SURVEYING THEORY AND PRACTICE

SURVEYING THEORY AND PRACTICE

BY

RAYMOND E. DAVIS, M.S., C.E., D. ENG. Professor of Civil Engineering, University of California

AND

FRANCIS S. FOOTE, E.M. Professor of Railroad Engineering, University of California

THIRD EDITION THIRTEENTH IMPRESSION

McGRAW-HILL BOOK COMPANY. INc. NEW YORK ANU LONDON

1940

CoPYRIGHT, 1928,1934, 1940,BY THE McGRAW-HILL BooK CoMPANY, INc.

PRINTED IN THE UNITED STATES OF .AMERICA

AU rights reserved. This book, or parts thereof, may not be reproduced in any form without permission of

the publishers.

PREFACE TO THE THIRD EDITION

The widespread distribution of the earlier editions of this book has brought from practicing engineers and teachers of surveying many valuable suggestions for improvement, with regard to both arrangement and subject matter. In order to take full advantage of these suggestions and in order to introduce new material, much of which has not been published in textbook form, the book has been rewritten. Many new drawings and photographs have been added, and most of the old figures have been redrawn. To meet the needs of students, portions of the text have been considerably condensed, detailed explanations and descriptions of alternate methods have been set in small type, and the use of examples has been made more extensive. In this manner, there has been preserved the quality of thoroughness-one of the distinguishing features of the earlier editions which made the book especially useful to practicing engineers and surveyors-while at the same time the book has been made more suitable as a text for classes in surveying.

Chapters have been rearranged in the interest of a more orderly presentation of the subject, and chapters have been added on Sur-veying Instruments and on Construction Surveys. Chapters on the Plane Table, Route Surveying, and Topographic Surveying have been extensively revised to include methods and practices that have come into general use. New types of surveying instruments are described. Account is taken of the growing use of state plane coordinate systems. There are given additional problems and examples of route, land, topographic, and hydrographic maps.

On a variety of surveys, even those of moderate extent, the advan-tages of wealth of detail, speed, accuracy, and low cost are over-whelmingly in favor of aerial photogrammetric methods, in con-junction with ground control. It would seem essential that every engineer and surveyor have a general knowledge of these methods and understand the conditions under which they may be advan-tageously employed. They have already been used on many surveys, and for certain types of surveys it seems safe to assume that the time is not far distant when they will entirely replace the more laborious ground methods. For these reasons, attention is especially directed to a new chapter on Photogrammetric Surveying written by Captain

v

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Vl PREFACE TO THE THIRD EDITION

B. B. Talley, Corps of Engineers, U. S. Army, whose extensive contributions to, and intimate knowledge of, practice in this field make him an outstanding authority.

Additional material for illustrations and tables has been taken or adapted from publications of the U. S. Coast and Geodetic Survey, the U.S. Geological Survey, and the General Land Office; and certain material has been furnished direct by these Federal agencies and by the Army Air Corps of the U.S. War Department. The California Division of Highways furnished the drawing from which a typical plan-profile sheet for route surveys was reproduced. The authors are indebted for additional photographs of equipment to the Abrams Aerial Survey Corporation, Lansing; Wm. Ainsworth and Sons, Denver; Fairchild Aerial Can;tera Corporation, Los Angeles; Fairchild Aerial Surveys, Los Angeles; Keuffel and Esser Company, New York; A. Lietz Company, San Francisco; and H. Wild, Heerbrugg, Switzerland. Grateful acknowledgment is due to the many survey-ing teachers from whom suggestions have been received and to the authors' colleagues, particularly to Professors Harmer E. Davis, H. D. Eberhart, S. Einarsson, Bruce Jameyson, and C. T. Wiskocil, all of the University of California.

The authors desire to express appreciation of the valuable services rendered by J. W. Kelly, Lecturer in Civil Engineering, University of California, in the preparation and editing of the manuscript and in the reading of the proof.

Ma11, 1940.

R. E. D. F. S. F.

PREFACE TO THE FIRST EDITION

This book is intended primarily as a text for use in surveying classes as ordinarily conducted in engineering schools during the freshman or sophomore year, but it has also been the aim of the authors to produce in a single volume a treatise on the subject of surveying sufficiently comprehensive to be found of value to prac-ticing engineers and surveyors.

To the end that it may be most useful to students, the more elementary phases of the theory and practice of surveying have been treated in considerable detail, and no pains have been spared to produce a book which will meet the needs of the classroom. The advice of teachers of surveying has been sought frequently and has been given freely.

In order that it may be found valuable to engineers and surveyors, the more advanced phases of the subject have been discussed, methods used on extensive surveys unde! a variety of conditions have been described, and the relative advantages of the various methods as affected by field conditions have been considered. Not only have the authors drawn upon their own experience but they have made free use of the works of others. The more specialized portions of the book have been reviewed by authorities in these fields.

The book is divided into three parts: Section 1 is an introduction to the subject, designed to give the

student a general familiarity with the fundamentals involved before proceeding to details, to furnish him with a speaking acquaintance with the rudimentary operations of field and office, and to present the general subject of errors, an understanding of which is so essential to good surveying practice. It is believed that this section will be found of particular value in those classes where field and office prac-tice are given concurrently with the work of the classroom. It may also prove instructive to inexperienced men who are coming in contact with the practice of surveying for the first time.

Section 2, dealing with the elements of surveying, treats in detail the fundamental operations common to all branches of surveying, involving the instruments for and methods of measuring angles, distances, and differences in elevation in the field, and of calculating

Vll

Vlll PREFACE TO THE FIRST EDITION

and plotting these quantities in the office. The material of this section is -~ssentially prerequisite to all surveying practice. It is, so to speak, the framework or skeleton about which any survey takes form. Here special attempt has been made thoroughly to develop principles and to describe the operations involved in sound surveying practice without resorting to statements of details which may best be learned through experience. Where there is more than one method of performing an operation, the aim has been to describe each method and to compare the several methods as to their relative advantages under varying conditions.

Section 3 is concerned with the practice of surveying as extended to entire surveys, including those for establishing boundaries of rural and urb'an lands; for locating railways, highways, and other routes; for the location and development of mining properties; and for topographic and photographic mapping, both terrestrial and aerial. Much of the material has been drawn from private sources, govern-ment publications, and periodicals.

In the preparation of this book, the authors have given careful study as to an arrangement and scope of subject matter which would result in a teachable text for the classroom, and, at the same time, would include additional material of great importance and value to those called upon to plan and carry out actual surveys, but which is ordinarily not given in elementary courses in surveying by reason of the limitation of time. In this study, they are happy to acknowl-edge the material assistance of experienced teachers by expressions of opinion of what ought to be included in a treatise of this kind. In order to render the greatest possible continuity to the book as a whole, all material relating to a given division of the subject has been placed in a single chapter, but those portions which are not normally included in the ordinary course in surveying are indicated either by articles or paragraphs in smaller type than that of the body of the text or are placed near the end of the chapter. Thus, in Chap. VIII, the elementary operations of differential leveling are given, following which precise methods are described, the precision of leveling measurements is considered, and methods of adjusting level circuits are shown. By this arrangement, it is felt that assign-ments for study in the most elementary course may be made to cover readily the desired ground without confusion to the student, even though the material of the course be considerably reduced from that presented in the text.

Experience has demonstrated the desirability of field and office exercises, involving the elementary operations of surveying, to be taken concurrently with the studv of the text. At the close of each

PREFACE TO THE FIRST EDITION IX

chapter dealing with these operations, there is outlined a series of problems which it is believed will be found useful in conducting classes in field and office practice. Many of the minor details of field and office procedure not mentioned in the text are given in these problem statements.

Though a knowledge of errors is so vital to sound surveying prac-tice, many surveyors display an ignorance of errors and their effects upon measurements that is truly lamentable; for this reason, it has seemed desirable that greater emphasis be put upon the subject of errors. To this end, Chap. V is devoted entirely to the considera-tion of errors, with particular reference to accidental errors and the law of probability, and throughout the body of the text, in connection with the various operations of surveying, the causes, kinds, and distribution of errors are discussed.

An understanding of field astronomy makes necessary certain new conceptions which are usually grasped with difficulty by the beginner, and are often not easily imparted by the instructor. It has been the view of the authors that in the classroom the develop-ment of principles is of greater importance than the mere recitation of facts. For these reasons, the subject of field astronomy has been treated at somewhat greater length than is ordinarily the case for a text on surveying, and considerable space has been devoted to describing in simple language the fundamental concepts of the celestial sphere. Thus, Chap. XVII is devoted to developing the principles of astronomy, and Chap. XVIII is devoted to a description of the common methods of determining latitude, longitude, and azimuth, which are applicable to surveys of ordinary precision.

In the chapters on Topographic Surveying, special attention has been given to methods applicable to intermediate- and large-scale mapping, and effort has been made to indicate the dependence of methods upon conditions as regards character of terrain, scale of map, extent of survey, etc.

Terrestrial photographic mapping has long been recognized as a particularly efficient method of portraying the relief of mountainous regions. With the rapid improvement in the instruments and methods employed in aerial surveying, it seems probable that, except where the areas involved are comparatively small, much of the topographic mapping of the future will be accomplished by aerial photography. Chapter XXVII presents the principles of photo-graphic surveying and more especially describes in some detail ttu:1 processes of aerial map making. Much of the material for this chapter has been secured from unpublished notes, and here appears for the first time in textbook form.

X PREFACE TO THE FIRST EDITION

In the preparation of this book, the authors have received sug-gestions, advice, and material from many sources. They are grateful for this assistance, without which this text would have been most incomplete. They especially desire to make the following acknowledgments:

Professor S. Einarsson, Department of Astronomy, University of California, has reviewed the manuscript for Chaps. XVII and XVIII and has made many suggestions which have resulted in sub-stantially strengthening the material on astronomy.

