. 19. The original drawing of a topographic sheet shall be verified by some competent person in addition to the topographer who compiles it, by comparison with field sheets, and such "proof -reading" shall be recorded on the appropriate form. 8. Elements of a Topographic Survey. From a con- structive point of view a map is a sketch corrected by loca- tions. The making of locations is geometric, that of sketch- ELEMENTS OF A TOPOGRAPHIC SURVEY. I 5 ing is artistic. However numerous may be the locations they form no part of the map itself, serving merely to correct the sketch which supplies the material of the map. Every map, whatever its scale, is a reduction from nature and conse- quently must be more or less generalized. It is therefore im- possible that any map can be an accurate, faithful picture of the country it represents. The smaller the scale the greater the degree of generalization and the farther must the map de- part from the, original. The larger the scale the smaller the area brought together on a given map, and the less it appeals to the eye which grasps so extended a view of nature. There is, however, for the purposes of making information maps, a scale which is best suited to every class of topography, and the best result only will be obtained by selecting the relation of horizontal scale and contour interval which fits the partic- ular topography mapped. By far the most important work of topographic mapping is the sketching (Arts. 13, 15, 17, and 193), and this should be done by the most competent man in the party presum- ably its chief. He should not only sketch the topography because of his superior qualifications for that work, but also because the party chief is responsible for the quality of all the work, and only in the sketching, which is the last act in map- making, has he full opportunity for examining the quality of the control and of the other elements of the work executed by his subordinates. The map-sketcher is therefore the topog- rapher, and it is in the matter of generalization or in the se- lection of scale and the amount of detail which should be shown for the scale selected that the judgment of the topog- rapher is most severely tested. This is the work in which the greatest degree of proficiency can only be attained after years of experience. The topographer must be able to take a broad as well as a detailed view of the country, and to understand the meaning of its broadest features that he may be able best to interpret details in the light of those features (Chap. VI). 1 6 KINDS OF MAP SURVEYS. It is only thus that he can make correct generalizations, and thus that he is enabled to decide which detail should be omitted and which preserved in order to bring out the pre- dominant topographic features of the region mapped. The correctness of the map depends upon: (1) The accuracy of the locations; (2) Their number per square inch of map; (3) Their distribution; (4) The quality of the sketching. The first three of these elements defines the accuracy of the map, and the greatest accuracy is not always desirable be- cause it is not always economical. The highest economy is in the proper subordination of means to ends, therefore the quality of the work should be only such as to insure against errors of sufficient magnitude to appear upon the scale of publication (Art. 6). The above being recognized, it is evi- dently poor economy to execute triangulation of geodetic re- finement for the control of small-scale maps, and, providing the errors of triangulation are not such as are cumulative, the maximum allowable error of location of a point on which no further work depends may be set at .01 of an inch on the scale of publication. The second condition, the number of locations for the proper control of the sketching, is not easily defined. It de- pends largely upon the character of the country and the scale and uses of the map. Any estimate of it must be based on unit of mapped surface and not of land area. For rolling or mountainous country of uniform slopes or large features (Fig. 4), from \\ to 3 locations and 2 to 5 inches of traverse per square inch of map should, with accompanying elevations, be sufficient. On the other hand, in highly eroded or densely wooded country (Fig. 34) as many as 3 to 6 locations and 5 to 10 inches of traverse, per inch of map may, with accompany- ing elevations, be necessary to properly control the sketching. Again, in very level plains country (Fig. 6) less than one lo- ACCUFACY OF MAP. I/ cation and but 2 to 5 inches of traverse, with accurate eleva- tions, will suffice to furnish adequate control. The same is true of the third element of accuracy, the distribution of locations. In rolling, hilly country of uniform slope the control should be obtained chiefly at tops and bot- toms and changes of slope. The same is true of heavy moun- tains, excepting that all summits and gaps on ridges must be fixed, as well as all changes in side slopes and a few positions distributed about the valley bottoms. In flat plains the posi- tions determined should be locations on the contours themselves and at changes in their direction. In highly eroded regions locations of all kinds should be distributed with consider- able uniformity, so as to control every change of feature or slope. The fourth element, the quality of the sketching, depends wholly upon the artistic and practical skill of the topographer in other words, upon his possession of the topographic sense, which may be described as his ability to see things in their proper relations and his facility in transmitting his im- pressions to paper. This is by far the most important and difficult requirement to meet, and one which takes a longer apprenticeship on the part of the topographer than all the others combined. CHAPTER II. SURVEYING FOR SMALL-SCALE OR GENERAL MAPS. 9. Methods of Topographic Surveying. Three general methods of making topographic surveys have usually been employed in the past : First, traversing or running out of contours by means of transit, chain or stadia, and level; Second, cross-sectioning the area under survey with the same instruments; and Third, triangulation of the territory under survey with such minuteness as to get a sufficient number of vertical and horizontal locations to permit of connecting these in office by contour lines. All three methods are slow and expensive, while the first two are unfitted to the survey of large areas, because of the inaccuracies introduced in linear or traverse surveys. A fourth method, and that which this book is designed to expound, is that always employed by the United States Geo- logical Survey as well as to a lesser degree by several other American and European surveys. It is fitted to make topo- graphic maps for any purpose, on any scales, and of any area. ' This consists of a combination of trigonometric, traverse, and hypsometric surveying to supply the controlling skeleton, supplemented by the " sketching in " of contour lines and details by a trained topographer. In this method the contour lines are never actually run out nor is the country actually cross-sectioned. Only sufficient trigonometric con- trol is obtained to tie the whole together, the minor control 18 METHODS OF TOPOGRAPHIC SURVEYING. IQ between this being filled in : first, in the most favorable tri- angulation country almost wholly by trigonometric methods; second, in less favorable triangulation country by traverses connecting the trigonometric points. There are two general methods of making a contour topo- graphic map which have been aptly styled the "regular" and the "irregular." These might be respectively called the old and the new. The old or regular method includes the surveying and leveling of a skeleton work of controlling traverse or triangulation and the cross-sectioning of the ter- rane into rectangular areas, the outlines of which are trav- ersed and leveled. In addition the leveled profiles and trav- erses are continued between this gridironing at places where important changes of slope occur, and finally the survey and leveling of flying lines or partial sections is extended from each station. By this method the base of each level section