UNIVERSITY OF CALIFORNIA AT LOS ANGELES HELD - Orncc METHODS STUDENTS IN SURVEYING. BY W1LLIA/ V \ D. PENCE, Professor of Civil Engineering. Purdue University. A\ILO S. KETCMUAV Assistant Professor of Civil Engineering University of Illinois. PUBLISHED BY THf: AUTHORS. Copyright. 1900. WILLIAM D. PKNCK AND MILO S. KKTCHUM; TA 55 \ TABLE OF CONTENTS. Page CHAPTER I. -GENERAL INSTRUCTIONS 1 CHAPTER II. THE CHAIN AND TAPE. 13 Problem A 1. Length of Pace 24 A 2. Distances by Pacing 24 A 3. Axeman and Flagman Practice 26 A 4. Range Pole Practice , 26 A 5. Standardizing Chain or Tape 26 A 6. Distances with Surveyors' Chain 27 A 7. Distances with Engineers' Chain 28 A 8. Distances with 100-foot Steel Tape 28 A 9. Horizontal Distance on Slope 30 A10. Angles of Triangle with Tape 32 All. Survey of Field with Tape 32 A12. Area by Perpendicular Method 32 A13. Area by Three-Side Method 34 A14. Area by Angle Method 34 A15. Area from Plat 34 A16. Survey of Field with Curved Boundary 38 A17. Area of Field with Curved Boundary 36 A18. Area (of same) from Plat 38 A19. Passing an Obstacle with Tape 38 A20. Obstructed Distance with Tape 40 A21. Running in Curve with Tape 40 A22. Discussion of Errors of Chaining 42 A23. Testing Standard of Length 42 A24. Constants of Steel Tape 44 A25. Comparison of Chains and Tapes 44 TABLE OF CONTENTS. Pas?e CHAPTER III. THE COMPASS. 45 Problem B 1. Declination of Needle 51 B 2. Angles of Triangle with Compass 52 B 3. Traverse of Field with Compass 54 B 4. Area of Field with Compass 51 B 5. Adjustment of Compass 56 B 6. Comparison of Compasses . . 56 CHAPTER IV. THE LEVEL. 57 Problem C 1. Differential Leveling with Hand Level 76 C 2. Differential Leveling, Engine ars' Level... 78 C 3. Profile Leveling for Drain 78 C 4. Railroad Profile Leveling 82 C 5. Vertical Curve 83 C 6. Establishing Grade Line 84 C 7. Survey of Line Shafting 84 C 8. Contour Leveling 87 C 9. Use of Contour Map 89 CIO. Delicacy of Bubble Vial 89 Cll. Comparison of Level Telescopes 90 C12. Tests of Wye Level 90 C13. Adjustment of Wye Level 91 C14. Sketching Wye Level 92 CIS. Tests of Dumpy Level 92 C16. Adjustment of Dumpy Level 92 C17. Sketching Dumpy Level 92 C18. Stretching Cross-Hairs 93 C19. Error of Setting Level Target 03 C20. Comparison of Engineers' Levels 94 TABLE OF CONTENTS. Page CHAPTER V. THE TRANSIT. 95 Problem D 1. Angles of Triangle with Transit 10- D 2. Prolongation of Line with Transit 104 D 3. Intersection of Two Lines with Transit. . .10'i D 4. Triangulation Across River 106 D 5. Passing Obstacle with Transit 106 D 6. Traverse of Field with Transit 108 D 7. Area of Field with Transit 108 D 8. Staking Out Building 110 D 9. Height of Tower with Transit 110 D10. Angles of Triangle by Repetition 1.12 Dll. True Meridian by Polaris at Elongation. .111 D12. True Meridian by Polaris at Any Time. . .115 D13. Comparison of Transit Telescopes 118 D14. Test of Transit 118 D15. Adjustment of Transit 118 D16. Sketching Transit L19 D17. Error of Setting Flag Pole 120 D18. Comparison of Engineers' Transits 120 CHAPTER VI. TOPOGRAPHIC SURVEYING. 121 Problem E 1. Stadia Constants., with Fixed Hairs 132 E 2. Stadia Reduction Table 134 E 3. Azimuth Traverse with Stadia 134 E 4. Plane Table Survey by Radiation 135 E 5. Plane Table Survey by Traversing 135 E 6. Plane Table Survey by Intersection 136 E 7. Three Point Problem with Plane Table... 136 E 8. Angles of Triangle with Sextant 13*i E 9. Coefficients of Standard Taps 139 E10. Measurement of Base Line... ...139 TABLE OF CONTENTS. Page Ell. Calculation of Triangulation System .... 139 E12. Sketching Topography 140 E13. Topography with Transit and Stadia 140 E14. Topography with Plane Table and Stadia . . 142 E15. Topographic Survey 143 E16. Survey for Street Improvements 143 CHAPTER VII. LAND SURVEYING. 145 Problem F 1. Investigation of Land Corner 157 F 2. Perpetuation of Land Corner 158 F 3. Reestablishing Quarter-Section Corner 159 F 4. Reestablishing Section Corner ISO F 5. Resurvey of Section 160 F 6. Resurvey of City Block 163 F 7. Resurvey by Metes and Bounds 163 F 8. Partition of Land .164 F 9. Design and Survey of Town Site 1M CHAPTER VIII. RAILROAD SURVEYING 167 Problem G 1. Review of Instrumental Adjustments 196 G 2. Use of Field Equipment 196 G 3. Preliminary Field Curve Practice 197 G 4. Indoor Curve Problems 198 CHAPTER IX. ERRORS OF SURVEYING. 199 CHAPTER X. METHODS OF COMPUTING 211 CHAPTER XL FREE HAND LETTERING 225 PREFACE. In preparing this manual the following points have been kept especially in view: (1) To provide a simple and com- prehensive text designed to anticipate and supplement, rather than replace, the usual elaborate treatise. (2) To bring the student into immediate familiarity with approved surveying methods. (3) To cultivate the student's skill in the rare arts of keeping good field notes and making reliable calculations. It is believed that the discussions of the different instru- ments, their use and theory, at the beginning of the several chapters is unusually simple, especially in the relations of the elementary lines. The several series of practice problems at the conclusion of the respective chapters are arranged so as to give the student familiarity with the use of the instrument before taking up its theory and adjustments, this ord>er bein^r more effective than the reverse. The interest of the student may be stimulated and 'his gain in skill promoted by giving him practice with level and transit very early in the course, after which the scope of the work may be much more flex- ible both for student and instructor. Since the list of problems is more extended than can be covered in the time usually available for surveying field practice, some range is permitted in the choice of work from year to year and under varying local conditions. By using some discrimination in selecting the more important prob- lems for actual field work, the others may be covered suf- ficiently by class room discussions. The consistent treatment of errors of surveying receives attention throughout the book. The methods of work both in field and office are designed both to reveal and. as far as possible, to eliminate blunders and errors, and the tests of precision are borrowed from the most rational current practice. The distribution of residual errors falling within the permissible limits likewise receives due consideration. An important innovation in this manual is the liberal use of field note and other forms executed according to the standard required of the student in like work. The nigh PREFACE. value of such samples in developing the student's skill in this important detail of field work has been well estab- lished. It will be seen that the forms are prescribed in liberal number in the earlier stages of the work while the student is engaged in fixing a standard of quality, but that farther on he is required more and more to devise his own forms. A valuable feature of this system is the liberal amount of practice obtained in freehand lettering and tl-e marked effect on the drafting and other kinds of work. It is suggested that the student should be trained to be self-reliant by requiring him to verify his own results be- fore submitting them for criticism. Likewise he should be encouraged to be genuine by placing him on his honor. This somewhat informal guide to field and office methods is issued primarily for the use of the authors' classes, but it is hoped that others ?s well may find it of value in pre- senting principles to the beginner, and in cultivating his spirit and manual skill. December, 1900 W. D. P. M. S. K. SPECIFICATIONS FOR A GOOD ENGINEER. "A good engineer must be of inflexible integrity, sober, truthful, accurate, resolute, discreet, of cool and sound judgment, must have command of his temper, must have courage to resist and repel attempts at intimidation, a firm- ness that is proof against solicitation, flattery or improper bias of any kind, must take an interest in his work, must be energetic, quick to decide, prompt to act, must be fair and impartial as a judge on the bench, must have experi- ence in his work ami in dealing with men, which implies s-cme maturity of years, must have business habits and knowledge of accounts. Men who combine these qualities are not to be picked up every day. Still they can be found. But they are greatly in demand, and when found, they are worth their price; rather they are beyond price, and their value can not be estimated by dollars." CJ> iff $t(irli)>y's Report to tJi<> .)