The Surveyor General of the General Land Office has kindly furnished data for tables bearing on the U. S. system of subdividing the public lands described in Chap. XX, and the Manual of I nstruc-tions of the General Land Office has been freely quoted.

The Director of the U.S. Coast and Geodetic Survey has supplied data for Tables IV and V and has furnished photographs from which have been prepared a considerable number of the cuts for Chaps. XXIV, XXV, and XXVIII.

The Director of the U. S. Geological Survey has furnished photo-graphs for numerous halftones for Chaps. XXIII, XXIV, XXV, and XXVII; and C. H. Birdseye, Chief Topographic Engineer, and W. H. Herron, Geographer in Charge of Central Division, both of the U. S. Geological Survey, have rendered very generous help in the preparation of those portions of the manuscript dealing with topographic and photographic mapping.

F. H. Peters, Surveyor General of the Topographical Survey of Canada, has gone to some trouble to supply suitable photographs from which Figs. 526a, 552a, and 552b have been prepared and has rendered valuable assistance in furnishing material on photographic and aerial mapping.

Major J. W. Bagley, Corps of Engineers, U. S. Army, formerly of the U. S. Geological Survey, has reviewed the manuscript for Chap. XXVII, dealing with photographic surveying; he has made extensive contributions of subject matter, and has suggested impor-tant improvements in arrangement.

To John Wiley & Sons, Inc., credit is due for permission to use Table IX, which is from Johnson's "Theory and Practice of Sur-veying," and Table X, which is from Searles and Ives' "Field Engineering."

It is desired to acknowledge the use of photographs of aerial surveying cameras and other apparatus which have been supplied by Brock and Weymouth, Philadelphia, and Fairchild Aerial Surveys, Inc., New York.

PREFACE TO THE FIRST EDITION Xl

Scattered throughout the text are halftones of surveying instru-ments, the photographs having been furnished by various manu-facturers. In this connection it is desired to acknowledge the assistance of W. and L. E. Gurley, Troy, N. Y.; Keuffel and Esser Company, New York; the A. Lietz Company, San Francisco, Calif:~ and C. L. Berger and Sons, Boston, Mass.

May, 1928.

R. E. D. F. S. F. W. H. R.

CONTENTS

PREFACE TO THE THIRD EDITION

PREFACE TO THE FIRST EDITION.

FIELD AND OFFICE PROBLEMS. .

Chapter I. Fundamental Concepts. Surveying-Uses of Surveys-The Earth a Spheroid-Plane Surveying-Geodetic Surveying-Kinds and Operations of Surveying-Definitions-Units of Measurement-Precision of Measurements-Principles Involved-Practice of Surveying -Requisites of a Good Surveyor.

Chapter II. Essential Features of Principal Surveying Instru-ments ........................ . Principal Instruments-The Engineer's Level-The Engi-neer's Transit-Essential Features-Level Tube-Sensitive-ness of Level Tube-Adjustment of Level Tube-Leveling Head-Telescope-Focusing-Objective-Objective Slides-Cross-hairs-Stadia Hairs-Eyepiece-Properties of the Telescope-Relation between Magnifying Power and Sensi-tiveness-Verniers-Clamps and Tangent-screws-Gradienter -Numerical Problems.

PAGE v

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XXV

1

13

Chapter III. Field Work . . . . . . . . . . . . . . . . . . 32 General-Student Field Practice-Study the Problem-Speed -Habit of Correctness-Consistent Accuracy-Relation be-tween Angles and Distances-Precision of Angular Measure-ments-Some Surveying Terms-Signals-Care and Handling of Instruments-Adjustment of Instruments-Field Notes-Notebook-Recording Data-Student Field Notes-Numeri-cal Problems.

REFERENCES.

Chapter IV. Computations . . . . . . . . . . . . . . . . . 47 General-Office Com put a tions-Checking-Significan t Fig-ures-Precision of Computations-Computations for Angles and Distances-Trigonometric Tables-Logarithms vs. Natu-ral Functions-Graphical and Mechanical Methods-Arith-metical Short Cuts-Use of Logarithms-Use of the Slide Rule-Polar Planimeter-Areas with Planimeter-Precision of Planimeter Measurements-Theory of Planimeter-Numer-ical Problems-Office Problem.

xiii

XlV CONTENTS PAGE

Chapter V. Errors . . . . . . . . . . . . . . . . . . . . . 71 General-Sources of Error-Kinds of Error-Systematic and Accidental Errors Compared-Discrepancy-Theory of Probability-Probable Value-Probable Error-Weighted Ob-servations-Adjustment of Weighted Observations-Errors in Computed Quantities-Numerical Problems.

REFERENCES.

Chapter VI. Map Drafting . . . . . . . . . . . . . . . . . 86 The Drawings of Surveying-Maps-Map Projection-Scales-Meridian Arrows-Profiles-Cross-sections-Letter-ing-Titles-Notes and Legends-Conventional Signs-Draw-ing the,Symbols-Colors Used on Maps-Flat Tints-Water Colors and Inks Compared-Drawing Papers-Tracings-Reproduction of Drawings-Blueprints-Vandyke Prints-Blackline Prints-Ozalid Prints-Photostat Process-Photo-offset Process-Duplicate Tracings-Pencils-Inks and Colors -Drawing Instruments-Scales-Protractors-Beam Com-pass-Railroad Curves-Road Pen-Contour Pen-Straight-edge-Proportional Dividers.

REFERENCES.

Chapter VII. Measurement of Distance. GENERAL METHODS.

Distance-Pacing-Stadia-Gradienter-Direct Measurement -Other Methods-Choice of Methods.

CHAINING.

General-Tapes-Chaining Pins-Range Poles-Chaining on Smooth Level Ground- Horizontal Measurements over Uneven or Sloping Ground-Measurements on Slope-Cor-rections for Slope-Errors in Chaining-Correction for Tem-perature-Correction for Tension-Correction for Sag-Elimination of Effect of Sag-Combined Corrections-Pre-cision of Measurements with the Tape-Mistakes in Chaining -Surveys with Tape-Measurement of Angles-Erecting Perpendicular to Line-Irregular Boundary-Obstructed Dis-tances-Numerical Problems-Field Problems.

REFERENCES.

Chapter VIII. Measurement of Difference in Elevation. GENERAL METHODS.

Definitions-Curvature and Refraction-Methods-Baromet-ric Leveling-Indirect Leveling.

DIRECT LEVELING.

General-Instruments-Dumpy Level-Wye Level-Locke Hand Level-Abney Hand Level and Clinometer-Leveling Rods-Self-reading Rods-Target Rods-Targets-Topogra-pher's Rod-Tape Rod-Rod. Levels-Turning Points-Set-ting Up the Engineer's Level-Reading the Rod.

115

146

CONTENTS

ADJUSTMENT OF THE LEVEL.

General-Desired Relations in Dumpy Level-Adjustment of Dumpy Level-Desired Relations in Wye Level-Adjust-ment of Wye Level-Adjustable Objective Slide-Adjustment of the Hand Level-Numerical Problems-Field Problems.

Chapter IX. Differential Leveling . . . . . . . . . . . . . General-Definitions-Procedure in Differential Leveling-Balancing Backsight and Foresight Distances-Differential-level Notes-Mistakes in Leveling-Precise Differential Level-ing-Leveling with Two Sets of Turning Points-Reciprocal Leveling-Errors in Leveling-Precision of Differential Leveling.

ADJUSTMENT OF ELEVATIONS.

Intermediate Bench Marks-Levels over Different Routes-Level Net-Numerical Problems-Fleld Problems.

REFERENCES.

XV PAGE

180

Chapter X. Profile Leveling; Cross-sections; Grades. . . . . . 206 Profile Leveling-Profile-level Notes-Cross-section Levels-Route Cross-sections.

LEVELING FOR EARTHWORK.

General-Borrow-pit Cross-sections-Road Cross-sections-Canal Cross-sections-Cuts and Fills-Setting Slope Stakes-Use of Ward Tape and Tape Rod.

GRADES.

General-Shooting-in Grade-Grades with Gradienter-Con-tour Leveling-Establishing Grade Contours-Vertical Curves -Location of Summit or Sag-Numerical Problems-Field Problems.

Chapter XI. Plotting Profiles and Cross-sections; Volumes of Earthwork. . . . . . . . . . . . . . . . . . . . . 231

PROFILES AND CROSS-SECTIONS.

The Profile-Fixing Grades-Finishing the Profile-Other Profiles-Plotting Cross-sections.

EARTHWORK CALCULATIONS.

Areas of Regular Cross-sections-Level Section-Three-level Section-Areas of Irregular Road Cross-sections-Volumes of Earthwork-Volume of Borrow Pit-Volumes by Average End Areas-Volumes by the Prismoidal Formula-Prismoidal Correction-Volumes from Road Profiles-Precision of Deter-mination of Volumes of Earthwork-Numerical Problems-Office Problems.

REFERENCES.

Chapter XII. Measurement of Angles and Directions. . . . . . 250 Location of Points-Angles and Directions-True Meridian -Magnetic Meridian-Magnetic Needle-Magnetic Declina-

XVI CONTENTS

tion-Isogonic Chart-Variations in Magnetic Declination-.-Local Attraction-Establishing the Meridian-Bearings-Azi-muths-Deflection Angles-Angles to the Right-Interior Angles-Traverses-Triangulation-Methods of Determining Angles-Direction with Magnetic Compass-Pocket Com-passes-Surveyor's Compass-Correction for Local Attraction -Sou1ces of Error; Adjustment of Compass-Numerical Problems-Field Problems.

REFERENCES.

Chapter XIII. The Engineer's Transit DESCRIPTION.

General-Types of Transit-Level Tubes-Telescope-Gradu-ated Circles-Verniers-Eccentricity of Verniers and Centers.

UsE OF THE TRANSIT.