or the contour line or line of equal elevation is determined by setting the instrument in position where this level line intersects the profile, and using the telescope as a leveling instrument with its cross-hairs fixed on a staff at the height of the optical axis, a line is then located by tracing successive positions of a stadia rod or by locating by intersection successive points on the level line, and a line drawn through these points locates the contour curve. In addition, parts of several level sec- tions are plotted from one station by intersection on, or location of a staff, and by the determination of its height above or below the instrument by vertical angulation. In this mode of topographic surveying pegs are usually driven at regular intervals and their heights determined by spirit-level and ver- tical angulation. The new or irregular method of topographic surveying consists in determining by trigonometric methods the po- sition and height of a number of critical points of the terrane and connecting these by traverses and levels, not run on a cross- section or rectangular system, but irregularly, so as to give 2O SURVEYING FOR SMALL-SCALE MAPS. plans and profiles of the higher and lower levels of the country, as ridge summits or divides and valley bottoms or drainage lines, such lines being run over the most easily traversed routes, as trails or roads. With the numerous positions and heights deter- mined by the triangulation, and on these traverses as controlling elements, contour lines are sketched in by eye and by the aid of the hand-level on a plane-table with the country in con- stant view. This is the method now generally employed by expert topographers, and the work is so conducted that the development of the map proceeds with the survey of the skeleton and rarely necessitates the return to a station when once occupied. Moreover, it calls for the location of less points and the running of fewer traverses and profiles, and these over more easily traveled routes, than the former method. It is therefore more expeditious, cheaper, and the resulting map is a better representation of the surface, as it possesses not only the mathematical elements of instrumental location, which in the old method are arbitrarily connected in office, but also the artistic element produced by connecting the lines of equal elevation in the field, with the country at all times immediately before the eye. 10. Geological Survey Method of Topographic Survey- ing. In average country, favorable for triangulation, com- paratively clear of timber and well opened with roads, a skele- ton trigonometric survey (Chap. IX) is made, by which the positions and elevations of all summits are obtained, as well as the horizontal positions of a few points in villages or at road crossings, junctions, etc. This constitutes the upper system of control (Fig. i). Below and between this is a net- work of road traverses (Chap. X) supplemented by vertical- angulation (Chap. XVII) or spirit levels (Chap. XV) for elevations, and these follow the most easy routes of travel, not cross-sectioning the country in the true sense, but follow- ing all the lower lines or stream bottoms, as well as the gradients pursued by roads (Fig. 2). Between these two RATIONAL METHOD OF TOPOGRAPHIC SURVEYING, 21 upper and lower sets of control points there are therefore many intermediate ones obtained by road traverses, and the topographer, by observation from the various positions which he assumes and with the knowledge he possesses of topographic forms, sketches the direction of the contour lines. These are tied accurately to their positions by the large amount of mathe- matical control already obtained, supplemented by additional traverses or vertical angles where such are found wanting. (Art. 162.) The instruments used are as various as are the methods of survey employed ; the essential instruments being the plane-table and the telescopic alidade (Chap. VII), which invariably replace the transit (Art. 85) or compass (Art. 91), so that all surveying is accompanied by mapping at the same time, and there is no tedious and confusing plotting from field- notes to be done later in office. Nor are any of the sa- lient features of the topography of the region lost through neglect to run traverses or obtain positions or elevations, all omissions of this kind being evident from an inspection of the map while in process of construction. The distances are obtained by triangulation with the plane-table (Art. 73) and by odometer measurements (Art. 98), supplemented off the roads by stadia measures (Chap. XII) or in very heavily wooded country by chaining (Art. 99) and pacing (Art. 95). The underlying principles of this method of topography are, first, a knowledge of and experience in various methods of surveying, and a topographic instinct or ability to appreciate topographic forms, which is acquired only after long practice; and, second, a constant realization of the relation of scale to the amount of control required and methods of survey pursued; no more instrumental work being done than is actually re- quired to properly control the sketching, and no more accu- rate method being employed than is necessary to plotting within reasonable limits of error. Thus, where trigonometric locations (Chap. IX) are sufficiently close together, crude 22 SURVEYING FOR SMALL-SCALE MAPS. odometer traverses (Art. 98) or even paced traverses (Art. 95) can be run with sufficient accuracy to tie between these with inappreciable errors. Where trigonometric locations are more distantly situated, the spaces between them must be cut up by more accurate traverses, as those with stadia (Chap. XII) or chain (Art. 99), these again being gridironed by less accu- rate odometer or paced traverses. Again, a primary system of spirit-leveling (Chap. XV) or accurate vertical triangula- tion (Chap. XVII) is employed only for the larger skeleton, these elevations being connected by less accurate vertical- angle lines or flying spirit-levels, and these again by aneroid (Art. 176), each method being employed in turn so that the least elements of control obtained may still be plotted well within a reasonable limit of error in horizontal location of contour line. Finally, speed and economy are obtained by traveling the roads and trails in wheeled vehicles or on horseback, at a rapid gait from instrument station to instrument station ; the slower process of walking being only resorted to where roads and trails are insufficient in number to give adequate control and view of every feature mapped. ii. Organization of Field Survey. The party organiza- tion and the method of distributing the various functions of topographic surveying among the members of the party must necessarily differ with the scale of the map and the character of the region under survey. The work involved in making a topographic or geographic map may comprise four operations: First. The location of the map upon the surface of the earth by means of astronomic observations. Second. The horizontal location of points, which is usually of three grades of accuracy : primary triangulation or trav- erse ; secondary triangulation or traverse ; and tertiary trav- erse and meander for the location of details. Third. The measurement of heights, which usually ac- companies the horizontal location and may be similarly di- ORGANIZATION OF FIELD SURVEY. 2$ vided into three classes, dependent upon their degree of accuracy. Fourth. The sketching of the map. If the area under examination is small or the scale be of topographic magnitude, the first of the foregoing operations may be omitted, when the topographic party will have (i) To determine the horizontal positions of points; (2) To measure the heights of these points; and (3) To sketch in the map details as controlled by the horizontal and vertical loca- tions so procured. Where map-making is executed for geographic or explora- tory purposes and on a small scale in open triangulation coun- try, as that in the arid regions of the West, the skilled force may consist of only the topographer in charge. Where the map scale is increased up to topographic dimensions or the country is hidden from view by timber or because of its lack of relief, the topographer may be assisted by one or more aides whose functions will be variously performed according to the conditions of the country. 