//.v.s-/.v.s- //>/nibh\ and every precau- tion-taken to verify data and results. Unchecked work may always be regarded as doubtful. A discrepancy which is found by the maker in time to be corrected by him before any damage is done is not necessarily discreditable, pro- vided the error is not repeated. However, Jmhitiuil error is not only discreditable but dishonorable as well, and noth- ing except intentional dishonesty injures the reputation of the engineer more quickly or permanently. Consistent Accuracy. The degree of precision sought in the field measurements should be governed strictly by the dictates of common sense and experience. Due considera- tion of the purposes of the survey and of the time available will enable one to avoid extreme precision when ordinary care would suffice, or crudeness when exactness is required, or inconsistency between the degrees of precision observed in the several parts of the survey. It is a very common practice of beginners, and of many experienced engineers as well, to carry calculated results far beyond the consistent exactness. Speed. Cultivate the habit of doing the field work quickly as well as accurately. True skill involves both quantity and quality of results. However, v/hile the habit of rapid work can and should be acquired, the speed at- tempted in any given problem should never be such as to cast doubt upon the results. Slowness due to laziness is intolerable. Familiarity with Instructions. The instructions for 2 GENERAL INSTRUCTIONS. the day's work should be read over carefully, and prelim- inary steps, such as the preparation of field note forms, should be taken so as to save time and make the work in the field as effective as possible. The ability and also the desire to understand and obey instructions are as essential as the skill to execute them. Inferior Instruments. Should a poor instrument or other equipment be assigned, a special effort should be made to secure excellent results. In actual practice, beginners often have to work with defective instruments, but they should never seek, nor are they permitted, to justify poor results by the character of the field equipment. The stu- dent should therefore welcome an occasional opportunity to secure practice with poor instruments. Alternation of Duties. The members of each party should alternate in discharging the several kinds of service involved in the field problems, unless otherwise instructed. Training in the subordinate positions is essential whether the beginner is to occupy them in actual practice or not, for intelligent direction of work demands thorough knowl- edge of all its details. Field Practice Decorum. The decorum of surveying field practice should conform reasonably to that observed in other laboratory work. THE CARE OF FIELD EQUIPMENT. Responsibility. The student is responsible for the prop- er use and safe return of all equipment. All cases of breakage, damage, loss or misplacement must be reported promptly. The equipment should be examined when as- signed and an immediate report made of any injury or de- ficiency, so that responsibility may be properly fixed. PRECAUTIONS. Careful attention to the following practical suggestions will save needless wear to the equip- ment and reduce the danger of accidents to a minimum, besides adding to the quality and speed of the work. Tripod. Inspect the tripod legs and shoes. The leg is of the proper tightness, if when lifted to an elevated posi- FIELD EQUIPMENT. 3 tion it sinks gradually of its own weight. The tripod shoes should be tight and have reasonably sharp points. Setting Up Indoors. In setting up the instrument in- doors press the tripod shoes firmly into the floor, prefer- ably with each point in a crack. Avoid disturbing other instruments in the room. Instrument Case. Handle the instrument gently in re- moving it from and returning it to the case. It is always best to place the hands beneath the leveling base in hand- ling the detached instrument. Considerable patience is sometimes required to close the lid after returning the in- strument. Mounting the Instrument. See that the instrument is securely attached to the tripod before shouldering it. Un- due haste in this particular sometimes results in costly accidents. When screwing the instrument on the tripod head, it should be turned in a reverse direction until a slight jar is felt, indicating that the threads are properly engaged. Sunshade. Always attach the sunshade regardless of the kind of weather. The sunshade is a part of the telescope tube and the adjustment of a delicate instrument may sometimes be affected by its absence. In attaching or re- moving the sunshade or object glass cap, always hold the telescope tube firmly with one hand and with the other twist the shade or cap to the rii/lit to avoid unscrewing the object glass cell. Carrying the Instrument. Do not carry the instru- ment on the shoulder in passing through doors or in climb- ing fences. Before shouldering the instrument, the prin- cipal motions should be slightly clamped; with the transit, clamp the telescope on the line of centers; and with the level, when the telescope is hanging down. In passing through timber with low branches, give special attention to the instrument. Before climbing a fence, set the instru- ment on the opposite side with tripod legs well spread. Setting Up in the Field. When setting up in the field, bring the tripod legs to a firm bearing with the plates ap- proximately level. Give the tripod legs additional spread in windy weather or in places where the instrument may be subject to vibration or other disturbance. On side-hill 4 GENERAL INSTRUCTIONS. work place one leg up hill. With the level, place two tripod shoes on the general direction of the line of levels. Exposure of Instrument. Do not expose the instru- ment to rain or dampness. In threatening weather the waterproof bag should be taken to the field. Should the instrument get wet, wipe it thoroughly dry before return- ing it to the case. Protect the instrument from dust and dirt, and avoid undue exposure to the burning action of the sun. Avoid subjecting it to sudden changes of tempera- ture. In cold weather when bringing an instrument in- doors cover the instrument with the bag or return it to the case immediately to protect the lenses and graduations from condensed moisture. Guarding the Instrument. Never leave an instrument unguarded in exposed situations, such as in pastures, near driveways, or where blasting is in progress. Never leave an instrument standing on its tripod over night in a room. Manipulation of Instrument. Cultivate from the very beginning the habit of delicate manipulation of the instru- ment. Many parts, when once impaired, can never be re- stored to their original condition. Rough and careless treatment of field instruments is characteristic of the un- skilled observer. Should any screw or other part of the in- strument work harshly, call immediate attention to it so that repairs may be made. Delay in such matters is very destructive to the instrument. Foot Screws. In leveling the instrument, the foot screws should be brought just to a snug bearing. If the screws are too loose, the instrument rocks, and accurate work can not be done; if too tight, the instrument is damaged, and the delicacy and accuracy of the observations are reduced. Much needless wear of the foot screws may be avoided if the plates are brought about level when the instrument is set up. With the level, a pair of foot screws should be shifted to the general direction of the back or fore sight before leveling up. Eyepiece. Before beginning the observations, focus the eyepiece perfectly on the cross-hairs. This is best done by holding the note book page, handkerchief, or other white object a foot or so in front of the object glass so as to ilium- FIELD EQUIPMENT. 