General-Setting Up the Transit-Measuring a Horizontal Angle-Laying Off a Horizontal Angle-Common Mistakes-Measuring an Angle by Repetition-Laying Off an Angle by Repetition-Measuring a Vertical Angle-Index Error-Double-sighting to Determine True Vertical Angle-Prolong-ing a Straight Line-Running a Straight Line between Two Points-Prolonging a Line Past an Obstacle-Determining an Inaccessible Distance-Intersection of Lines-Me~;tsuring an Angle when Transit Cannot Be Set at Vertex.

ADJUSTMENT OF THE TRANSIT.

Desired Relations-Adjustments-Suggestions. ERRORS IN TRANSIT wORK.

General-Instrumental Errors-Personal Errors-Natural Errors-Precision of Angular Measurements-Numerical Problems-Field Problems.

REFERENCES.

PAGE

274

Chapter XIV. Transit-tape Surveys . . . . . . . . . . . . . 319 General-Transit Party-Equipment of Transit Party-Transit Stations-Transit Lines-Transit Surveys-Radia-tion-Intersection-Traversing-Deflection-angle Traverse-Azimuth Traverse-Traverse by Angles to the Right-Interior-angle Traverse-Checking Traverses-Precision of Transit-tape Traverses-Specifications for Traversing-Refer-encing Transit Stations-Details from Transit Lines-Locating Details-Field Problems.

REFERENCES.

Chapter XV. Stadia Surveying. . . . . . . . . . . . . . . . 345 The Stadia Method-Stadia Hairs-Stadia Rods-Observa-tion of Stadia Interval-Principle of the Stadia-Stadia Con-stants-Stadia Interval Factor-Inclined Sights-Permissible Approximations-Stadia Reductions-Beaman Stadia Arc-Uses of the Stadia-Indirect Leveling by Stadia-Transit-stadia Surveying: Elevations Not Required-Transit-stadia

CONTENTS xvii PAGE

Surveying: Elevations Required-8tepping Method-Errors in Stadia Surveying-Precision of Stadia Surveying-Numerical Problems-Field Problems.

Chapter XVI. Triangulation. . . . . . . . . . . . . . . . . 373 GENERAL.

General-Classification of Triangulation Systems-Triangula-tion Figures-Choice of Figure-Strength of Figure-Base Nets.

METHODS.

General-Reconnaissance-Signals and Instrument Supports -station Marks-Angle Measurements-Instruments for Measuring Angles-Azimuth Determinations-Base-line Meas-urement; the Tape-Measuring the Base Line-Errors in Base-line Measurements-Corrections-Reduction to Sea Level-Discrepancy between Bases-Specifications for Base-line Measurement.

CoMPUTATIONS.

General-Reduction to Center-Correction for Spherical Excess-Adjustment of a Chain of Triangles-Adjustment of a Quadrilateral-Adjustment of a Chain of Figures between Two Base Lines-Computation of Triangles and Coordinates-Computation of Geodetic Position-Systems of Plane Coordi-nates-Three-point Problem-Numerical Problems-Field Problem.

REFERENCES.

Chapter XVII. The Plane Table . . . . . . . . . . . . . . . 414 General-Relation between Transit and Plane Table-Tables -Coast Survey Table-Johnson Table-Traverse Table-Alidades-Peep-sight Alidade-Telescopic Ali dade-Plane-table Sheet-Setting Up and Orienting the Table-Radiation -Traversing-Intersection-Graphical Triangulation-Resec-tion-Resection after Orientation by Magnetic Needle-Re-section after Orientation by Backsighting-Resection and Orientation: Three-point Problem-Trial Method-Tracing-cloth Method-Resection and Orientation: Two-point Prob-lem-Verification-A Special Case-Measurement of Differ-ence in Elevation-Adjustments of the Plane-table Alidade-Sources of Error-Field Checks-Advantages and Disadvan-tages-Numerical and Office Problems-Field Problems.

REFERENCES.

Chapter XVIII. Plotting Maps. . . General-Process of Making a Map-Methods of Plotting Horizontal Control-Protractor Method-Tangent Method -Tangent Protractor-Chord Method-Checking-Cut-off Lines-Intersecting Lines-Method of Rectangular Coordi-nates-Latitudes and Departures-Error of Closure-Bal-ancing the Survey-Adjustment of Angular Error-Compass

439

XVlll CONTENTS

and Transit Rules for Balancing a Survey-Crandall Method of Balancing a Survey-Summary of Methods of Balancing a Survey-Computation of Coordinates-Plotting Control by Coordinates-Advantages and Disadvantages of Coordinate Method of Plotting-Omitted Measurements-Length and Bearing of One Side Unknown-Length of One Side and Bear-ing of Another Side Unknown-Length of Two Sides Unknown -Direction of Two Sides Unknown-Plotting Details-Numerical Problems-Office Problems.

REFERENCES.

PAGE

Chapter XIX. Calculation of Areas of Land . . . . . . . . . . 475 General-Methods of Determining Area-Area by Triangles -Area by Coordinates-Principles of Double-meridian-dis-tance Method-Area within Closed Traverse by D.M.D. Method-Double Parallel Distances-Area of Tract with Irregular or Curved Boundaries-Offsets at Regular Intervals: Trapezoidal Rule-Offsets at Regular Intervals: Simpson's One-third Rule-Rules Compared-Offsets at Irregular Inter-vals-Area of Segments of Circles-Partition of Land-Area Cut Off by a Line between Two Points-Area Cut Off by a Line Running in a Given Direction-To Cut Off a Required Area by a Line through a Given Point-To Cut Off a Required Area by a Line Running in a Given Direction-Numerical Problems-Office Problem.

Chapter XX. Principles of Field Astronomy . . . . . . . . . . 500 General-The Celestial Sphere-Observer's Position; Lati-tude and Longitude-Position of a Celestial Body; Right Ascension and Declination-Astronomical Tables Used by the Surveyor-Hour Angle and Declination-Equator Systems Compared-Horizon System-Relation between Horizon and Equator Systems-Spherical Trigonometry-Solution of the PZS Triangle-Azimuth at Elongation-Azimuth of a Circumpolar Star-Altitude of a Star-Time-True and Mean Suns-Apparent (True) Solar Time-Civil (Mean Solar) Time -Equation of Time-Sidereal Time-Relation between Longi-tude and Time-Standard Time-Numerical Problems.

REFERENCES.

Chapter XXI. Azimuth, Latitude, Longitude, and Time . ....

General-Angular Measurements. SoLAR 0BsERV ATIONs.

General-Parallax Correction-Refraction Correction-Decli-nation of the Sun-Latitude by Observation on Sun at Noon-Azimuth by Direct Solar Observation-Time by Observation on Sun at Noon-Longitude by Observation on Sun at Noon-Azimuth and Longitude by Solar Observation-Solar Attach-ments-Smith Solar Attachment-Azimuth with Smith Solar Attachment-Adjustments of Smith Solar Attachment-Saegmuller Solar Attachment-Burt Solar Attachment-Declination Settings for Use with Solar Attachment.

529

CONTENTS

OBsERVATIONs ON STARS.

General-Polaris-Latitude by Observation on Polaris at Culmination-Azimuth by Observation on Polaris at Elonga-tion-Azimuth by Observation on Polaris at Any Time-Observations on Other Stars-Determination of Latitude-Determination of Time-Determination of Longitude-Deter-mination of Azimuth-Numerical Problems-Field Problems.

REFERENCES. >

Chapter XXII. Land Surveying-Rural and Urban ...... . General-Kinds of Land Surveys-Instruments and Methods -Corners, Monuments, and Reference Marks-Boundary Records-Legal Terms-Legal Interpretation of Deed Descrip-tion-Riparian Rights-Meander Lines-Property Lines of Riparian Owners-Adverse Possession-Legal Authority of the Surveyor-Liability of the Surveyor .

RuRAL-LAND SuRVEYS. Description of Rural Land-Metes and Bounds-Coordinates -Subdivisions of Public Land-Original Survey-Resurvey-Subdivision Survey of Rural Land.

URBAN-LAND SuRVEYS.

Description of Urban Land-Subdivision Survey of Urban Land-City Surveying-Cadastral Surveying-Field and Office Problem.

REFERENCES.

.

XIX PAGE

57n

Chapter XXIII. United States Public-land Surveys. . . . . . . 604 General-Laws Relating to Public-land Surveys-Historical Notes-General Scheme of Subdivision-Standard Lines-Townships-Sections-Establishing the Standard Lines-Convergency of Meridians-To Lay Off a Parallel of Latitude -Solar Method-Tangent Method-Secant Method-Estab-lishing Township Exteriors-Allowable Limits of Error-Rectangular Limits of Error-Subdivision of Townships-Subdivision of Sections-Subdivision by Protraction-Sub-division by Survey-Meandering-Field Notes-Marking Lines between Corners-Corners-Witness Corners-Corner Monuments-Marking Corners-Corner Accessories-Restor-ation of Lost Corner-Proportionate Measurement-Field Process-Numerical Problems.

REFERENCES.

Chapter XXIV. Topographic Maps . . . . . . . . . . . . . . 638 General-Representation of Relief-Relief Model-Shading -Hachures-Contours and Contour Lines-Characteristics of Contour Lines-Contour Interval-Contour-map Construc-tion-Interpolation-Systems of Ground Points-Finishing the Map-Tests for Accuracy-Choice of Map Scale-Specifications for Topographic Maps-Cross-sections and Profiles from Contour Maps-Earthwork Quantities-Earth-

XX CONTENTS

work for Roadway--Reservoir Areas and Volumes-Route Location-Office Problems.

REFERENCES.

PAG:II

Chapter XXV. Topographic Surveying. . . . . , . . . 659 General-Choice of Contour Interval-General Field Methods.

CONTROL.

General-Horizontal Control-Traversing-Triangulation-Vertical Control-Accuracy Required-Trigonomijtric Leveling.

LOCATION OF DETAILS.