12. Surveying Open Country In making a geographic map on scales varying, say, from one-half mile to four miles to the inch in open, rolling, or mountainous country suited to tri- angulation, all sketching and the execution of the plane-table triangulation (Chap. IX) or other control should be done by the topographer in charge. He may be aided by one to three assistants according to the speed with which he is able to work and the difficulties encountered by the assistants in leveling (Chap. XV). It is assumed that the topographer has a fixed area to map, and that within this area he is in posses- sion of the geodetic positions (Chap. XXIX) of two or more prominent points and the altitude of at least one. With the positions of these points platted on his plane- table sheet (Art. 188) he proceeds, as outlined in Article 54, to make a reconnaissance of the area for the erection of sig- nals and to locate prominent points on summits and in the 24 SURVEYING FOR SMALL-SCALE MAPS. lower or drainage lines of the country by plane-table triangu- lation (Art. 73). Meantime, one assistant may be running lines of spirit-levels (Chap. XV) for the control of the verti- cal element, while one or two assistants are making odometer (Art. 98) or stadia traverses (Chap. XII) of roads or trails for the control of the sketching and the mapping in plan of the roads and streams. This preliminary control executed, the topographer adjusts to his triangulation locations the traverses run by the assistants (Art. Si), and writes upon them in their proper places the elevations determined by leveling or or vertical angulation (Chap. XVII). In Fig. I is shown a typical triangulation control sheet, the directions of the sight lines being indicated so as to show the mode of derivation of the various locations. The stations anfl located intersection points are numbered in order to show the sequence in which they were procured. The traversing executed for the same region is illustrated in Fig. 2, from which it will be seen that merely the plans of the roads with their various bends, stream crossings, and the houses along them were mapped. Hill summits and other prominent ob- jects to one side or other of the traversed route were inter- sected (Art. 84) in order to give additional locations and to facilitate the adjustment of the traverse to the triangulation. The closure errors of the various traversed circuits are shown, and an inspection of these makes it clear that in every case the errors in traverse work are so small as not to affect the quality of the control, because the adjustment of the traverses by means of points on them which are located by the plane- table triangulation will distribute the errors in .the various road tangents in such manner as to make them imperceptibly small on the resulting map. The product of such adjustment is shown on Fig. 3, which is the base on which the topog- rapher begins his sketching. On this sketch sheet are the locations obtained by him in the execution of his plane-table triangulation, the traverses as adjusted to this control, and SURVEYING OPEN COUNTRY. xxxfx^' 3&3&EL-, / /'' /Sampson \ / *>rV 1 )\ ;> x \ X\/ i \ \ S \ X V'' i#'Cath.Chy,rch\ \ ffChitruujf \ v v v ^'' "- v ^ ^'f i \ \ X \ \ x "i. \ ,' \ ^X'' VV N' / f/^ \ Ch. i/'' ' /~~~~' ~// ~-^- ^J // j -Bownd ro^d^><\ | XN \ ^f^^Wxxx'xvu / /" ~j Wooded^l^^ FIG. i. DIAGRAM OF PLAN*.- i ABLE IRIANGLLATION. FROSTBURG, MD. Scale 26 SURVEYING FOR SMALL-SCALE MAPS. X FIG. 2. ROADS, HOUSES, AND LOCATIONS RESULTING FROM TRAVERSE. FROSTBURG, MD. Scale ^. TOPOGRAPHIC CONTROL. .2005 '1 2100 FIG. 3. ADJUSTED SKETCH SHEET. FROSTBURG, MD. Scale 28 SURVEYING FOR SMALL-SCALE MAPS. elevations from vertical angulation or spirit-leveling written in their appropriate places. If the work be the making of a topographic map on scales larger than those above described, and the country be still of the same topographic character namely, open, with salient summits, a system of control similar to the above must in like manner first be executed by the development of plane-table triangulation and the running of control, traverse, and level lines. But the after- work of sketching the map will be con- ducted in a different manner than for the smaller scales, because of the greater detail required, the shorter distances to be traveled by the topographer in performing the work, and his consequent nearness to the various features which he is to map. 13. Sketching Open Country. Having the control platted on the sketch sheet as shown in Fig. 3, and where roads are sufficiently abundant to cut up the map with trav- erses so near one to the other that the topographer may not have to sketch more than one-half to one inch to either side of his position, the sketching of the topography proceeds as follows : Taking the sketch sheet on a board in his lap, the topog- rapher for cheapness and convenience, because of the speed, drives over every road. Where these are not sufficiently near one to the other he walks in between them, pacing distance (Art. 95), and getting direction by sighting fixed objects, while he sketches the plan of the contour lines (Art. 193) as far as he can safely see them to either side of his path. This operation is performed by setting out from such fixed points as a road junction, a located house, or a stream crossing, the position of which is platted on his map and the elevation of which is known. Adjusting the index of his aneroid at the known elevation (Art. 176), he drives along, keeping the platted direction of the road parallel to its position on the ground and marking on the map the positions at which the SKETCHING OPEN COUNTRY. 2Q various contours are crossed by his route. Thus, if his contour Interval be twenty feet, at every change of twenty feet as indi- cated by the barometer he stops, and, knowing his position on the map either by reference to bends in the roads, houses, or by having counted the revolutions of his wheel from a known point, he glances along the trend of the slopes to one side or the other, following by eye the level line of his con- tour, and this he sketches in horizontal plan upon the map. At first he may be aided in this by a hand-level (Art. 156), but as he acquires skill with practice he is able to estimate the position and direction of the contour line to either side with great accuracy, and finally to interpolate other contours above and below that on which he is placed with such preci- sion as not to affect the quality of the resulting map by a con- tour interval. The aneroid being an unreliable instrument, he must not drive more than two or three miles without checking it at a well-determined elevation. This he is usually able to do at houses, or hill-summits, or other points the positions of which have been determined by his prior control. If he is not able so to check his aneroid, he hastily sets up his plane-table, reads with the telescopic alidade a few vertical angles (Art. 162) to hilltops or houses in sight and the elevations of which are known, and, with these angles and the distances which he can measure from his position to the points sighted as shown on the adjusted control, he is at once able to compute the elevation of his position (Art. 161) within two or three feet and thus check his aneroid. At the same time he is in simi- lar manner able frequently to throw out other elevations by sighting from the position thus determined to houses or sum- mits near by which may have been located by the traverse (Art. 84), and the heights of which he determines now from his angulation. The topographer thus sketches the whole area assigned him, not only mapping the contours, drainage, political boundaries, and other topographic features, but also 30 SURVEYING FOR SMALL-SCALE MAPS. checking the positions of houses and summits and the direc- tions and bends of roads and streams as located by the trav- erseman (Fig. 4). Where the hills are more prominent and the slopes bolder and steeper, the topqgrapher sketches these from his