5 inate the hairs; and then, by means of the eyepiece slide, focus the microscope on a speck of dust on the cross-hairs near the middle of the field. To have the focusing true for natural vision, the eye should be momentarily closed sev- eral times between observations in order to allow the lenses of the eye to assume their normal condition. The omission of this precaution strains the eye and is quite cer- tain to cause parallax. After the eyepiece is focused on the cross-hairs, test for parallax by sighting at a well denned ob- ject and observing whether the cross-hairs seem to move as the eye is shifted slightly. Clamps. Do not overstrain the clamps. In a well de- signed instrument the ears of the clamp screw are purpose- ly made small to prevent such abuse. Find by experiment just how tight to clamp the instrument in order to prevent slipping, and then clamp accordingly. Tangent Screws. Use the tangent screws only for slight motions. To secure even wear the screws should be used equally in all parts of their length. The use of the wrong tangent movement is a fruitful source of error with beginners. Adjusting Screws. Unless the instrument is assigned expressly for adjustment, do not disturb the adjusting screws. Magnetic Needle. -Always lift the needle before should- ering the instrument. Do not permit tampering with the needle. If possible, avoid subjecting the needle to mag- netic influences, such as may exist on a trolley car. Should the needle become reversed in its polarity or require re- magnetization, it may be removed from the instrument and brought into the magnetic field of a dynamo or electric motor for several minutes, the needle being jarred slightly during the exposure; or a good bar or horshoe magnet may be used for the same purpose. The wire coil counterbalance on the needle will usually require shifting after the fore- going process. Lenses. Do not remove or rub the lenses of the tele- scope. Should it be alwiliitcli/ mvi-xxdrii to clean a lens, use a very soft rag with caution to avoid scratching or marring the polished surface. Protect the lenses from flying sand 6 GENERAL INSTRUCTIONS. and dust, which in time seriously affect the definition of the telescope. Plumb Bob. Do not abuse the point of the plumb bob and avoid needless knots in the plumb bob string. Cleaning Tripod Shoes. Remove the surplus soil from the tripod shoes before bringing the instrument indoors. Leveling Rods. Leveling rods and stadia boards should not be leaned against trees or placed where they may fall. Avoid injury to the clamps, target and graduations. Do not mark the graduations with pencil or otherwise. Avoid needless exposure of the rod to moisture or to the sun. Flag Poles. Flag poles should not be unduly strained, and their points should be properly protected. Chains and Tapes. Chains should not be jerked. Avoid kinks in steel tapes, especially during cool weather. When near driveways, in crowded streets, etc., use special care to protect the tape. Band tapes will be done up in 5-foot loops, figure 8 form, unless reels are provided. Etched tapes should be wiped clean and dry at the end of the day's work. Axes and Hatchets. Axes and hatchets will be em- ployed for their legitimate purposes only. Their wanton use in clearing survey lines is forbidden, and their use at all for such purpose on private premises must he governed xtririli/ by the rights of the owner. Stakes. The consumption of stakes should be controlled by reasonable economy. Surplus stakes will be returned to the general store. For the protection of mowing machines in meadows, etc., hub stakes should be driven flush with the surface of the ground, and other stakes should be left high enough to be visible. Whenever practicable, stakes which may endanger machines should be removed after serving the purpose for which they were set. FIELD NOTES. Scope of Field Notes. The notes should be a complete record of each day's work in the field. In addition to the title of the problem and the record of the data observed, the field notes should include the date, weather, organiza- tion of party, equipment used, time devoted to the prob- FIELD NOTES. 7 lem, and any other information which is at all likely to be of service in connection with the problem. No item proper- ly belonging to the notes should be trusted to memory. Should the question arise as to the desirability of any item, it is always safe to include it. The habit of rigid self criti- cism of the field notes should be cultivated. Character of Notes. The field notes should have char- acter and force. As a rule, the general character of the student's work can be judged with considerable certainty by the appearance of his field notes. A first-class page of field notes always commands respect, and tends to estab- lish and stimulate confidence in the recorder. The notes should be arranged systematically. Interpretation of Notes. The field notes should have one and only one reasonable interpretation, and that the correct one. They should be perfectly legible and easily understood by anyone at all familiar with such matters. Original Notes. Each student must keep complete notes of each problem. Field notes must not be taken on loose slips or sheets of paper or in other note books, but the orij/huil record must be put in the prescribed field note book durlnij the i'o'exx of tlie ficlil irork. Field Note Book. The field record must be kept in the prescribed field note book. For ease of identification the name of the owner will be printed in bold letters at the top of the front cover of the field note book. Pencil. To insure permanency all notes will be kept with a hard pencil, preferably a 4H. The pencil should be kept well sharpened and used with sufficient pressure to indent the surface of the paper somewhat. Title Page. An appropriate title page will be printed on the first page of the field note book. Indexing and Cross Referencing. A systematic index of the field notes will be kept on the four pages following the title page. Related notes on different pages will be lib- erally and plainly cross referenced. The pages of the note book will be numbered to facilitate indexing. Methods of Recording Field Notes. There are three general methods of recording field notes, namely, (1) by 8 GENERAL INSTRUCTIONS. sketch, (2) by description or narration, and (3) by tabula- tion. It is not uncommon to combine two or perhaps all three of these methods in the same problem or survey. Form of Notes. All field notes must be recorded in the form below, except where circumstances require modifi- cation. If no form is given, the student will devise one suited to the needs of the particular problem. Lettering. Field notes will be printed habitually in the ''Engineering Nws" style of freehand lettering, as treated in Reinhardt's "Freehand Lettering." The body of the field notes will be recorded in the slanting letter and the head- ings will be made in the upright letter. The former slants to the right 1:2.5 and the so-called upright letter is made to slant to the left slightly, say 1:25. Lower case letters will be used in general, capitals being employed for initials and important words, as required. In the standard field FIELD NOTES. 