General-Accuracy Required-Details by Controlling-point Method-Transit and Stadia-Plane Table-Transit and Plane Table-Details by Cross-profile Method-Details by Checkerboard Method-Details by Trace-contour Method-Field Problems.

REFERENCES.

Chapter XXVI. Route Surveying. . . . . . . . . . . . . . . 687 General-Procedure-Reconnaissance-Preliminary Survey-Transit-tape-level Method-Transit-stadia Method-Plane-table Method-Preliminary Profile and Map-Location Sur-vey; Paper Location-Location Survey; Field and Office Work-Construction Surveys-Haul-Survey for Highway-Survey for Railway-Survey for Canal-Survey for Power-transmission Line-Field Problem.

REFERENCES.

Chapter XXVII. Route Curves. General.

CIRCULAR CURVES.

General-Geometry of the Circular Curve-Curve Formulas-Length of Curve-Curves by Deflection Angles-Laying Out Curve by Deflection Angles-Transit Set-ups on the Curve-Laying Out Curve by Tape Alone.

SPIRAL CURVES.

Superelevation-Railway Spirals-Highway Spirals-Numer-ical Problems-Field Problem.

REFERENCES.

703

Chapter XXVIII. Construction Surveys. . . . . . . . . . . . 717 General-Highways-Streets-Railways-Sewers and Pipe Lines-Canals-Tunnels-Bridge Sites-Bridges-Culverts-Building Sites-Buildings-Dams.

REFERENCES.

Chapter XXIX. Mine Surveying .............. Definitions.

UNDERGROUND SuRVEYING.

General-Stations-Illumination-Distances-Mining Transit -Use of Auxiliary Telescope-Adjustment of Auxiliary Tele-

730

CONTENTS

scope-Setting Up and Leveling the Transit-Connecting Surface and Underground Surveys-Computations-Field Notes and Office Records-To Give Line for a Connection-To Mark a Property Boundary Underground-To Measure Dif-ference in Elevation Down a Vertical Shaft-Tunnel Surveys.

MINERAL-LAND SURVEYING.

Subsurface Ownership Ordinarily Defined by Vertical Bound-ing Planes-Lode Claims; General-Special Cases-Field Work-Numerical Problems.

REFERENCES.

XXl PAGE

Chapter XXX. Hydrographic Surveying and Flow Measurement 750 HYDROGRAPHIC SURVEYS.

General-Horizontal Control-Vertical Control-Shore Details -Establishing Datum-Location of Soundings-Range Line and Angle Read from Shore-Known Range and Time Inter-vals-Intersecting Ranges-Two Angles Read from Shore-Transit and Stadia-Distances along a Wire Stretched between Stations-Two Angles Read from Boat-The Sextant-Adjust-ments of the Sextant-Measuring Angles with the Sextant-Equipment Used in Making Soundings-Making the Sound-ings-Reducing Soundings to Datum-Plotting the Soundings -Hydrographic Maps.

SPECIAL HYDROGRAPHIC SURVEYS.

Sweep or Wire Drag-Determination of Stream Slope-Meas-urement of Surface Currents-Measurement of Dredged Material-Capacity .of Existing Lakes or Reservoirs-Snow Surveys.

FLOW MEASUREMENT.

General-Discharge and Volume Units-Factors Controlling Discharge-Selecting the Control for Gaging-Water-stage Registers-Staff Gages-Chain Gage-Recording Tide and River Gages-Hook Gage-Measuring the Cross-section-Instruments for Measuring Current Velocity-Floats-Method of Making Float Measurements-Current Meters-Price Meter-Ellis Meter-Haskell Meter-Fteley Meter-Hoff Meter-Meter Supports-Rating Current Meters-Meter Rating Curves-Velocity Measurements-Vertical-velocity-curve Method-Two-tenths and Eight-tenths Method-Six-tenths Method-Integration Method-Subsurface Method-Recording Field Measurements-Measurements with Current Meter-Wading Method-Bridge Method-Cable-car Method -Discharge Measurements under Ice-Station Rating Curve -Discharge Computations-Discharge by the Slope Method -Kutter's Formula and Coefficients-Value of the Slope Method-Weirs: General-Definitions-Rectangular Weirs-Correction for Velocity of Approach-Submerged Weirs-Tri-angular and Trapezoidal Weirs-Use of Dams as Weirs-Con-struction of .Weirs-Numerical Problems.

REFERENCES.

xxii CONTENTS

Chapter XXXI. Photogrammetric Surveying. PHOTOGRAMMETRY.

General-Historical Development-Definitions-Basic Prin-ciples.

STEREOSCOPY.

Monocular Vision-Binocular Vision-Stereoscopic Observa-tion-Stereoscopes.

TERRESTRIAL PHOTOGRAMMETRY.

General-Phototheodolite- Terrestrial Photography-Accu-racy of Measurement-Automatic Plotting Machines.

AERIAL PHOTOGRAMMETRY.

General-Aerial Photography-Scale of the Photograph-Determination of Flight Altitude-Coverage of Aerial Photo-graphs-Interval between Exposures-Index Maps-Photo-graphic Airplanes-Aerial Cameras-Single-lens Aerial Cam-eras-Multiple-lens Aerial Cameras-Displacement of Image Points on Photographs. Displacement Due to Relief-Effect of Tip and Tilt-Determination of Elevations by Measure-ment of Parallax-Parallax Tables-Map Control-Radial-line Method-Slotted-templet Method-Section-line Method -Aerial Triangulation-Map Projection-Compilation of Detail from Photographs-Contouring-Automatic Stereo-scopic Plotting Machines-The Aerocartograph-The Stereo-planigraph-The Multiplex Aero Projector-The Stereocom-paragraph-Numerical Problems.

REFERENCES.

PAGE 806

Chapter XXXII. Map Projections . . . . . . . . . . . . . . 869 Maps of Small Areas-Maps of Large Areas-Map Projection Defined-Ideal vs. Practicable Projection-Types of Projections -Gnomonic Projection-Stereographic Projection-Ortho-graphic Projection-Geometric Projections to a Cylinder-Geometric Projections to a Cone-Polyconic Projection-Lam-bert Conformal Conic Projection-Mercator Projection-Transverse Mercator Projection-Spheroidity of the Earth.

REFERENCES.

INDEX ... 1005

Table I.

Table II.

Table III.

TABLES Correction for Refraction and Parallax, to Be Sub-

tracted from the Observed Altitude of the Sun Correction for Refraction, to Be Subtracted from

the Observed Altitude of a Star. . . . . . . . Refraction Corrections to Be Applied to Apparent

Declinations . . . . . . . . . . . . . . . . Table III(a). Latitude Coefficients. . . . . . . . . . . . . . Table IV. Local Civil Time of Upper Culmination of Polaris

in the Year 1937 ............. . Table IV(a). Mean Time Interval between Upper Culmination Table V. Table V(a).

Table V(b).

Table VI.

and Elongation. . . . . . . . . . . . . . . Azimuth of Polaris at Elongation, 1936-1945 . . . Correction to Azimuth of Polaris, for Day of the

Year . .... .. ... . .. . .. . For Reducing to Elongation Observations Made

Near Elongation . . . . . . . . . . . . . . Solar-diurnal Variation of Magnetic Declination at

Three Places in ='J orth America. . . . . . . . Table VII. Azimuth of Polaris at All Hour Angles. . . . . . Table VII(a). Corrections to Azimuth of Polaris for Change of Table VIII. Table IX.

Table X. Table XL

Table XII. Table XIII. Table XIV.

Declination. . . . . . . . . . . . . . . . . Polar Distance of Polaris for Each Year, 1937-1945 Horizontal Distances and Elevations from Stadia

Readings . . .. ...... .. . . ... . Minutes in Decimals of a Degree . . . . . . . . Convergency of Meridians, Six Miles Long and Six

Miles Apart, and Differences of Latitude and Longitude ................ .

Azimuths of the Secant . . . . . . . . . . . . Offsets, in Links, from the Secant to the Parallel Coefficients ca for Sharp-crested Rectangular Weirs

with Two Complete End Contractions (Smith) Coefficients ca for Sharp-crested Rectangular Weirs

with Both End Contractions Suppressed (Smith) Coefficients Cd for Sharp-crested Rectangular Weirs

with Two Complete End Contractions (Smith) Table XVII. Coefficients cd for Sharp-crested Rectangular Weirs

Table XV.

Table XVI.

with Both End Contractions Suppressed (Smith) Table XVIII. Logarithms of Numbers ........... . Table XIX(a). Values of S, T, and C in Table XIX ...... . Table XIX. Logarithmic Sines, Cosines, Tangents, and Cotan-

Table XX. Table XXI. Table XXII.

gents . . . . . . . . . . . . . Natural Sines and Cosines ..... . Nat ural Tangents and Cotangents. . . Trigonometric Formulas. . . . . . .