various view points by interpolating contours between the located con- trol points. With the sketch-board in his lap or on the tripod and approximately oriented, looking about in various direc- tions at hill-summits, houses on slopes, spurs, etc., which may with their elevations be platted on his map, he first sketches in plan the streams and drainage lines as well as the directions of slopes. Then he sketches the position of con- tour lines about such control points as summits, salients, and his own position. With these as guides he is then unable to go astray in the interpolation of the intermediate contours which complete the map of the area immediately about him. The sketching of the topography for large-scale maps dif- fers rather in degree than in kind from the above. The large- scale map covering as it does a relatively small area, the to- pographer is not under the necessity of traveling with such speed as to necessitate his using wheeled conveyance. At the same time the largeness of the scale places the roads at much greater distances apart on the map and necessitates his traveling between these to greater extent. It will thus be seen that the scale and the ability to travel over the coun- try work harmoniously one with the other. For the smaller geographic scales the roads are so close together on the map as to afford sufficient control and sufficient number of viewing points for sketching the topography of the average open country, whereas on large-scale topographic maps these roads are in plan much farther apart, but the time consumed in walking between them is a comparatively small item be- cause of the decrease in the distances to be covered. In sketching a large-scale map the topographer will have about the same relative amount of primary control as above FIG. 4. COMPLETED TOPOGRAPHIC MAP, FROSTBURG, MD. Scale i to 62,500. Contour interval 20 ft. SURVEYING WOODLAND. 33 indicated. Starting out with some known point and on foot, accompanied by one or more stadiamen, he sets up and ori- ents his plane-table, and, having considerable areas to fill in on his map between his present position and his next recog- nizable natural feature, he posts the stadiamen at convenient changes in the slope of the country or at houses or trees or bends in the streams, and drawing direction lines and reading distances by stadia to these positions he obtains additional locations to control the sketching (Art. 101), which is exe- cuted as above described. In the progress of this work he not only determines horizontal positions by sighting to the rods held by his stadiamen, but also the vertical positions of the same points (Art. 102). For very large-scale maps and under some conditions the work may be expedited by permitting the assistants to sketch the contours immediately adjacent to their stadia stations, and these sketch notes must, be given the topographer at frequent intervals to be trans- ferred to his map. In this manner one topographer may handle from one to three stadiamen, providing he uses judg- ment in the selection of his and their positions. For smaller- scale topographic mapping the work may be expedited by the stadiamen riding on horseback from one position to another, or even by the topographer himself using this means to get about. 14. Surveying Woodland or Plains. The securing of control in densely wooded country, as that of the Adirondack region or the woods of Minnesota, Michigan, and of Washing- ton ; or the securing of control for very flat plains country, as that of the Dakotas and Nebraska, is accomplished by dif- ferent means than must be adopted in open triangulation country. Be the scale of the resulting map large or small, the primary control may be obtained most economically either by triangulation or by traverse methods. If the country is wooded and rolling, it may be more economical to clear the higher summits or to erect high viewing scaffolds upon them, 34 SURVEYING FOR SMALL-SCALE MAPS. from which to conduct a skeleton plane-table triangulation. Intermediate positions may be obtained by placing signal- flags in tall trees and locating these by .intersection or using them to obtain other positions by resection. With prac- tice the topographer will thus triangulate the most forbid- ding woods country more expeditiously than it could otherwise be controlled, by taking advantage of every out- look, as a rock on a hillside, a lake, a small clearing for a farm, or by clearing or signaling the commanding summits. He will thus occupy only such points as those just described, locating by intersection (Art. 73) from them the flags on the more wooded and forbidding ones which may be the more commanding positions, and using the latter again for carrying on his work by resection (Art. 74). In level plains or in wooded plateau land the control may of necessity be executed only by traverse methods. In such case where the scale is of geographic dimensions one or two astronomic stations should be determined (Part VI), or for larger scales it may suffice to assume the initial position. From this primary traverse lines should be run (Art. 226) at con- siderable distance one from the other, depending upon the scale. For the one-mile scale a nearness of fifteen to twenty miles will suffice. For the two-mile scale these primary traverse lines may be double the distance apart ; for a large topographic scale a relatively smaller distance, depending upon the map scale ; for all scales a distance corresponding to fifteen to twenty-five inches on the map according to the topography. Between these primary traverse lines others of less accu- racy should be run as a secondary control. On these dis- tances should be measured by wheel (Art. 98) when the vehicle can be driven in straight tangents, by stadia (Art. 101) in open irregular country, or by chain (Art. 99) or tape (Art. 97) through underbrush or dense wood. Elevations will be secured in the woods by vertical angulation to stadia (Art. 102) or by spirit-leveling (Chap. XV); in the open SKETCHING PLAINS LAND 35 or plains by vertical angulation to fixed objects, as the eaves or chimneys or window-sills of houses, the platforms of windmills, etc. (Art. 160), or to the stadia-rod, as well as by spirit-leveling. The secondary traverse is usually executed by the party chief while his assistants are engaged in tertiary traverse for the filling in of topographic details or the procur- ing of vertical control. The primary and secondary control having been procured as above, this should be platted on sketch sheets of the cus- tomary large plane-table size for open country (Art. 68), and preferably in small detached pieces placed on small boards of about six inches square, where the latter have to be carried through woods and underbrush. These control sheets will be not dissimilar to those described in Article 13, excepting that they will lack the location of points procured by angula- tion and will consist almost wholly of platted traverse lines. In order that the topographer when sketching may identify these lines on the ground, trees must be frequently blazed in woods when the traverses are being run and station num- bers or elevations be written on the blazings. 