9 note alphabet the height of lower case letters a, c, e, i, ra, n, etc., is 3-50 (say 1-16) inch, and the height of lower case b, d, t, g, h, etc., and of all capital letters and all numerals is 5-50 (1-10) inch; lower case t is made four units (4-50) inch high. This standard accords with best current prac- tice and is based upon correct economic principles. (See chapter giving discussion of freehand lettering.) The standard field note alphabets are given on the bookmark scale which accompanies this manual. The student is ex- pected to make the most of this opportunity to secure a liberal amount of practice in freehand lettering. Field Note Sketches. Sketches will be used liberally in the notes and will be made in the field. If desired, a ruler may be used in drawing straight lines, but the student is urged to acquire skill at once in making good plain free- hand sketches. The field sketches should be bold and clear, in fair proportion, and of liberal size so as to avoid con- fusion of detail. The exaggeration of certain details in a separate sketch sometimes adds greatly to the clearness of the notes. The sketches should be supplemented by de- scriptive statements when helpful, and important points of the sketch should be lettered for reference. The precise scaling of sketches in the field note book, while sometimes necessary, is usually undesirable owing to the time con- sumed. It is also found that undue attention to the draft- ing of the sketch is very apt to occupy the mind and cause omissions of im'portant numerical data. Since recorded figures and not the size of the field sketch itself must usual- ly be employed in the subsequent use of the notes, it is im- portant to review the record before learing tlie field to detect omissions or inconsistencies. Making sketches on loose sheets or in other books and subsequently copying them into the regular field book is very objectionable practice and will not be permitted in the class work. Copies of field notes or sketches are never as trustworthy as the original record made diiritif/ the progress of the field work. In very rapid surveys where legibility of the original record must perhaps suffer somewhat, it is excellent practice to tran- scribe the notes at once to a neighboring page, thus pre- serving the original rough notes for future reference. The 10. GENERAL INSTRUCTIONS. original has more weight as evidence, but the neat copy made before the notes are "cold" is of great help in inter- preting them. Numerical Data. The record of numerical data should be consistent with the precision of the survey. In obser- vations of the same class a uniform number of decimal places should be recorded. When the fraction in a result is exactly one-half the smallest unit or decimal place to be observed, record the even unit. Careful attention should be given to the legibility of numerals. This is a matter in which the beginner is often very weak. This defect can be corrected best by giving studious attention and practice to both the form and vertical alinement of tabulated numerals. Erasures. Erasures in the field notes will be strictly avoided. Should a figure be incorrectly recorded, it should be crossed out and the correct entry made near by. The neat cancellation of an item in the notes inspires confi- dence, but evidence of an erasure or alteration casts doubt upon their genuineness. When a set of notes becomes so confused that erasure seems desirable, it should be tran- scribed, usually on another page. Rejection of a page of notes should be indicated by a neat cross mark, and cross reference should' be made between the two places. Office Copies. Office copies of field notes will be sub- mitted promptly, as required. These copies must be actual transcripts from the original record contained in the field note book of the individual submitting the copy. When office copies are made, a memorandum of the fact should be entered on the page of the field note book. When so specified, the office copies will be executed in india ink. Criticism of Field Notes. The field notes must be kept in shape for inspection at any time, and be submitted on call. All calculations and reductions must be kept up to date. The points to which chief attention should be direct- ed in the criticism of the field notes are indicated in the following schedule. The student is expected to criticise his own notes and submit them in as perfect condition as pos- sible. For simplicity the criticisms will be indicated by stamping on the note book page the reference letters and numbers shown in the schedule. FIELD NOTES. 11 SCHEDULE OF POINTS FOR THE CRITICISM OF FIELD NOTE BOOKS. A. SUBJECT MATTER. (1) General: (a) Descriptive title of problem. (b) Date. (c) Weather. (d) Organization of party. (e) Equipment used. (f) Time devoted to the problem. (g) Indexing and cross referencing, (h) Page numbering. (i) Title page. (j) Identification of field note book. (2) Record of Data: (a) Accuracy. (b) Completeness. (c) Consistency. (d) Arrangement. (e) Originality. B. EXECUTION. (1) Lettering: (a) Style. ("Engineering News.") (b) Size, (a, c, e, i, etc., 3-50 (say 1-16) inch high; b, d, f, g, etc., A, B, C, etc., and 1, 2, 3, etc., 5-50 (1-10) inch high; t, 4-50 inch.) (c) Slant. (In body of notes, "slanting," 1:2.5 right; in headings, "upright," about 1:25 to left.) (d) Form. (See Reinhardt's "Freehand Lettering.") (e) Spacing. (Of letters in words; of numerals; of words; balancing in column or across page.) (f) Alinement. (Horizontal; vertical.) (g) Permanency. (Use sharp hard pencil with pressure.) (2) Sketches. (a) To be bold, clear and neat. (b) To be ample in amount. (c) To be of liberal size. (d) To be in fair proportion. (e) To be made freehand. (f) To be made in the field. 12 GENERAL INSTRUCTIONS. Importance of Office Work. Capable office men are comparatively rare. Skill in drafting and computing is within the reach of most men who will devote proper time and effort to the work. Men who are skillful in both field and office work have the largest opportunity for advance- ment. Calculations. All calculations and reductions of a per- manent character must be shown in the field note book in the specified form. Cross references between field data and calculations should be shown. Consistency between the precision of computed 1 results and that of the observed data should be maintained. Computed results should be verified habitually, and the verified results indicated by a check mark. Since most computers are prone to repeat the same error, it is desirable in checking calculations to employ in- dependent methods and to follow a different order. A fruitful source of trouble is in the transcript of data, and this should be checked first when reviewing doubtful cal- culations. Skilled computers give much attention to methodical arrangement, and to contracted methods of computing and verifying results. Familiarity with the slide rule and other labor saving devices is important. (See chapter on methods of computing.) Drafting Room Equipment. The student is respon- sible for the proper use and care of drafting room furniture and equipment provided for his use. Drafting. The standard of drafting is that indicated in Reinhardt's "Technic of Mechanical Drafting." Drafting Room Decorum. The decorum of the student in the drafting room will conform to that observed in first- class city drafting offices. CHAPTER II. THE CHAIN AND TAPE. METHODS OF FIELD WORK. Units of Measure. In the United States the foot is used by civil engineers in field measurements Fractions of a foot are expressed decimally, the nearest 0.1 being taken in ordinary surveys, and the nearest 0.01 foot (say 1-8 inch) in more refined work. In railroad and similar "line" surveys in which a station stake is set every 100 feet, the unit of measure is really 100 feet instead of the foot. The term "station" was originally applied only to the actual point indicated by the numbered stake, but it is now universal practice in this country to use the word station in referring to