XXlll

PAGE

877

878

879 881

882

882 884

885

886

887 888

890 891

892 900

901 902 903

904

904

905

905 906 932

934 979 991

1003

FIELD AND OFFICE PROBLEMS PAGE

CHAPTER IV. CoMPUTATIONS 1. Area with Planimeter. 70

CHAPTER VII. MEASUREMENT OF DISTANCE 1. Pacing 141 2. Chaining over Level Ground with Tape. 142 3. Standardization of Tape and Chaining over Uneven Ground. 142 4. Survey of Field with Tape. 143 5. Survey of Field with Irregular Boundary . . 144 6. Determining Obstructed Distance with Tape. 145

\ CHAPTER VIII. MEASUREMENT OF DIFFERENCE IN ELEVATION

1. Magnifying Power of Telescope . . 17& 2. Radius of Curvature of Level Tube. 178 3. Adjustment of the Engineer's Level. 179

CHAPTER IX. DIFFERENTIAL LEVELING 1. Differential Leveling with Engineer's Level and Self-reading

Rod . . . . . . . . . . . . . . . . . . . . . . . . 202 2. Differential Leveling with Engineer}s Level and Target Rod . 203 3. Reciprocal Leveling. . . . . . . . . . . 203 4. Test of Accuracy of Setting Level Target . . . . . . 204

CHAPTE~ X. PROFILE LEVELING; CRoss-sECTIONs; GRADES 1. Profile Leveling for a Road . . . . 229 2. Profile Leveling for a Pipe Line. . . 229 3. Setting Slope Stakes; Cross-sections 230

C:aAPTER XI. PLOTTING PROFILES AND CRoss-sEcTIONS; VoLUMES OF EARTHWORK

1. Plotting Profile . . . . . . . . . . . . . . . 248 2. Plotting Cross-sections; Quantities of Earthwork. 249

CHAPTER XII. MEASUREMENT OF ANGLES AND DIRECTIONS 1. Determination of Magnetic Declination. . . . . . . . . . . 272 2. Survey of Field with Surveyor's Compass and Tape . . . . . 272 3. Retracing Survey with Compass and Tape. Two Adjacent

Corners Known . . . . . . . . . . . . . . . . . . . . 273

CHAPTER XIII. THE ENGINEER's TRANSIT 1. Measurement of Horizontal Angles with Transit . 314 2. Measurement of Angles by Repetition . . . . . 315

XXV

XXVI FIELD AND OFFICE PROBLEMS PAGE

3. Laying Off an Angle by Repetition . . . . . . . . 315 4. Measurement of Vertical Angles with Transit . . . 316 5. Prolongation of a Line by Double-sightjng with Transit. 316 6. Prolongation of Line Past Obstacle. . . . . . . . . . . . . 316 7. Running a Straight Line between Two Points Not Intervisible 317 8. Determination of Inaccessible Distance . . . . . . . . . . . 317 9. Intersection of Lines with Transit . . . . . . . . . . . . . 317

10. Measurement of Angle when Transit Cannot Be Set at Vertex 317 11. Adjustment of the Transit. . . . . . . . . . . . . . . . . 318

CHAPTER XIV. TRANSIT-TAPE SuRVEYS 1. Open Deflection-angle Traverse with Transit and Tape . 342 2. Closed Azimuth Traverse with Transit and Tape. 343 J. Details with Transit and Tape. . . . . . . . . 344

CHAPTER XV. STADIA SURVEYING ' Determination of Stadia Interval Factor . . . . . . . . 371 " Preliminary Traverse of Route with Transit and Stadia. . 371 :3. Traverse and Location of Details with Transit and Stadia. 372

CHAPTER XVI. TRIANGULATION 1. Measurement of Base Line . . .... 412

CHAPTER XVII. THE PLANE TABLE 1. Adjustment of the Plane-table Alidade . 436 2. Traverse with Plane Table. . . . . . . 437 3. Plane-table Survey of Field . . . . . . 437 4. Three-point Problem with Plane Table . 438 5. Two-point Problem with Plane Table. . 438

CHAPTER XVIII. PLOTTING MAPS 1. Plotting by Tangents; Map Construction . . . . 472 2. Plotting by Coordinates; Map Construction . . . 473

CHAPTER XIX. CALCULATION OF AREAS OF LAND 1. Area of Field Surveyed with Tape . . . . . . . . . . 499

CHAPTER XXI. AziMUTH, LATITUDE, LoNGITUDE, AND TIME 1. Latitude by Observation on Sun at Noon . . . . . 574 2. Azimuth by Direct Solar Observation . . . . . . . 574 3. Latitude by Observation on Polaris at Culmination. 574 4. Azimuth by Observation on Polaris at Elongation . 575

CHAPTER XXII. LAND SuRVEYING-RURAL AND URBAN 1. Survey of Tract for Deed Description. . . . . . . . . 602

CHAPTER XXIV. TOPOGRAPHIC MAPS 1. Topographic-map Construction . . . 2. Profile from Topographic Map. . . . 3. Volume of Earthwork from Contours .

657 657 657

FIELD AND OFFICE PROBLEMS XXVll PAGE

CHAPTER XXV. ToPOGRAPHic S"LRVEYING 1. Topographic Survey by Checkerboard Method . 685 2. Topographic Survey by Trace-contour Method Using Plane

Table and Engineer's Level . . . . . . . . . 686

CHAPTER XXVI. RouTE SuRVEYING 1. Preliminary Survey for Road (Topography by Cross-profile

Method) . . . . . . . . . . . . . . . . . . . . . . . 701 CHAPTER XXVII. RouTE CuRVES

1. Laying Out a Circular Curve . . . .... ' 716

SURVEYING THEORY AND PRACTICE

CHAPTER I

FUNDAMENTAL CONCEPTS

1. Surveying.-8urveying has to do with the determination of the relative location of points on or near the surface of the earth. It is the art of measuring horizontal and vertical distances between terrestrial objects, of measuring angles between terrestrial lines, of determining the direction of lines, and of establishing points by predetermined angular and linear measurements.

Incidental to the actual measurements of surveying . are mathe-matical calculations. Distances, angles, directions, locations, areas, and volumes are thus determined from data of the survey. Also, much of the information of the survey is portrayed graphically by the construction of maps, profiles, cross-sections, and diagrams.

Thus the process of surveying may be divided into the field work of taking measurements and the office work of computing and drawing necessary to the purpose of the survey.

2. Uses of Surveys.-The earliest surveys known were for the purpose of establishing the boundaries of land, and such surveys are still the important work of many surveyors.

Every construction project of any magnitude is based to a greater or less degree upon measurements taken during the progress of a survey and is constructed about lines and points established by the surveyor. Aside from land surveys, practically all surveys of a private nature and most of those conducted by public agencies are of assistance in the conception, design, and execution of engineering works.

For many years the government, and in some instances the individ-ual states, have conducted surveys over large areas for a variety of purposes. The principal work so far accomplished consists in the fixing of national and state boundaries, the charting of coast lines and navigable streams and lakes, the precise location of definite

1

2 FUNDAMENTAL CONCEPTS [Chap. I

reference points throughout the country, the collection of valuable facts concerning the earth's magnetism at widely scattered stations, and the mapping of certain portions of the interior, particularly near the seacoasts, along the principal rivers and lakes, in the localities of valuable mineral deposits, and in the older and more thickly settled territories.

Summing up, surveys are divided into three classes: (1) those for the primary purpose of establishing the boundaries of landed properties, (2) those forming the basis of a study for or necessary to the con-struction of public or private works, and (3) those of large extent and high precision conducted by the government and to some extent by the states. There is no hard and fast line of demarcation between surveys of one class and those of another, as regards the methods employed, results obtained, or use of the data of the survey.

3. The Earth a Spheroid.-The earth is an oblate spheroid of revolution, the length of its polar axis being somewhat less than that of its equatorial axis. The lengths of these axes are variously computed, as follows:

Polar axis, ft. Equatorial axis, ft.

Clarke (1866) ....................... 41,710,242 41,852,124 Hayford (1909) ..................... 41 '711, 920 41,852,860 Adopted (1924) by International Geo-

detic and Geophysical Union ....... . 41 1 711 1 940a 41,852,860

a Computed from equatorial axis by assuming that the flattening of the earth is exactly 1 -;- 297.

The lengths computed by Clarke have been generally accepted in the United States and have been used in government land surveys. Hayford's values are now regarded as being more nearly correct than those of Clarke. The values adopted by the International Geodetic and Geophysical Union are published by the United States Naval Observatory.

It is seen that the polar axis is shorter than the equatorial axis by about 27 miles. Relative to the diameter of the earth this is a very small quantity, less than 0.34 per cent. Imagine the earth as shrunk to the size of a billiard ball, still retaining the same shape. In this condition, it would appear to the eye as a smooth sphere, and only by precise measurements could its lack of true sphericity be detected.

Let us consider that the irregularities of the earth have been l''emoved. The surface of this imaginary spheroid is a curved surface

Art. 3] THE EARTH A SPHEROID 3

every element of which is normal to the plumb line. Such a surface is termed a level surface. The particular surface at the average sea. level is termed mean sea level.

Imagine a plane as passing through the center of the earth, as in Fig. 3a. Its intersection with the level surface forms a continuous line around the earth. Any portion of such a line is termed a level line, and the circle defined by the intersection of such a plane with the mean level of the earth is termed a great circle of the earth. The distance between two points on tt~ earth, as A and B (Fig. 3a)~ is the; length of the arc of the great circle passing through the poi:uts, and is always somewhat more than the chord intercepted by this drc. The arc is a level line; the chord is a mathematically straight line.

If a plane is passed through the polef' of the earth and any other-point on the earth's surface, as A (Fig. 3b), the line defined by the

FIG. 3a

' ' ,,

f/

NP.

Meridian SP. FIG. 3b.

N.P.

SP.' FIG. 3c.

intersection of the level surface and plane is called a meridian. Imagine two such 'planes as passing through two points as A and B (Fig. 3b) on the earth, and the section between the two planes r~moved like the slice of an orange, as in Fig. 3c. At the equator-the two meridians are parallel; above and below the equator they converge, and the angle of convergency increases as the poles are approached. No two meridians are parallel except at the equator.

Imagine lines, normal to the meridians, drawn on the two cut surfaces of the slice. If the earth be regarded as a perfect sphere these lines converge at a point at the center of the earth. Consider-itig the lines on either or both of the cut surfaces, no two are parallel.

I

The radial lines may be considered as vertical or plumb lines, and hence we arrive at the deductions that all plumb lines converge at the earth's center and that no two are parallel. Strictly speaking, this is not quite true, owing to the unequal distribution of the earth mass and owing to the fact that normals to an oblate spheroid do not all meet at a common point.