15. Sketching Woodland or Plains. With the control platted on the sketch sheet as just described, the topographer in plains work starts out and drives over the country much as described in Article 1 3 , traveling over all the traversed roads and checking his aneroid by setting in at known elevations or by angulation to and from buildings and similar objects. As the country is relatively flat, the contour lines are at considerable distances apart in plan, and consequently a very small differ- ence in vertical elevation makes a considerable change in the horizontal location of a contour. Therefore the determina- tion of the vertical element should be of greater relative accu- racy, that the resulting map may be correct. In the woods the sketching is executed in an entirely dif- ferent manner. Little skill- is required in the depiction of the topography, as it is impossible to see the country and 30 SURVEYING FOR SMALL-SCALE MAPS. therefore to sketch it in the ordinary sense. The topographer is limited to sketching that which is directly under foot in other words, to mere contour crossings and in order that these may be connected the traverses must be much nearer together, and not only the topographer but his more skillful assistants are all engaged in sketching and traversing at the same time. Starting out with the primary and secondary control as obtained in the last article, the topographer travels over those traversed routes which have been blazed and sketches the contours upon these while his assistants run addi- tional traverses over controlling routes, as along stream beds and ridge crests, and so close together as to completely command all the country under foot. These traverses will be of crude quality, directions being obtained by sight alidade (Art. 62) and traverse-table (Art. 61), and distances by pacing (Art. 95) or by dragging a light linen tape (Art. 97). Each day the topographer must adjust to his control sheet the traverses with accompanying sketching as executed by his assistants. With such a skeleton of topography on highest and lowest lines, i.e., contour crossings of streams and ridges, he can readily interpolate contours for most of the inter- mediate spaces and, following after his assistants, fill in those places which are not fully mapped. In the execution of a survey under such conditions the topographer's work is largely supervisory and consists chiefly in the management of the work of his assistants, the adjust- ment of their sketching, and its inspection as he fills in the details omitted by them. There is little room for them to go astray, because they only sketch that which they walk over. The topographer should invariably reserve for himself the higher ridges, the ponds, and the more open places in order that quality and speed may be obtained by the utilization of his skill in that work which gives some opportunity for sketch- ing at a distance from the traveled route. 16. Control from Public Land Lines In the western CONTROL FROM PUBLIC LAND LINES. 37 United States where the public land surveys have been exe- cuted in recent years and with sufficient accuracy to furnish horizontal control, this may come almost wholly from the township and section plats filed in the United States Land Office. The topographer takes into the field paper on which sections and quarter sections are ruled and numbered. On these he writes at the proper section corners the elevations as determined from the primary spirit-levels (Chap. XV). He also indicates on the northern and western margins of each township the offsets and fractional sections as shown on the published land plats (Fig. 5). At some period during the progress of field-work the topographer adjusts the land-line work to positions determined either by primary triangulation (Chap. XXV) or traverse (Chap. XXIII), supplementing this by additional control where necessary. 17. Sketching over Public Land Lines. With the con- trol sheet prepared as described in the last article, the topog- rapher proceeds to drive over the section lines on which roads have been opened. The control sheet is attached to a plane- table board. Starting from a known section corner, he drives in a straight line down one of the section lines to other sec- tion corners, determining his position by counting revolutions of the wheel (Art. 98) and sketching contour crossings as he progresses. Starting out with a known elevation from spirit-levels (Chap. XV), he determines other elevations as he proceeds by setting up his plane-table at a section corner or opposite a house which he can locate by odometer distance, and reads vertical angles from the point of known elevation to houses, windmills, or other objects in sight (Art. 162), drawing direc- tion lines to them as an aid in their identification (Art. 84). Driving on until he comes to one of these objects and being thus able to locate it on his plane-table, he measures the dis- tance from it to the point from which the angle was taken and at once computes his elevation (Art. 161). Or, setting up his SURVEYING FOR SMALL-SCALE MAPS. ^5 -10 ,,- Hjf- FIG. 5. LAND SURVEY CONTROL FOR TOPOGRAPHIC SKETCHING. NORTH DAKOTA. Original scale 2 inches to I mile. SKETCHING OVER PUBLIC LAND LINES. 39 plane-table board from some known position, as determined from his section lines and odometer, he reads vertical angles to houses or windmills, the heights of which have already been determined by vertical angulation, and thus brings down to his present position an elevation by means of the angle read and distance measured on his board. In conducting vertical angulation in this manner care must be taken to sight at some well-defined point, as a platform or top of a windmill, the gable or top of a house or top of door-sill, etc. As the sketching is a comparatively simple process under these conditions because of the flatness of the terrane, his work may be expedited by permitting his more skillful assist- ants to aid in sketching. In order that he may control their work he drives and sketches over those roads which parallel the roads of his assistants on either side, and in such manner obtains a clear insight into the work performed by them. The assistants may determine elevations either by vertical angulation, as does the party chief, or by aneroid frequently checked, say at distances not exceeding tw'o miles between the better elevations obtained by the topographer. On such a sketch sheet as it comes from the plane-table board (Fig. 6) the roads have been clearly marked over the section lines and additional diagonal roads have been traversed or sketched directly on the plane-table board, controlled by section cor- ners, the outlines of lakes having been obtained by stadia (Art. 101). Where the topographic map is made at the same time as the subdivision of the public lands, as was the case in the Indian Territory surveys of the United States Geological Survey, the cost of executing the topographic survey scarcely exceeds the cost necessarily involved in making the land sub- division or cadastral survey. The only additional cost in the execution of the topographic survey is that for leveling. Fig. 33 is an example of the cadastral map resulting from such a survey of the public lands. The topographic map of 40 SURVEYING FOR SMALL-SCALE MAPS. the same region corresponds in appearance almost identically with that shown in Fig. 6, being shorn of the various sym- bols used on the Land Survey Maps. 18. Cost of Topographic Surveys As indicated in Tables I, II, and III, the cost of topographic surveying varies widely with the character of the country, the scale of the map, and the contour interval. Such topographic surveys as are executed by the United States Geological Survey range in cost for maps of a scale of one mile to the inch and 2O-foot contour interval, similar to those described for open country in Articles 12 and 13, from $10.00 to $20.00 per square mile. Such as are described in Articles 14 and 15, for plains or woodland, range in price from $8.00 to $12.00 per square mile for the former to between $15.00 and $30.00 for the latter. The highest-priced work of this kind which can be executed being the woodland survey, and the cheapest country to map topographically being the open plain. Land-survey country, as that instanced in Article 16, which is a survey of a rJortion of North Dakota, ranges in cost from $5.00 to $8.00 per square mile, where the topographic map is made on a scale of two miles to one inch and in 2O-foot con- tours. For the same scale and in mountainous country, as that of the South and West, the cost is from $8.00 to $12.00 per square mile. If any endeavor is made to do work for other purposes than the procurement of a topographic map, as for che deter- mination of land lines or the staking out of canals or railroads, the cost of the survey is at once greatly enhanced. It is this which has added so greatly to the relative cost as shown in the tables cited of some private topographic surveys as well as of the cadastral surveys. 19. Art of Topographic Sketching Mr. A. M. Well- ington aptly said of topographic surveying that " the sketch- ing of the form of the terrane by eye is truly an art as distinguished from a science, which latter, however difficult it THE ART OF TOPOGRAPHIC SKETCHING. 