either the point or the 100-foot unit distance. A fractional station is called a "plus" for the reason that a plus sign is used to mark the decimal point for the 100-foot unit, the common decimal point being reserved for fractions of a foot. The initial or starting stake of such a survey is numbered 0. The 100-foot chain is commonly called the "engineers' chain" to distinguish it from the 66-foot or 100-link chain which is termed the "surveyors' chain" because of its special value in land surveys involving acreage. The latter is also called the Gunter chain after its inventor, and is otherwise known as the four-rod or four-pole chain. British engineers use the Gunter chain for both line and land sur- veys. The United States rectangular surveys were made throughout with the 66- foot chain. In the Spanish-American countries the vara is generally used in land surveys. The Castilian vara is 32.8748 inches long, but the state of California has adopted 32.372 inches, and Texas 33 1-3 inches, as the legal length of the vara. While the metric system is used exclusively or in part in each of the several United States government surveys, ex- cept the public land surveys, little or no progress has been made toward its introduction in other than government surveys. 14 THE CHAIN AND TAPE. Linear Measuring Instruments. Two general types of linear measuring devices are used by surveyors, viz., the common chain and the tape. There are several kinds of each, according to the length, material and method of grad- uation. Fig. 1. The common chain is made up of a series of links of wire having loops at the ends and connected by rings so as to afford flexibility. The engineers' chain is shown in (a), Fig. 1. the illustration being that of a 50-foot chain, or one- half the length generally used. The surveyors' or Gunter METHODS OF FIELD WORK. 15 chain is shown in (b), Fig. 1. In the common chain the end graduation is the center of the cross bar of the handle, and every tenth foot or link is marked by a notched brass tag. In the 100-foot or 100-link chain the number of points on the tag indicates the multiple of ten units from the near- er end, and a circular tag marks the middle of the chain. The chain is done up hour glass shape, as shown in the cut. Chaining pins made of steel wire are used in marking the end of the chain or tape in the usual process of linear measurement. A set of pins usually numbers eleven, as indicated at (c), Fig. 1. The pins are carried on a ring made of spring steel wire. The flat steel band, shown in (d) and fe), Fig. 1, is the best form of measuring device for most kinds of work. The band tape is usually 100 feet long. The end graduations of the band tape are usually indicated by brass shoulders, which should point in the same direction, as shown in (f), Fig. 1. The 100-foot band tape is commonly graduated every foot of its length, and the end foot to every 0.1 foot, every fifth foot being numbered on a brass sleeve. Brass rivets are the most common mode of graduating this tape. The band tape may be rolled up on a special reel, as indi- cated in (d) and (e), although some engineers dispense with the reel and do up the tape in the form of the figure 8 in loops of five feet or so. The steel tapes shown in (g) and (h) have etched gradu- ations. This style of tape is commonly graduated to 0.01 foot or 1-8 inch. It is more fragile than the band tape and" is commonly used on more refined work. The form of the case shown in (h) has the advantage of allowing the tape to dry if wound up while damp. The "metallic" tape, (i), Fig. 1, is a woven linen line hav- ing fine brass wire in the warp. The steel tape is superior to the common chain chiefly because of the permanency of its length. The smoothness and lightness of the steel tape are often imporrant advan- tages, although the latter feature may be a serious draw- back at times. The tape is both easier to break and more difficult to mend than the common chain. 16 THE CHAIN AND TAPE. Chaining. In general, the horizontal distance is chained. Two persons, called head and rear chainmen, are required. The usual process is as follows: The line to be chained is first marked with range poles. The head chainman casts the chain out to the rear, and after setting one marking pin at the starting point and checking up the remaining ten pins on his ring, steps briskly to the front. The rear chainman allows the chain to pass through his hands to detect kinks and bent links. Just before the full length is drawn out, the rear chainman calls "halt," at which the head chainman turns, shakes out the chain and straightens it on the true line under the direction of the rear chainman. In order to allow a clear sight ahead, the front chainman should hold the chain handle with a pin in his right hand well away from his body, suporting the right elbow on the right knee, if de- sired. The rear chainman holds the handle in his left hand approximately at the starting point and motions with his right to the head chainman, his signals being distinct both as to direction and amount. Finally, when the straight and taut chain has been brought practically into the true line, the rear chainman, slipping the handle behind the pin at the starting point with his left hand, and steadying the top of the pin with his right, calls out "stick." The head chainman at this instant sets his pin in front of the chain handle and responds "stuck," at which signal and not before the rear chainman pulls the pin. Both now proceed, the rear chainman giving the prelim- inary "halt" signal as he approaches the pin just set by the head chainman. The chain is lined up, stretched, the front pin set, and the rear pin pulled on signal, as described for the first chain length. This process is repeated until the head chainman has set his tenth pin, when he calls "out" or "tally," at which the rear chainman walks ahead, counting his pins as he goes and, if there are ten, transfers them to the head chainman who also checks them up and replaces them on his ring. A similar check in the pins may be made at any time by remembering that the sum, omit- ting the one in the ground, should be ten. This safeguard should be taken often to detect loss of pins. The count of tallies should be carefully kept. METHODS OF FIELD WORK. 17 When the end of the line is reached, the rear chainman steps ahead, and reads the fraction at the pin, noting the units with respect to the brass tags on the chain. The number of pins in the hand of the rear chainman indicates the number of applications of the chain since the starting or last tally point. A like method is used in case inter- mediate points are to be noted along the line. On sloping ground the horizontal distance may be ob- tained either by leveling the chain and plumbing down from the elevated end, or by measuring on the slope and correcting for the inclination. In ordinary work the former is preferred, owing to its simplicity. In "breaking chain" up or down a steep slope, the head chainman first carries the full chain ahead and places it carefully on the true line. A plumb bob, range pole or loaded chaining pin should be used in plumbing the points up or down. The segments of the chain should be in multiples of ten units, as a rule, and the breaking points should be "thumbed" by both chain- men to avoid blunders. Likewise, special caution is re- quired to avoid confusion in the count of pins during this process. The general method of measuring with the band tape is much the same as with the common chain. The chief dif- ference is due to the fact that the handle of the tape extends beyond the end graduation, so that it is more convenient for the head chainman to hold the handle in his left hand and rest his left elbow on his left knee, setting the pin with his right hand. Another difference is in the method of reading fractions. It is best to read the fraction firxf l>u