4 FUNDAMENTAL CONCEPTS [Chap. I

Consider three points on the mean surface of the earth. Let us make these three points the vertices of a triangle, as in Fig. 3d. The surface within the triangle ABC is a curved surface, and the lines forming its sides are arcs of great circles. The figure is a spherical triangle. In the figure the dotted lines represent the plane triangle whose vertices are points A, B, and 0. 1 Lines drawn tangent to the sides of the spherical triangle at its vertices are shown. The angles a, b, and c of the spherical triangle are seen to be greater than the corresponding angles a', b', and c' of the plane triangle. The amount

of this excess would be small if the points were near together, and the surface forming the triangle would not depart far from a plane passing through the three points. If the points were far a part the difference would be con-siderable. Evidently the same conditions would obtain for a figure of any number of sides. Hence we see that angles on the surface of the earth are spherical angles. FIG. 3d.

In everyday life we are not concerned with these facts. We think of a line passing along the surface of the earth directly between two points as being a straight line, we think of plumb lines as being parallel, we think of a level surface as a fiat surfac~, and we think of angles between lines in such a surface as being plane angles.

As to whether the surveyor must regard the earth's surface as curved or may regard it as plane (a much simpler premise) depends upon the character and magnitude of the survey and upon the pre-cision required.

4. Plane Surveying.-That type of surveying in which the mean surface of the earth is considered as a plane, or in which its spheroidal shape is neglected, is generally defined as plane surveying. With regard to horizontal distances and directions, a level line is considered as mathematically straight, the direction of the plumb line at any point within the limits of the survey is considered as parallel to the direction of the plumb line at any other point, and the angles of polygons are considered as plane angles.

By far the greater number of all surveys are of this type. When it is considered that the length of an arc 1172 miles long lying in the earth's surface is only 0.05 ft. greater than the subtended chord, and further that the difference between the sum of the angles in a plane triangle and the sum of those in a spherical triangle is only one second for a triangle at the earth's surface having an area of 75.5

1 Actually the "auxiliary plane triangle" of geodetie work has sides equal in length to the arcs of the corresponding sphericrul triangle.

Art. 6] GEODETIC SURVEYING 5

square miles, it will be appreciated that the shape of the earth need be taken into consideration only in surveys of precision covering large areas.

Surveys for the location and construction of highways, railroads, canals, and, in general, the surveys necessary for the works of man are plane surveys, as are also the surveys made for the purpose of establishing boundaries, except state and national. The United States system of subdividing the public lands employs the methods of plane surveying but takes into account the shape of the earth in the location of certain of the primary lines of division.

The operation of determining elevation is usually considered as a division of plane surveying. Elevations are referred to a spheroidal surface, a tangent at any point in the surface being normal to the plumb line at that point (most commonly this imaginary surface of reference is mean sea level). This curved surface is called a "datum" or, curiously, a "datum plane." The procedure ordinarily used in determining elevations automatically takes into account the curvature of the earth, and elevations referred to the curved surface of reference or "datum plane" are secured without extra effort on the part of the surveyor. In fact it would be more difficult for him to refer elevations to a true plane than to the imaginary spheroidal surface which he has chosen. Imagine a true plane, tangent to the surface of mean sea level at a given point. At a horizontal distance of 10 miles from the point of tangency the vertical distance (or elevation) of the plane above the surface represented by mean sea level is 67ft., and at a distance of 100 miles from the point of tangency the elevation of the plane is 6,670 ft. above mean sea level. Evi-dently the curvature of the earth's surface is a factor which can not be neglect~d in obtaining even very rough values of elevations.

This book deals chiefly with the methods of plane surveying. 6. Geodetic Surveying.-That type of surveying which takes into

account the shape of the earth is defined as geodetic surveying. All surveys employing the principles of geodesy are of high precision and generally extend over large areas. Where the area involved is not great, as for a state, the required precision may be obtained by assuming that the earth is a perfect sphere. Where the area is large, as for a country, the true spheroidal shape of the earth is considered. Surveys of the latter character have been conducted only through the agencies of governments. In the United States such surveys have been conducted principally by the U.S. Coast and Geodetic Survey and the U. S. Geological Survey. Such surveys have also been conducted by the Great Lakes Survey, the Mississippi River Commission, several boundary commissions, and others.

6 FUNDAMENTAL CONCEPTS [Chap. I

Surveys conducted under the assumption that the earth is a perfect sphere have been completed by such large cities as Washington, Baltimore, Cincinnati, and Chicago.

Though only a few engineers and surveyors are employed in geodetic work, the data of the various geodetic surveys are of great importance in that they furnish precise points of reference to which the multitude of surveys of less precision may be tied. For each state, a system of plane coordinates has been devised, to which all points in the state can be referred without significant error in distance or direction arising from the difference between the reference surface and the actual surface of the earth.

6. Kinds and Operations of Surveying.-The nature of the meas-urements made by the surveyor has been indicated in preceding articles.

In land surveying his work consists in:

1. Rerunning old land lines to determine their length and direction. 2. Reestablishing obliterated land lines from recorded lengths and

directions and such other information as it is possible to secure. 3. Subdividing lands into parcels of predetermined shape and size. 4. Setting monuments to preserve the location of land lines. 5. Locating the position of such monuments with respect' to permanent

landmarks. 6. Calculating areas, distances, and angles or directions. 7. Portraying the data of the survey on a land map. 8. Writing descriptions for deeds.

A topographic survey is a survey made to secure data from which may be made a topographic map indicating the relief, or elevations and inequalities of the land surface. The work consists in:

1. Estalvlishing by angular and linear measurements the horizontal location of certain points for the skeleton of the survey, termed the horizontal control.

2. Determining the elevation of control points by the operation of leveling, termed the vertical control.

3. Determining the horizontal location and elevation of a sufficient number of ground points to provide data for the map.

4. Locating such other natural or artificial details as the requirements of the survey demand.

5. Calculating angles, distances, and elevations. 6. Plotting and finishing the topographic map (see also "Photogram-

metric Surveying," later in this article).

Route surveying as the term is here used has reference to those surveys necessary for the location and construction of lines of trans-portation or communication, such as highways, railroads, canals, transmission lines, and pipe lines. The preliminary work usually

Art. 6] KINDS AND OPERATIONS OF SURVEYING 7

consists of a topographic survey. The location and construction surveys may further consist in:

1. Locating the center line by stakes at short intervals. 2. Running levels to determine the profile of the ground along the

center line. 3. Plotting such profile, and fixing grades. 4. Taking cross-sections. 5. Calculating volumes of earthwork. 6. Measuring drainage areas. 7. Laying out structures, such &s culverts and bridges. 8. Locating right-of-way boundaries.

Hydrographic surveying has reference to surveying bodies of water for purposes of navigation, water supply, or subaqueous construction. Broadly speaking, the operations of hydrographic surveying may consist in:

1. Making a topographic survey of shores and banks. 2. Taking soundings to determine the depth of water and the character

of the bottom. 3. Locating such soundings by angular and linear measurements. 4. Plotting the hydrographic map showing the topography of the

shores and banks, the depths of soundings, and other desirable details. 5. Observing the fluctuation of the ocean tide or of the change in level

of lakes and rivers. 6. Measuring the discharge of streams. In a sense, the surveys for drainage and for irrigation are hydro-

graphic in character, but the principal work is essentially either topographic or route surveying.

Mine surveying makes use of the principles of land, topographic, and route surveying, with modifications in practice made necessary by altered conditions. Both surface and underground surveys are required. The work of the mine surveyor consists in:

1. Establishing (on the surface) the boundaries of claims for mineral patent (on the order of the Surveyor General of the state in which the claim is located) and fixing reference monuments.

2. Locating (on the surface) shafts, adits, bore-holes, railroads, tram-ways, mills, and other details.

3. Making a topographic survey of the mine property. 4. Constructing the surface map. 5. Making underground surveys neeessary to delineate fully the

mine workings. 6. Constructing the underground plans showing the workings in plan,

longitudinal section, and transverse section. 7. Constructing the geological plan. 8. Calculating volumes removed. Cadastral surveying, a practically obsolete term, has particular referenc~ to extensive surveys made for the purpose of locating

8 FUNDAMENTAL CONCEPTS [Chap. I

property lines and improvements in detail, primarily for use in connection with the extent, value, ownership, and transfer of land.

City surveying is the term frequently applied to the operation of laying out lots and to the municipal surveys made in connection with the construction of streets, water-supply systems, and sewers. There is no distinction between such surveys and those just described except that the degree of refinement observed in making measure-ments is made proportional to the value of the land with which the survey is concerned.

Recently the term "city survey" has come to mean an extensive coordinated survey of the area in and near a city for the purposes of fixing reference monuments, locating property lines and improve-ments, and determining the configuration and physical features of the land. Such a survey is of value for a wide variety of purposes, particularly for planning city improvements. The work consists in:

1. Establishing horizontal and vertical control, as described for topographic surveying.

2. Making a topographic survey and topographic map. 3. Marking critical points such as street corners with suitable monu-

ments referred to a cilmmon system of rectangular coordinates. 4. Making a property map, with layout and dimensions of properties. 5. Making a wall map. 6. Making a map, or maps, to show underground utilities.

Photogrammetric surveying is the application to surveying-usually topographic work-of the science of measurement by means of photographs. With specially designed cameras, photographs are taken either from airplanes (sometimes from balloons) or from ground stations. In connection with limited ground surveys made for the purpose of accurately establishing visible control points, aerial photogrammetry is employed on many topographic surveys by making certain necessary adjustments and projections. Recent important advancements and simplifications in the technique of aerial photo-grammetry have made this method by far the most rapid and accurate except perhaps where the ground is relatively fiat, where elevations must be determined within less than 5 ft., or where the area is small. The advantages of aerial photogrammetry are the speed with which the field work is accomplished and the wealth of detail secured. The method is used not only for military purposes but also for general topographic surveys, preliminary route surveys, and even for surveys of agricultural areas.