43 may be, is always susceptible to rigorous and exact analysis. An art, on the other hand, is something which cannot be taught by definite, fixed rules which must be exactly fol- lowed, though instruction may be given in its general prin- ciples." In representing the heights and slopes of a given piece of country by contour lines, every case presents some peculiari- ties which must be met, as they are presented, by the topog- rapher's own resources. No hard-and-fast limit of minute- ness of detail can be previously fixed. The scale chosen for the topographic map limits this to a certain extent, but its exact limits must be set by the topographer's own experience and good judgment, that he may discriminate between impor- tant and trifling features ; those which are usual and common to the region being mapped, and those which are accidental or uncommon, and which should therefore be accentuated. Above all, the topographer must exhibit an alertness to dis- tinguish as to what amount of detail should be omitted and that which should be included. Hesitancy in this is the chief source of slow progress. Valuable time may be wasted in the representation of features which may be lost on the scale of the work and which are common in all localities to the topographic forms being sketched ; while features characteristic of such special topographic forms as those produced by erup- tion, erosion, or abrasion, or those indicative of the structure of the region and which give distinctive character to its topog- raphy, may be lost sight of or be covered up in the map by too careful attention to minute details. The characteristic features of a terrane are best observed from a point nearly on the same level ; and as between sketching features from above or below for a reasonable range, sketching from below is the better, as features viewed from any considerable height above are apt to appear dwarfed and much detail of undulation of the surface lost sight of. Yet, as a precise representation of the land requires sketch- 44 SURVEYING fOR SMALL-SCALE MAPS. ing its forms from numerous positions at intervals not far apart, the necessity will rarely arise of observing surface forms from points of observation much above or below the surface represented, excepting in case of very small scale geographic or exploratory surveys. 20. Optical Illusions in Sketching Topography In sketching topographic forms by eye there are a number of optical illusions to which it is well to call attention, though the effect of these can be entirely overlooked in the sketching of detailed topography such as would be mapped on scales less than one mile to the inch. But for the sketching of topographic maps on smaller scales, where the eye has to be more depended upon, these illusions become more important. Most of these have been well classified by Mr. A. M. Welling- ton in his admirable work on railway location, and they are here summarized, with variations, from that work. Among the more serious of such illusions are the following: 1. The eye foreshortens the distance in an air line and materially exaggerates the comparative length of a lateral off- set so as to greatly exaggerate the loss of distance from any deflection. 2. The eye exaggerates the sharpness of projecting points and spurs, and accordingly exaggerates the angles. 3. In looking, however, at smooth or gentle slopes from a distance, the tendency of the eye is to decrease the angle so that in such country as the rolling plains of the West slopes look much gentler, the inclinations much less, than they are in fact. 4. In this connection the eye is liable to make slopes looked at from a distance appear steeper and higher than they are in fact, when they are compared with known slopes and elevations of lesser dimensions near by. 5. Again, the unaccustomed eye, which mentally meas- ures all dimensions by referring them to those with which it is acquainted, is apt to make a divide or pass appear lower OPTICAL ILLUSIONS IN SKETCHING TOPOGRAPHY. 45 than a nearer divide or pass to which it is referred in one sweep of the vision, whereas it may be higher (Fig. 7). FIG. 7. OPTICAL ILLUSION AS TO RELATIVE HEIGHTS OF DIVIDES. A is nearer and lower than B. 6. The eye invariably exaggerates the steepness of the slopes of mountains, these appearing to have inclinations of from 60 degrees to almost vertical, whereas in fact the steepest slopes are rarely as great as 45 degrees. 7. The eye trained to estimate slopes and distances in regions of large topographic features that is, regions of ex- treme relief or differences of elevation will be at a disadvan- tage in making similar estimates in a country in which the differences of elevation are small. The tendency of one accustomed to estimating the topographic forms in the Rocky Mountains, where differences of elevation and distances visible to one sweep of the eye are great, will be to overestimate heights and distances in the less rugged country of the Eastern States, where great detail in topography exists, and thus de- ceives the eye into an exaggerated notion of the amount of the relief. 8. In viewing the terrane with an idea of estimating its roughness as affording a possible route for railways, canals, or similar works, a rugged mountain gorge with occasional pre- cipitous narrows, separated by river flats, may appear much more difficult and much rougher than it is in fact. This is especially so as compared with a gently undulating or rolling 46 SURVEYING FOR SMALL-SCALE MAPS. country, which, when viewed from a distance, appears to be comparatively level, while a nearer view will show it to be full of elevations or depressions which will render construction most expensive, because of the rapid and numerous succession of large cuts and fills. The effect on the eye and the mind is to exaggerate the ruggedness of a country which is difficult to travel because of such impediments as broken stone, fallen timber, creeks, and swamps, whereas a region where travel is easy and free, as in open rolling plains country or where good roads abound, is often estimated to be much simpler and more level topo- graphically than is the other region. CHAPTER III. SURVEYING FOR DETAILED OR SPECIAL MAPS. 21. Topography for Railway Location. Some of the worst errors in engineering location originate in reconnais- sance, for the reason that the average reconnaissance sur- veys are not of areas, but of routes or lines, and there is great danger of serious error in the selection of the line to be sur- veyed. It may, accordingly, be stated that a railway recon- naissance should not be of a line, but of an area sufficiently wide on each side of an air line between the fixed termini to include the most circuitous routes connecting these. The results of such a survey should be embodied in a topographic map of greater or less detail, according to the nature and ex- tent of the country. If the reconnaissance be of a great rail- road, such as some of the Pacific roads, built through hun- dreds of miles of unknown country the resulting map should be on a small scale, perhaps 2 to 4 miles to the inch, and with contour intervals varying from 20 to 100 or 200 feet, according to the differences of elevation encountered and the probable positions of several locations. With such maps as those of the U. S. Geological Survey, the number of possible routes may be reduced to two or three, and a more detailed topographic survey should then be made of these on which to plan the final location. As ordinarily practiced, topographic surveys for railways are made by the older methods, with transit and chain or stadia and with spirit-level ; notes of the surveys are kept with accompanying sketches in note-books, and these are reduced to map form in the office. The same results can be much 47 48 SURVEYING FOR DETAILED OR SPECIAL MAPS. more satisfactorily and more rapidly procured by using the plane-table in place of the transit, and the resulting map, being plotted in the field, is a more accurate and available representation of the terrane than can possibly be made from plotting