estimation, as with the chain, making sure of the feet; then shifting the tape along one foot, getting an exact decimal record of the fraction by means of the end foot graduated to tenths; the nearest 0.01 foot is estimated, or in especially refined work, read by scale. In railroad and similar line surveys, chaining pins are usually dispensed with and the ends of the chain are indi- cated by numbered stakes. The stake marked corre- sponds to the pin at the starting point, and the station stakes are marked thence according to the number of 100-foot units laid off. 18 THE CHAIN AND TAPE. Perpendiculars. Perpendiculars may be erected and let fall with the chain or tape by the following methods. (a) By the 3:4:5 method, shown in (a). Fig. 2, in which a triangle having sides in the ratio stated, is constructed. (b) By the chord bisection method, shown in (b), Fig. 2, in which a line is passed from the bisecting point of the chord to the center of the circle, or vice \ersa. (c) By the semicircle method, shown in (c), Fig. 2, in which a semicircle is made to contain the required perpen- dicular. The first method corresponds to the use of the triangle in drafting. Good intersections are essential in the second and third methods. Results may be verified either by using another process, or by repeating the same method with the measurements or position reversed, as indicated in (d), Fig. 2. In locating a perpendicular from a remote point, the ratio method shown in (e), Fig. 2, may be used; or a careful trial perpendicular may be erected at a point estimated by plac- ing the heels squarely on line and swinging the arms to the front, then proving by precise method. Fig. 2. METHODS OF FIELD WORK. 19 Parallels. Parallels may be laid off with the chain in various ways, a few of the simpler of which are: (a) By equal distances, as in (a), Fig. 3, in which two equal distances are laid off, usually at right angles to the given line. (b) By similar triangles, as in (b) and (c), Fig. 3. The ratio may, of course, have any value. (c) By alternate angles, as in (d), Fig. 3, in which two equal angles are laid off in alternation. The first method is adapted to laying off a rectangle, as in staking out a building, in which case a good check is found in the equality of the diagonals. Precision of aline- ment is important, especially where a line is prolonged. Angles. Angles may be determined by linear measure- ments in the following ways: (a) By the chord method, shown in (a), Fig. 4, in which the radius is laid off on the two lines forming the angle, and the chord measured. (b) The tangent method, shown in (b), Fig. 4, in which a perpendicular is erected at one end of the radius, and the length of the perpendicular intercepted by the two lines measured. (c) The sine-cosine method, (c), Fig. 4, which is better suited to constructing than to measuring angles. The chord method is usually the most satisfactory. The tangent method may be applied to the bisected angle when its value approaches a right angle. Measurement of the supplementary angle affords an excellent check. A 100-foot radius is commonly used, although good results may be had with the 50-foot tape. Careful alinement is of the first im- portance in angular measurements. It is sometimes necessary to determine angles, at least approximately, when no tables are at hand. Fair results may be had on smooth ground by measuring the actual arc struck off to a radius of 57.3 feet. For very small angles, the sine, chord, arc and tangent, (d), Fig. 4, are practically equal. Thus, sin 1 is .017452 and tan 1, .017455, or either (say) .01745, or 1% per cent. Also, arc 1' is .000291, or (say) .0003 (three zeros three); and, arc 1" is .00000485, (say) .000005 (five zeros five). 20 THE CHAIN AND TAPE. Location of Points. Points are located in surveying field practice in the following seven ways. (a) By rectangular coordinates, that is, by measuring the perpendicular distance from the required point to a given line, and the distance thence along the line to a given point, as in (a), Fig. 5. (b) By focal coordinates or tie lines, that is, by meas- uring the distances from the required point to two given points, as in (b), Fig. 5. (c) By polar coordinates, that is, by measuring the angle between a given line and a line drawn from any given point of it to the required point; and also the length of this latter line, as in (c), Fig. 5. (d) By modified polar coordinates, that is, by a distance from one known point and a direction from another, as in (d), Fig. 5. (e) By angular intersection, that is, by measuring the angles made with a given line by two other lines starting from given points upon it, and passing through the re- quired point, as in (e), Fig. 5. (f) By resection, that is, by measuring the angles made with each other by three lines of sight passing from the required point to three points, whose positions are known, as in (f), Fig. 5. (g) By diagonal intersection, that is, by two lines joining two pairs of points so as to intersect in the required point, as in (g), Fig. 5. Fig. 5, METHODS OP FIELD WORK. In each of these methods, except (f), the point is deter- mined by the intersection of either two right lines, or two circles, or a right line and a circle. Methods (a) and (b) are best suited to chain surveys; (c) and (d) are used 1 most in the location of railroad curves; (e) and (f) are employed chiefly in river and ma- rine surveys for the location of soundings, the latter being commonly known as the "three-point problem;" the last method, (g), is much used for "referencing out" transit points in railroad and similar construction surveys. Location of Objects. The location of buildings and topographic objects usually involves one or more of the foregoing methods of locating a point. In Fig. 6, (a), (b), (c), and (d) suggest methods of locat- ing a simple form, and (e) and (f) illustrate more complex cases. Tie Line Surveys. For many purposes tie line surveys, made with the chain or tape alone, are very satisfactory. The skeleton of such surveys is usually the triangle, the detail being filled in by the methods just outlined. Much time may be saved by carefully planning the survey. A few typical applications of the tie line method are shown in Fig. 7. JLJLJL HOC 22 THE CHAIN AND TAPE. Ranging in Lines. The range or flag pole is usually painted with alternate feet red and white, and the lower end is shod or spiked. A temporary form of range pole, called a picket, is sometimes cut from straight sapplings. In flagging a point, the spike of the pole is placed on the tack and the pole plumbed by holding it symmetrically be- tween the tips of the fingers of the two hands, the flagman being squarely behind the pole. In hilly or timbered country the two land corners or other points between which it is desired to range in a line, are often invisible one from the other. In many cases two in- termediate points C' and D', (a), Fig. 8, may be found, from which the end points B and A, respectively, are visible; so that after a few successive linings in, each by the ather, the true points, C and D, are found. Otherwise, as shown at (b), Fig. 8, a random line may be run from A towards B. The trial line is chained and marked, the perpendicular from B located, and points inter- polated on the true line. If the desired line is occupied by a hedge or other ob- struction, an auxiliary parallel line may be established in the adjacent road or field, after one or two trials, as in (c), Fig. 8. A line may be prolonged past an obstacle by rectangular offsets or by equilateral triangles. Fig. 8. Fig. 9. Signals. There is little occasion for shouting in survey- ing field work if a proper system of sight signals is used. Each signal should have but one meaning and that a per- fectly distinct one. Signals indicating motion should at METHODS OF FIELD WORK. 23 once show clearly both the direction and