Terrestrial photogrammetry, or photographic surveying from ground stations, has been found a useful adjunct to other methods in the small-scale mapping of mountainous areas. The work consists in

Art. 8] UNITS OF MEASUREMENT 9

taking photographs from two or more control stations and in utilizing the photographs for the projection of details of the terrain in plan and elevation.

7. Definitions.-A level surface is one parallel with the mean spheroidal surface of the earth. A body of still water provides the best example.

A horizontal plane is a plane tangent to a level surface. A horizontal line is a line tangent to a level surface. A horizontal angle is an angle formed by the intersection of two lines

in a horizontal plane. A vertical line is a line normal to a level surface. A plumb line is

an example. A vertical plane is a plane of which a vertical line is an element. A vertical angle is an angle between two intersecting lines in a

vertical plane. In surveying it is commonly understood that one of these lines is horizontal, and a vertical angle to a point is under-stood to be the angle in a vertical plane between a line to that point and the horizontal plane.

In surveying, measured angles are either vertical or horizontal. In plane surveying, distances measured along a level line are termed

horizontal distances. The distance between two points is commonly understood to be the horizontal distance from the plumb line through one point to the plumb line through the other. Measured distances may be either horizontal or inclined, but in most cases the inclined distances are reduced to equivalent horizontal lengths.

The elevation of a point is its vertical distance above (or below) some arbitrarily assumed level surface, or datum.

A contour is a line which joins all points of equal elevation on the ground. The corresponding line on the map is called a contour line.

The vertical distance between two points is termed the difference in elevation. It is the distance between an imaginary level surface containing the high point and a similar surface containing the low point. The operation of measuring difference in elevation is called leveling.

Additional definitions are given in Art. 33. 8. Units of Measurement.-The operations of surveYing entail

both angular and linear measurements. The units of angular measure are the degree, minute, and second.

On most surveys, measurement to the nearest minute is sufficiently exact. On precise surveys, angles are frequently determined to tenths of seconds.

In all English-speaking countries the measurement are the yard, foot, and inch.

common units of linear On most surveys in these

10 FUNDAMENTAL C&NCEPTS [Chap. I

countries, distances are measured in feet, tenths of feet, and hun-dredths of feet; and surveyor's tapes are usually graduated in these units. In laying out construction work for men of the building trades, the surveyor will often find it necessary to employ the foot, the inch, and the eighth of an inch. Most measurements in surveying need not be taken closer than hundredths of a foot, and often dis-tances to the nearest foot or even to the nearest 10 ft. are sufficient for the purpose of the survey.

Formerly the rod and the Gunter's chain were units much used in land surveying, and the Gunter's chain as a unit of length is employed in the subdivision of the United States public lands. The Gunter's chain is 66 ft. long and is divided into 100 links each 7.92 in. long. 1 mile = 80 chains = 320 rods = 5,280 ft.

Many other civilized countries of the world employ the meter as the unit of length. 1 meter = 39.37 in. = 3.2808 ft. = 1.0936 yd. The meter is the unit of length employed by the U. S. Coast and Geodetic Survey.

The vara is a Spanish unit of linear measurement used in Mexico and several other countries falling under early Spanish influence. In portions of the United States formerly belonging to Spain or to Mexico, the surveyor will frequently have occasion to rerun property lines from old deeds in which lengths are given in terms of the vara. 1 vara = 32.9931 in. (Mexico), 33 in. (California), or 33;Ya' in. (Texas).

In the United States the units of area commonly used are the square foot and the acre. Formerly the square rod and the square Gunter's chain were also used.

1 acre = 10 sq. Gunter's chains = 160 sq. rods = 43,560 sq. ft. The units of volumetric measurement are the cubic foot and the

cubic yard. 9. Precision of Measurements.-In dealing with abstract quanti-

ties, we have become accustomed to thinking largely in terms of exact values. At the start, the student of surveying ought to appreci-ate that he is dealing with physical measurements which are correct only within certain limits, owing to errors that cannot be completely eliminated. The degree of precision of a given measurement depends upon the methods and instruments employed and upon other conditions surrounding the survey. It is desirable that all measure-ments be made with high precision, but unfortunately a given increase in precision is accompanied by more than a directly proportionate increase in the time and labor of the surveyor. It therefore becomes his duty to maintain a degree of precision as high as justified by the purpose of the survey, but not higher. It is important, then,

Art. 12] REQUISITES OF A GOOD SURVEYOR 11

that he have a thorough knowledge of the sources and kinds of errors, of their effect upon field measurements, and of methods to be fol-lowed in keeping the magnitude of the errors within allowable values. It follows that he must understand the intended use of the survey data.

Before beginning work, the surveyor ought to consider the follow-ing questions:

1. What is the purpose of the survey? 2. What degree of accuracy is required for that purpose? 3. What are the sources of error? 4. What methods must be employed to reduce these errors within

allowable limits? 5. How is the correctness of the work to be verified? 6. What instruments should be used to facilitate the work? 7. How may the work be organized to reduce the labor to a

minimum? 10. Principles Involved.-The underlying principles of plane sur-

veying are not difficult. They involve a thorough knowledge of geometry and plane trigonometry, and to a less degree a knowledge of physics, of astronomy, and of the theory and methods of adjust-ment of errors. Such portions of the last three subjects as are necessary to the understanding of the text will be given in succeeding chapters as the need arises. Geodetic surveying requires an expert knowledge of all the above subjects.

11. Practice of Surveying.-Like other arts based upon the sciences, the practice of surveying is complex, and no amount of theory will make a good surveyor unless he has the requisite skill in the art of observing and is versed in field and office practice. The student should realize the importance of a knowledge of the practical phases of the subject and seek to become as well grounded in the practice as possible.

Often surveying is one of the first professional subjects studied by the engineering student. He may not expect to become a surveyor, but he ought to understand that the training he will receive in the art of observing and computing, in the study of errors and their causes and effects, and in the practice of mapping will directly contribute to success in other subjects, regardless of the branch of engineering in which he may be interested.

12. Requisites of a Good Surveyor.-As the term "surveyor" is here used it has reference not only to that individual who makes his chief livelihood from surveying and expects so to continue in the remote future, but also to that individual of a large army of engineers to whom surveying is merely one of the arts of his profession, to

12 FUNDAMENTAL CONCEPTS [Chap. I

whom the survey is perhaps the work of today and the adaptation of the results to the engineering problem is the work of tomorrow.

A thorough knowledge of the theory of surveying and skill in its practice are the first requisites of the surveyor; but, upon the evi-dence of employers themselves, it is also true that traits of character are far more potent factors in the success of the surveyor or engineer than is technical knowledge or skill. Therefore, it should be stated with all emphasis that, while mastering the theory and practice of surveying, the student will do himself a great benefit if he also develops traits of character and habits of mind which will be advan-tageous to him whatever may be his later work. This can be accom-plished only by diligent application of the laws of habit formation, which are fairly well known. Some definiteness may be given to this suggestion by the mention of a few of the traits which should be possessed by the surveyor.

He should maintain the attitude of the scientist, that no result is trustworthy until every reasonable test of its accuracy has been applied.

He should be reliable. He should be of sound judgment. He should possess initiative and should attack a problem with

resourcefulness and energy. He should be thorough, not content with his work until it has

been finished in a workmanlike fashion. He should be able to think without confusion, and to reason logi-

cally without prejudice. He should be of good temper, thoughtful of those coming under his

direction, commanding the respect of his associates, and watchful of the interests in his employer.

CHAPTER II

ESSENTIAL FEATURES OF PRINCIPAL SURVEYING INSTRUMENTS

13. Principal Instruments.-The principal surveying instruments and accessories and their uses are listed below:

Tape .-A graduated flexible ribbon used for measuring distance (see Figs. 112a and 112b).

Chaining Pins.-Steel pins about 1 ft. long, for temporarily mark-ing the location of the ends of the tape as distances are measured (see Fig. 113).

Engineer's Level.-A telescope to which is attached a spirit-level tube, all revolving about a vertical axis and mounted on a tripod (see Fig. 141a) . A level is employed for determining difference in elevation. Its use is termed leveling, and the operator is called a levelman.

Level Rod.-A graduated wooden ,rod which, in conjunction with the level! is used in determining difference in elevation. Graduations are usua ly in hundredths of feet. The rod may be either in a single piece or jointed. Common length when extended is 12 or 13 ft. (see Figs. 146a-c).

Surveyor's Compass.-Mounted on a tripod and equipped with sight vanes. Used for determining the direction of lines by means of the magnetic needle. Nearly obsolete except for rough surveys, as in forestry (see Fig. 236a).

Flag, Flagpole, or Range Pole.-A pole, either of steel or of wood shod with a steel point, painted with bands of alternating red and white. Used as a sighting rod in connection with either angular or linear measurements (see Fig. 114).

Engineer's Transit.-The universal instrument. Used principally for measuring horizontal and vertical angles and for prolonging straight lines. The transit has a telescope which may be revolved about either a horizontal or a vertical axis. It is usually equipped with a magnetic needle and is mounted on a tripod (see Fig. 241a). The ope:rator is called a transitman.

Plane Table.-A drawing board mounted on a tripod, and an alidade, or straightedge equipped with a telescope, which can be moved about on the board. The plane table is used for mapping (see Fig. 339a).

13

14 FEATURES OF SURVEYING INSTRUMENTS [Chap. II

14. The Engineer's Level.-Figure 14a is a diagram of the principal parts of the engineer's level. The level consists of the telescope A mounted upon the level bar B which is rigidly fastened to the spindle C. Attached to the telescope and parallel with it is the level tube D. The spindle fits into a cone-shaped bearing of the leveling head E, so

1----+--+-+-.,..+--.:::---t,, Cross 1701/r

Cross h01ir ' '

FIG. 14a. FIG. 14b.

that the level is free to revolve about the spindle C as an axis. The leveling head is screwed to a wooden tripod F. In the tube of the telescope are cross-hairs at G, ~hich appear on the image viewed through the telescope as illustrated by Fig. 14b. The bubble of the level is centered by means of the leveling screws H.