notes in an office. The Germans, who are very thorough in taking topography for railroads, divide the work into three separate surveys of different degrees of accuracy : first, recourse is had to the government topographic maps on a scale of approximately i: 100,000, and on this a preliminary route or routes are laid down : second, a more detailed topographic survey is made in the field on a scale of 1 : 2500 as a maximum or i : 10,000 as a minimum, with contour lines of 15 feet interval. This map is limited in area from a few yards to a few hundred yards in width, according to the nature of the country. Where no previous small-scale topographic survey exists, the base of this more detailed or second survey is a transit (Art. 87) or plane-table (Art. 83) and level (Art. 129) traverse, follow- ing as nearly as possible the approximate route of the pro- posed railway. Bench-marks (Art. 135) are established along this at distances of from 500 to 1000 feet, by which the ane- roid may be checked. With this transit line completed on the proper scale, the topographer goes over the ground and, by means of distances from pacing (Art. 95) or odometer (Art. 98), and elevations by aneroid (Art. 176), constructs a hasty contour map on which are indicated all roads, water- courses, structures, high-water marks of bridges, width and height of existing bridges and culverts ; and all other necessary topographic details as to the position of rock masses, strike and dip of strata, swamps, springs, quarries, etc. On such a map as this, hastily and cheaply made, it is possible to plan the detailed topographic map, limited from a few yards to 100 or 200 yards in width and covering what will practically be the final route of the located line as obtained from the second survey. This final detailed survey. DETAILED TOPOGRAPHIC SURVEYS. 49 from which the paper location is to be taken, should be on a scale of from 1:500 up to I : 1000 and with contours of about 5 feet interval, more or less, according to the nature of the land. There is plotted on the plane-table sheet the transit and level base line previously run for the second survey, and the instruments now used by the topographer are of a more accurate nature, consisting of a plane-table (Arts. 58 and 83) for direction and mapping, two or more stadia rodmen for distances (Art. 102), while elevations are had by vertical angles with the alidade (Art. 59). On this final map are shown much the same topographic details as on the second, but all are more accurately located and the eleva- tions are of a more refined nature. The data furnished by this final map will serve all the purposes of making a last paper location of the line, from which the engineer will in the field possibly deviate according to the appearance of the route traveled as presented to his eye when the location is laid down. Mr. Wellington's location of the Jalapa branch of the Mexican Central Railway (Fig. 8) is an excellent example of a detailed contour topographic map for railway location. This was platted in the field on the scale of I : 1000, or about 83^ feet to i inch. The contour interval was 2 meters, or 6.56 feet. 22. Detailed Topographic Surveys for Railway Loca- tion Prior to making the location, which may be made in part from the notes of preliminary surveys, a narrow belt of topography should be mapped in detail, its width being re- stricted as far as possible, providing the preliminaries have been skillfully conducted or have been preceded by a small- scale topographic map executed with especial care along the possible routes of the location (Art. 21). On the detailed topographic map a paper location may be made, from which full notes of the alignment can be derived, the points of curve and tangent taken off, and a profile of the paper location pre- SURVEYING FOR DETAILED OR SPECIAL MAPS. DETAILED TOPOGRAPHIC SURVEYS. 5 I pared, For the making of the paper location the topography should be as exact and the contour lines should be as accu- rately placed as the scale of the map will permit, in order that a line may be located upon the map and a profile called off from it which shall agree as closely, as possible with the sub- sequent transit location and spirit-level profile. In running the field location from a paper location, the projected profile and not the projected alignment must be run. In making such a map it is neither necessary nor possible to locate every point on each contour, the horizontal and ver- tical locations of the contours being at such distances apart that their projections on the map will be so close together that in connecting them by eye in the field the topographer cannot go astray by an appreciable distance. With a detailed contour map made as described for the location of canals (Art. 23), a grade contour or location line may be drawn which will show where the plane of the roadbed will cut the natural sur- face and from which it will at once be seen whether or not the location is the most favorable the topography will permit. The error into which many have fallen is in assuming too much or too little for the topography as a guide to location. The topographic map fails to show many essentials requisite in making a location, as it gives no evidence of the materials to be encountered, nor does it convey an adequate idea of the magnitude of the excavations and fills. The topographic map must be supplemented by a careful visual reconnaissance of the line which it covers. Such topography should there- fore be restricted in its width and amount, and no attempt should be made to make a final location from such a map. On the other hand, where a topographic map is not made, and too much reliance is placed on the visual reconnaissance of the country, the greatest errors are at once introduced in encoun- tering a bad system of gradients, in overlooking important towns, or in otherwise selecting inappropriate routes. 52 SURVEYING FOR DETAILED OR SPECIAL MAPS. In planning the location on a detailed topographic map, the engineer should begin at a summit or similar fixed point, assuming or taking from a guide-map an initial elevation. Then with a pair of dividers he should step off such distances that these will correspond to the grade chosen and their termini end on the map above or below such contours as will give the proper differences in elevation to produce such grades. By this means a grade contour can be sketched in on the map and then connected by tangent lines. The latter must, in turn, be connected by throwing in curves the radii of which shall be as large as possible, care being taken that the grades on these shall be properly compensated. With such a paper location it is then possible, by means of scale and protractor, to take off the directions and distances in a note-book, when, with these as a guide, the located line may be run on the ground and changed or modified in the field as the visual observation of the engineer may suggest. Speed in mapping railway topography varies greatly with the scale selected and the character of the land mapped. One party working in flat, desert country in Utah ran 20 linear miles in a day of 9 hours, including running of spirit- levels. The same party working later in mountainous country in Washington averaged during a long period of time less than \ mile a day, in one instance working six weeks on a location through i miles of canyon. A party working on railway location and mapping topography on the plains of Kansas made an average speed of 2.1 miles a day at an average cost, including all expenses, of $i 1.03 per linear mile. The Utah work averaged about $2.50 per mile, and the cost of much of the Washington work exceeded $100.00 per linear mile. 23. Topographic Survey for Canal Location. Surveys for canal lines or lines of conduits, etc. , are best made by having the leveling (Chap. XV) precede the plane-table or transit work. The level will then run out a grade contour having the requisite fall per mile, and the transit (Art. 87) or plane-table TOPOGRAPHIC SURVEY FOR CANAL LOCATION. 