amount of motion desired. Some of the signals in common use are as follows: (a) "Right" or "left," the arm is extended distinctly in the desired direction and the motion of the forearm and hand is graduated to suit the lateral motion required. (b) "Up" or "down," the arm is extended laterally and raised or lowered distinctly with motions to suit the magni- tude of the movement desired. Some levelers use the left arm for the "up" signal and the right for "down." (c) "Plumb the pole (or rod)," if to the right, that arm is held vertically with hand extended and the entire body, arm included, is swung distinctly to the right, or vice versa. (d) "All right," both arms are extended full length hori- zontally and waved vertically. (e) "Turning point" or "transit point," the arm is swung slowly about the head. (f) "Give line," the flagman extends both arms upward, holding the flag pole horizontally, ending with the pole in its vertical position. If a precise or tack point is meant, the signal is made quicker and sharper. (g) Numerals are usually made by counted vertical swings with the arm extended laterally. A station number is given with the right hand and the plus, if any, with the left; or a rod reading in like manner. The successive counts are separated by a momentary pause, emphasized, if desired, by a slight swing with both hands. Stakes and Stake Driving. A flat stake is used to mark the stations in a line survey, and a square stake or hub to mark transit stations, (a) and (b), Fig. 9. The station stake is numbered on the rear face, and the hub is witnessed by a flat guard stake driven slanting 10 inches or so to the left, Fig. 9. The numerals should be bold and distinct, and made with keel or waterproof crayon, pressed into the surface of the wood. , Having located a point approximately with the flag pole, the stake should be driven truly plumb in order that the final point may fall near the center of its top. In driving a stake, the axeman should watch for signals. It is better to draw the stake by a slanting blow than to hammer the stake over after it is driven. Good stake drivers are scarce. 24 THE CHAIN AND TAPE. PROBLEMS WITH THE CHAIN AND TAPE. General Statement. Each problem is stated under the following heads: (a) Equipment. In which are specified the articles and in- struments assigned or required for the proper performance of the problem. A copy each of this manual and of the regulation field note book, with a hard pencil to keep the record, form part of the equipment for every problem as- signed. (b) Problem. In which the problem is stated in general terms. The special assignments will be made by program. (c) MethiHlK. In which the methods to be used in the as- signed work are described more or less in detail. In some problems alternative methods are suggested, and in others the student is left to devise his own. PROBLEM Al. LENGTH OF PACE. (a) Equipment. (No instrumental equipment required.) (b) Problem Investigate the length of pace as follows: (1) the natural pace; (2) an assumed pace of 3 feet; and (3) the effect of speed on the length of the pace. (c) Method*. (1) On an assigned course of known length count the paces while walking at the natural rate. Observe the nearest 0.1 pace in the fraction at the end of the course. Secure ten consecutive results, with no rejections, varying not more than 2 per cent. (2) Repeat (1) for an assumed 3-foot pace. (3) Observe in duplicate time and paces for four or five rates from very slow to very fast, with paces to nearest 0.1 and time to nearest second. Record data and make reductions as in form opposite. PROBLEM A2. DISTANCES BY PACING. (a) Equipment. (No instrumental equipment required.) (b) Problem. Pace the assigned distances. (c) .VHIifdH. (1) Standarize the pace in duplicate on measured base. (2) Pace each line in duplicate, results dif- fering not more than 2 per cent. Record and reduce as in form. PROBLEMS. 25 26. THE CHAIN AND TAPE. PROBLEM A3. AXEMAN AND FLAGMAN PRACTICE. (a) Equipment. Flag pole, axe, 4 flat stakes, 1 hub, tacks. (b) Problem. Practice the correct routine duties of axe- man and flagman. (c) Method*. (1) Number three station stakes to indicate representative cases and drive them properly. (2) Drive a hub flush with ground and tack it; number a witness stake and drive it properly. (3) Arrange program of signals with partner, separate l.OCO feet or so and practice same. (4) Signal say five station numbers to each other and after- wards compare notes. Make concise record of the fore- going steps. " PROBLEM A4. RANGE POLE PRACTICE. (a) Equipment. 4 flag poles. (b) Problem. Given two hubs 1.000 feet or so apart, inter- polate a flag pole say 100 feet from one hub, remove the dis- tant pole, prolong the line by successive 100-foot sights and note the error at distant hub. Repeat process for 200-foot and 300-foot sights. (c) Method* (1) Set distant flag pole precisely behind hub and hold spike of pole on tack of near hub; lying on ground back of near hub, line in pole 100 feet (paced) dis- tant; remove pole from distant hub, and prolong by 100 -foot sights up to distant hub, noting error to nearest 0.01 foot. (2) Repeat in reverse direction, using 200-foot sights. (3) Repeat with 300-foot sights. Avoid all bias. Record data in suitable form, describing steps concisely. PROBLEM A5. STANDARDIZING CHAIN OR TAPE. (a) Ei/nipment. Chain or tape assigned in any problem where standard length of chain may be of value. (b) Problem. Determine the length of the assigned chain or tape by comparison with the official standard under the conditions of actual use. (c) Method*. In standardizing tape, reproduce the condi- tions of actual use as regards tension, support, etc., bring PROBLEMS. 27 one end graduation of chain or tape to coincide with one standard mark, and observe fraction at the other end with a scale. As a general rule, observe one more decimal place than is taken in the actual chaining. PROBLEM A6. DISTANCES WITH SURVEYORS' CHAIN. (a) Etiu'tpinetit. Surveyors' chain set of chaining pins, 2 plumb bobs, 2 flag poles, (unless instructed otherwise). (b) PruMnn.Qn an assigned chaining course about one mile long measure distances with the surveyors' chain to the nearest 0.1 link, and repeat the measurements in the opposite direction. (c) MrtlHKlx.d) Standardarize the chain before and after as prescribed in A5. (2) Chain along the assigned course, noting the distances from the starting point to the several intermediate points and to the end station. Observe frac- tions to the nearest 0.1 link by estimation. (3) Repeat the chaining in the opposite direction, noting the distances from the end point, as before. The difference between the totals J27 30 JOt eojs. " \ ! T. ./., c~- 'A; tty*,- II 28 THE CHAIN AND TAPE. in the two directions should not exceed 1:5,000. Retain the same party organization throughout the problem. Record the data as in the prescribed form. PROBLEM A7. DISTANCES WITH THE ENGINEERS- CHAIN. (a) Equipment. Engineers' chain, set of chaining pins, 2 plumb bobs, 2 flag poles (unless instructed otherwise.) (b) Problem. On an assigned chaining course about cne mile long measure distances with the engineers' chain to the nearest 0.1 foot, and repeat the measurements in the op- posite direction. (c) Method*. (I) Standardize the chain before and after, as prescribed in A5. (2) Chain along the assigned course, noting the distances from the starting point to the several intermediate points and to the end station. Observe frac- tions to the nearest 0.1 foot by estimation. (3) Repeat the chaining in the opposite direction, noting the distances from the end point, as before. The difference between the totals in the two directions should not exceed 1:5,000. Retain the same party organization throughout the problem. Record the data as in the form opposite. PROBLEM A8. DISTANCES WITH 100-FOOT STEEL TAPE. (a) Equipment. 