FIG. 15a. Elevation

FIG. 15b.

~ Verf.Angle

I I

15. The Engineer's Transit.-Figures 15a and 15b illustrate, in plan and elevation, respectively, the principal parts of the engineer's transit. The transit consists of the telescope A, mounted on a horizontal axis B which is supported by standards D. Attached beneath the telescope is a spirit-level tube (not shown), similar to that for the level just described. Angles of rotation of the telescope in a vertical plane are indicated by the vertical circle C which is

,' -,

Art. 17] LEVEL TUBE 15

graduated in degrees and which is read by means of the index V attached to one of the standards. The standards rest on the upper plate E which is equipped with spirit levels (not shown) and which rotates about the vertical axis 0 on a spindle G called the inner spindle. The lower plate F revolves about the vertical axis on the outer spindle I; the outer rim of its upper face is a circle graduated in degrees and read by means of an index H on the upper circle. The spindles G and I are supported by the leveling head J, which is screwed to a wooden tripod L. The bubbles of the level tubes on the upper plate are centered by means of the four leveling screws K. A magnetic compass (not shown) is centered on the upper plate.

A detailed description of the transit is given in Chap. XIII. For the present discussion it is sufficient to state that:

1. The instrument can be leveled by means of the plate levels and the leveling screws.

2. The telescope can be rotated about the horizontal axis to measure vertical angles, or about the vertical axis to measure hori-zontal angles.

3. Horizontal angles are measured by clamping the graduated lower plate and observing the rotation of the upper plate between pointings of the telescope.

4. The telescope can be leveled by means of the telescope level tube, and hence the transit can be employed for direct leveling.

5. Vertical angles are measured by reading the graduations on the vertical circle.

6. Small movements about the vertical axis and the horizontal axis are accomplished by means of clamp-screws and tangent-screws, described in Art. 22.

7. Readings of each graduated circle are facilitated by the use of a vernier scale, described in Art. 21, at the index.

8. By means of the magnetic compass, directions can be observed and horizontal angles checked.

16. Essential Features.-Essential features of the engineer's level are a level tube and a telescope. For the transit, verniers are also employed for reading the graduated circles. These features also apply to the plane-table ali dade; and verniers are used on leveling rods, sextants, and planimeters. The magnetic compass as applied to surveying is discussed in Chap. XII.

17. Level Tube.-A level tube (Fig. 17a) is a glass vial with the inside ground barrel-shaped, so that a longitudinal line on its inner surface is the arc of a circle. The tube is nearly filled with sulphuric ether or with alcohol. The remaining space is occupied by a bubble of air which takes up a location at the high point in the tube. The

16 FEATURES OF SURVEYING INSTRUMENTS [Chap. II

tube is usually graduated in both directions from the middle; thus by observing the ends of the bubble it may be "centered," or its center brought to the mid-point of the tube. The tube is set in a protective metal housing, usually with plaster of paris. The housing is attached to the instrument by means of screws which permit adjustment, as shown in the figure.

FIG. 17a.-Level tube.

A line tangent to the longitudinally curved inside surface at its mid-point is called the axis of the level tube. When the bubble is centered, the axis of the level tube is horizontal.

A reversion level is one graduated on both top and bottom and so mounted that it can be used when the telescope is either normal or inverted.

17a. Sensitiveness of Level Tube.-If the radius of the circle to which the level tube is ground is large, a small vertical movement of one end of the tube will cause a large displacement of the bubble; if the radius is small, the displacement will be small. Thus the radius of the tube is a measure of its sensitiveness. The sensitiveness is generally expressed in seconds of the central angle whose arc is one division of the tube. The sensitiveness expressed in this manner is

Radius of Seconds of arc for Instrument curvature, 2-mm. division

ft. of tube

Better grade of engineer's levels ....... 68 20 Precise level (U.S. Coast and Geodetic

Survey) .......................... 677 2 Engineer's transit:

Telescope level .................... 45 30 Plate levels ....................... 18 75

Plane table: Telescope level .................... 30 45 Control level on vertical circle ...... 23 60

Art. 17b] ADJUSTMENT OF LEVEL TUBE 17

inversely proportional to the number of seconds. For many instru-ments the length of a division is 2 mm., while for others it is 0.1 in. (2.5 mm.); the practice is not uniform among manufacturers of surveying instruments. For this reason, the sensitiveness expressed in seconds of arc is not a definite measure unless the spacing of graduations is known. The values shown in the table on p. 16 roughly represent common practice for various instruments.

A simple method of determining the radius of curvature in the field is explained in field problem 2, Art. 163.

The more sensitive the tube, the longer the time required to center the bubble. Hence, time is wasted if the tube is more sensitive than the device to which it is attached. For example, in a telescope level tube the first noticeable movement of the bubble should be accompanied by an apparent movement of the line of sight as inJtcated by the cross-hairs.

17b. Adjustment of Level Tube.-The principle involved in bring-ing the axis of the level tube into the proper relation with the device

4 Ax1s of Level Tube~ _

()1, -t_ A

(q)

(c)

tl

BorA~AorB t I

(cO Fw. 17b.-Adjustment of level tube by reversion.

to which it is attached is invariably that of reversion, or reversing the level tube end for end. There are two general cases: (1) when the tube is fixed to a telescope or plate which can be rotated about a vertical axis, as on a transit plate; and (2) when the tube can be lifted from the support and reversed end for end thereon, as on a plane-table alidade. However, the method of adjustment is. the same in either case.

The steps involved in adjustment are shown in Fig. 17b. In view (a) is shown the tube out of adjustment by the amount of the angle a, but with the bubble centered; the support is therefore not level. In view (b) the level tube has been lifted and reversed end for end.

18 FEATURES OF SURVEYING INSTRUMENTS [Chap. II

(In the case of a support on a vertical axis the same relations would exist if the support were rotated 180 about the vertical axis.) The axis of the level tube now departs from the horizontal by 2a, or double the error of the setting. In view (c) the bubble has been brought back halfway to the middle of the tube by means of the adjusting screw C, without moving the support; the tube is now in adjustment. Finally, in view (d) the bubble is again centered by raising the low end of the support; the support is now level and the adjustment may be checked by reversing the tube.again.

If it were desired to level the support in the direction of the tube without taking time to adjust the tube, this could be accomplished by centering the bubble as in view (a), Fig. 17b; reversing the tube as in view (b); and raising the low end of the support until the bubble is brought halfway back to the center of the tube. This po~ition of the bubble corresponds to the error of setting of the tithe; and whenever the bubble is in this position the support will be level.

18. Leveling Head.-On the level, transit, and one type of plane table, the head of the instrument is leveled by means of leveling

}

c,., FIG. 18.-Leveling head.

screws, or foot screws. A sim-plified cliagram is shown in Fig. 18, in which the spindle A revolves in the socket of the leveling head B. Near the bottom of the leveling head is a ball-and-socket joint C, which makes a flexible connection with the foot plate D. The level-ing head has four radial arms, into each of which is threaded a level-ing screw E. (Only two of the

screws are shown in the figure.) The leveling screws bear on the foot plate, and by means of these screws the leveling head can be tilted.

The engineer's level, which has only one level tube, is leveled as follows: The instrument is turned about the vertical axis until the level tube is approximately over one pair of opposite leveling screws, and the level bubble is brought approximately to the center by turning that pair of screws, keeping both screws lightly in contact with the foot plate and thus keeping the ball-and-socket joint lightly in bearing. It is convenient to remember that the bubble travels in the same direction as the left thumb. The instrument is then rotated 90, and the level bubble is centered over the other pair of opposite leveling screws. This process is repeated alternately over the two pairs of screws until (if the level tube is in adjustment) the bubble will remain centered for any direction of pointing of the instrument.

Art. 19] TELESCOPE 19

If the instrument has two level tubes perpendicular to each other, the process of leveling is similar except that it is not necessary to rotate the instrument. Each level tube is alined with one pair of opposite leveling screws and is controlled by that pair. If the instrument has a universal or" bull's-eye" type of level, the process of leveling is also similar. On instruments equipped with three leveling screws instead of four the universal type of level is sometimes used.

It is a waste of time to center the bubble exactly over one pair of leveling screws before bringing it approximately to center over the other pair. It is best to leave all four screws rather loose, or barely in bearing, until the instrument is almost level. If one pair of screws turns hard, the other pair should be loosened slightly. The final centering of the bubble will be facilitated by turning one screw rather than by attempting to manipulate two opposite screws at the same time.

19. Telescope.-Figure 19a shows the principal parts of the telescope as it is commonly constructed. Rays of light emanating from an object within the field of view of the telescope are caught

FIG. 19a.-Longitudinal section of external-focusing telescope.

FIG. 19b.-Longitudinal section of internal-focusing telescope.

by the objective lens A and are brought to a focus and form an image in ti1e plane of the cross-hairs B. The lenses of the eyepiece C form a microscope which is focused on the image at the cross-hairs. The objective lens is screwed in the outer end of the objective slide D which fits in the telescope tube E. The objective lens is focused by the screw F at the inner end of which is a pinion that engages the teeth of a rack fixed to the objective slide. The eyepiece slide G is held in position laterally by rings Hand J, through which it may be moved in a longitudinal direction for focusing. By means of screws the ring J may be moved transversely so that the intersection of the cross-hairs will appear in the center of the field of view.

20 FEATURES OF SURVEYING INSTRUMENTS [Chap. II

The line of sight is defined by the intersection of the cross-hairs and the optical center of the objective lens. The instrument is so constructed that the optical axis of the objective lens coincides (or practically coincides) with the axis of the objective slide; in other words, a given ray of light passing through the optical center of the objective always occupies the same position in the telescope tube regardless of the longitudinal position of the lens. The cross-hairs can be so adjusted that the line of sight and the optica