53 (Art. 83) with chain measurements (Art. 99) will follow the level, locating this grade contour. Topography may be taken on either side by stadia (Art. 101) and plane-table so that in the final location of the canal the preliminary grade contour may be shifted to suit the sketched topography, much as the line of a railway location would be shifted from similar data (Art. 22). An interesting example of a detailed topographic survey for the final location of an irrigation canal is that made by Mr. J. B. Lippincott of the Santa Ana Canal, through a rocky can- yon. This location was made upon a carefully prepared topographic map drawn on a scale of 50 feet to I inch, with contour interval of 5 feet. The maps were plotted from cross- section notes based on two connected and approximately par- allel preliminary lines, the contour curves being sketched in the field to indicate intervening irregularities of surface. The preliminary controlling lines were carefully run with transit and chain, were frequently connected, and had a vertical in- terval of 70 feet. The space between and for thirty feet above the upper line, or for a total of 100 feet vertically, was carefully contoured. From the map thus prepared a more accurate cross-sectioning was made, and from these notes a new contour map of the ground was prepared on a scale of 30 feet to an inch over the more difficult portions of the line, after a preliminary location had been selected on the first con- tour map. Fig. 9 gives a plat of one of the roughest por- tions of this line, and on it are shown in small circles the various points located on each contour. The plane-table was used and was set up generally as shown by the station num- bers and triangles on the preliminary and plotted traverses, and directions were measured to stadia-rods held at various points on the lo-foot contour lines (Art. 101). The posi- tions of the contour lines at these points were therefore plotted, and the corresponding elevations were immediately connected as contour lines on the plane-table sheet. In this 54 SURVEYING FOR DETAILED OR SPECIAL MAPS. TOPOGRAPHIC SURVEY FOR CANAL LOCATION. 5$ way enough points were located on each contour to sufficiently control it, and the immediate 2-foot contour lines were in- terpolated by eye estimation in the field. In doing this work three various methods were tried : (i) f by locating the contour lines with slope-board and rod ; (2), by locating the contours at right angles to the stations occu- pied by a levelman using a hand-level (Art. 156); and (3), by means of the plane-table and stadia (Art. 101). Mr. Lip- pincott says that as a result of these tests there is no question between the quality of the three classes of work ; that without plane-table the work had to be plotted up in office and located points connected by estimation or from rough sketches; with the plane-table the same points were plotted immediately, in the field, and the connections between these made with the terrane in view, and that the resulting map by plane-table much more accurately expressed the slopes of the land than did the maps made by the other methods. The speed by the various methods was about the same. The party consisted generally of five persons, including the topographer, levelman, and rodman, and the speed was from 2500 to 4000 linear feet per day, actually locating four lO-foot contours and sketching in five or six- more, a total of 100 feet vertical interval, and interpolating the 2-foot contours. Where side canyons and ravines were passed the slope-board was found to be entirely inadequate and helpless, while by the use of levelman and hand-level without the plane-table, and with taped traverse lines, the conditions were improved, but the work was of the crudest character so far as its topographic expression was concerned. An example of a preliminary topographic survey of a canal line, made under the author with plane-table and on a small scale to determine the possibility of bringing the water from a stream or reservoir to certain lands for purposes of irrigation, is illustrated in Fig. 10. The scale of this illus- tration is denoted by the land section lines, each section SURVEYING FOR DETAILED OR SPECIAL MAPS. \ SURVEYS FOR RESERVOIRS. 57 being a mile on a side. The original survey was made on a scale of 3000 feet to the inch, with a contour interval of 4 feet. The plane-table was accompanied by a spirit-level to determine grade, in order that the canal line might be given the required fall per mile. 24. Surveys for Reservoirs. In making surveys of reservoirs for storage of water for city water-supply or for irrigation and similar purposes, the scale and contour interval depend necessarily on the dimensions of the reservoir. The former should be from 400 to 1000 feet to the inch, and the latter from 2 to 5 feet vertical interval. Special surveys should be made of possible sites for dams and waste-weirs on larger scales and with a contour interval of I or 2 feet, and several cross-sections of the dam site should be run and the topography taken in detail for a sufficient distance above and below the center line. If sufficient borings or trial-pits are sunk, a contour map of the foundation material may be constructed. Perhaps the most satisfactory manner of making surveys of reservoir sites is instanced in the following practical ex- ample of one made by the author. A standard or base transit (Art. 87) and level (Art. 129) line is first run across the dam site, carrying the same a little above the highest possible flow line of the reservoir. From this should start a main transit and level line which should follow up the lowest or drainage line of the reservoir basin (Fig. 11, A, D t G), and this should be extended until it reaches an elevation corresponding to that of the highest probable flow line of the dam. Bench-marks (Art. 135) should be left as this line progresses, and stadia distances measured (Art. 102), and level elevations taken to points within the range of the level-tele- scope, as at A, B, etc. Based on this main transit and level line, a plane-table and stadia line (Art. 101), accompanied by spirit-leveling, should be run from the highest flow line of the dam cross-section around the corresponding contour line ffini - 58 SURVEYING FOR DETAILED OR SPECIAL MAPS. on one side of the reservoir, H, /, /, etc., and if the land be clear, stadia and level sights may be' taken to the other contour lines within the range of the instrument, including sights on lines of equal elevation on the opposite side of the reservoir if the latter be small. If large, however, a number of flags may be located on the opposite side by triangulation (Art. 73) or by stadia observations, and cross-section lines be run to these, from which the data for constructing a contour topographic map can be obtained as at / and L. Another example of a reservoir survey is illustrated in Fig. 12, which is a portion of the map of the Jerome Park reservoir site in the city of New York, and was platted on a scale of 400 feet to the inch with a contour interval of 10 feet. From such a map it is possible to compute the contents of a reservoir for each additional five feet of elevation, and on it land lines and property lines are shown in such manner as to indicate the damage which will be done by submergence. 25. Survey of Dam Site. A typical illustration of the topographic map resulting from the survey of a site for a dam for closing a storage reservoir is shown in Fig. 13. This survey was executed with a plane-table (Art. 73), chain (Art. 99), and spirit-level (Art. 129) on a field scale of 400 feet to I inch, with a contour interval of 2 feet. The result of such a topographic survey is to indicate clearly the best alignment for the dam, providing the borings which must necessarily follow the selection of such alignment prove its feasibility. An example of a topographic survey executed for selec- tion of a site for a weir or diversion dam in a river is that illustrated in PI. III. This shows the topography of the flood- bed of the Snake River between its high bluff banks, as well as the contouring of the bed of the river as shown by soundings. On this is indicated the best alignment for the diversion weir as well as for the canal head and headworks. The field work of the survey was executed with transit.