100-foot steel band tape with end foot graduated to tenths, set of chaining pins, 2 plumb bobs, 2' flag poles, (unless instructed otherwise). (b) Problem. On an assigned chaining course about one mile long measure distances with the 100-foot steel band tape to the nearest 0.01 foot, and repeat the measurements in the opposite direction. (c) Methods. (1) Standardize before and after, as pre- scribed in A5. (2) Chain along the assigned course, noting the distances from the starting point to the several inter- mediate points and to the end station. In observing the fractions, first determine the foot units, then estimate the nearest 0.1 foot, then shift the tape along one foot and read the exact fraction on the end of the tape, estimating the PROBLEMS. 100.10 /00./Z t**a J7+.J iA* -4 ENGINEERS' C /O0-Ft CA** Ao J ( Loc#*r /Yo.JS. l i '-t f"' ''' 1 II 1 cm A *o, B,C,0 1-( 30. THE CHAIN AND TAPE. nearest 0.01 foot. (3) Repeat the measurement in the oppo- site direction, noting the distances from the end point, as before. The difference between the totals in the two direc- tions should not exceed 1:10,000. Retain the same party organization. Record data as in form. PROBLEM A9. HORIZONTAL DISTANCE ON SLOPE WITH STEEL TAPE. (a) Equipment 100-foot steel tape with etched gradua- tions to 0.01 foot, set of chaining pins, 2 plumb bobs, 3 flag poles, axe, supply of pegs, engineers' level and rod, (unless otherwise instructed). (b) Problem. Determine the horizontal distance between two assigned points on a steep slope, (1) by direct horizon- tal measurement, and (2) by measurement on the slope and reduction to the horizontal. (c) Method*. (I) Standardize the tape for each method, as prescribed in A5, both before and after the day's chain- ing. (2) In chaining down hill, rear c1in(lH.(l) Measure each angle with the steel tape by both the chord and tangent methods, 100-foot radius, the difference in the two results not to exceed 2 minutes. If the angle is near 90, the tangent method may be applied to the bisected angle. (2) After securing satisfactory check on an angle with the steel tape, make a rapid but careful measurement with the metallic tape, radius 50 feet. The results may be taken to the nearest half minute. (3) Meas- ure at least one angle, preferably on smooth ground, by lay- ing out an arc with radius of 57.3 feet, setting pins every few feet, and measuring the actual arc. Give close attention to alinement throughout. Record data and make reductions as in form on preceding page. PROBLEM All. SURVEY OF FIELD WITH STEEL TAPE. (a) Eiiiciit. 100-foot steel tape, set of chaining pins, 2 plumb bobs, 4 flag poles, five-place table of functions. (b) Problem Make survey of an assigned field with tape, collecting all data required for plotting the field and calcu- lating its area by the "perpendicular," "three-side," and "angle" methods. (c) .VetJitMl*. Standardize the tape once. (2) Examine the field carefully and plan the survey. (3) Measure the re- quired angles with tape. (4) Locate the perpendiculars. (5) Chain all necessary lines, and also take distances to feet of perpendiculars. Follow form. PROBLEM A12. AREA OF FIELD BY PERPENDICULAR METHOD. (a) Ei<'nt. Five-place table of logarithms. (b) Problem Calculate the area of the assigned field by PROBLEMS m = OOOOOHSS63C, *<. A-B-C-0-E, PERPtr- ICULAR METHOD. o. /fl^e 34 THE CHAIN AND TAPE. the perpendicular method, using the data collected in Problem All. (c) Methuds. (1) Prepare form for calculation; transcribe data, and carefully verify transcript. (2) Calculate double areas of the several triangles by contracted multiplication, perpendicular method, preserving a consistent degree of precision. (3) Make the same calculations with logarithms, as a check. (4) Combine the verified results, as shown in form. PROBLEM A13. AREA OF FIELD BY THREE-SIDE METHOD. (a) Equipment. Five-place table of logarithms. (b) Problem. Calculate the area of the assigned field by the three-side method. (c) Mettled*. (1) Prepare form for calculation; tran- scribe data, and carefully verify transcript. (2) Calculate the areas of the several triangles by logarithms, three-side method preserving proper units in the results. (3) Carefully review the calculations, and combine the verified results, as in the form opposite. PROBLEM A14. AREA OF FIELD BY ANGLE METHOD. (a) Equipment. Five-place table of logarithms. (b) Problem. Calculate the area of the assigned field by the "two sides and included angle" method, using the data collected in All. (c) Me11inds. (\) Prepare form, transcribe data, and ver- ify copy. (2) Calculate the double areas of the several tri- angles by contracted multiplication, angle method, preserv- ing consistent accuracy in results. (3) Make same calcula- tions by logarithms, as a check. (4) Combine the checked results. Follow the form opposite. PROBLEM A15. AREA OF FIELD FROM PLAT. (a) Equipment. Drafting instruments, papar. etc.. pla- nimeter, (as assigned). (b) PrrMfin. Determine the area of the assigned field directly from the plat. PROBLEMS. 36 X t%'." l f ^'-"-r. ni"f t ?** CO Tr.,1.. Si TION (s-bJ S-C) ir.oof Tr.or^l. A,., t LiM* L.-,* fo.b-c) VsCS-o^s-bKi-cJ Ft. Ft. Ft. Ft L*^arlthm*. Sf Ft ABE A6-a JJ676 Soiil 2 .7OO8S /\ BC- e 4ZS6+ /6S+6 Z .2/369 7 \ CA.l !"*+ 76 Jt i.aetse ^ e ^ 2 1 i tOO++4 z ^S +O65O ^ BDE BO'. ijaet 7+O.4J 2 869SZ /^fl.; Df-t 6/6 SJ 301 aa I 47fJ EO'<- *2 S&f- IIJJS a *jza 4 !+ lcs *. "" ^ ' *^J * S702J 33300 BCD flc-o 4S*S 6fJ66 z et/,f CO -t +9J7^ 22860 t 3SSZ3 OAml +JS6' 1039* 2 J22/0 i^ /387J/ 133. OS 1_066J_ osjee 2) * 9 ^ s 92/60 44111J- i rlyjS ^"jr S.ll>J*c. V 36 THE CHAIN AND TAPE. (c) Methods. (I) Make an accurate plat of the field from the notes secured in All, using a prescribed scale. (2) De- termine the area of the field by resolving the polygon into an equivalent triangle. (3) Determine the area from the plat by the polar planimeter and by one of the following "home-made" planimeters: "bird shot" planimeter, "jack knife" planimeter, cross-section paper, parallel strip, weigh- ing, etc. (4) Prepare on the plat a tabulated comparison of results secured by the several methods. (5) Finish the plat, as required. PROBLEM A16. SURVEY OF FIELD WITH CURVED BOUNDARY. (a) Equipment. 100-foot tape, 50-foot metallic tape, set of chaining pins, 2 plumb bobs, 4 flag poles. (b) Problem-. Make survey with tape of an assigned tract having a curved boundary, collecting all data required for plotting the field and calculating its area. (c) Methods. (1) Standarize the tape once to nearest 0.01 foot. (2) Examine the tract carefully and plan the survey so as to secure a simple layout of base lines designed to give short offsets to the curved boundaries. (3) Locate the per- pendiculars, if any, and chain all lines; on the curved sides, take offsets so as to secure a definite location, and as a rule take equal intervals on the same line. Follow the form opposite. PROBLEM A17. AREA OF FIELD WITH CURVED BOUNDARY. (a) Equipment. (No instrumental equipment required). (b) Problem. Calculate the area of the assigned field with curved boundary by "Simpson's one-third rule", using the data collected in Problem A16. (c) Methods (1) Prepare form for calculation; transcribe data in convenient form for calculation, and carefully check copy. (2) Calculate the area of the polygon formed by the base lines, preferably by the perpendicular method. (3) Calculate the areas of the curved figures by "Simpson's one- PROBLEMS. 210981 38 THE CHAIN AND TAPE third rule," which is as follows: "Divide the base line into an even number of equal parts and erect ordinates at the sum by one-third of the common distance between ordi- nates, twice the sum of all the other odd ordinates, and four times the sum of all the even ordinates; multiply the sum by one-third of the common distance between ordi nates." The field notes might have been taken with special reference to the rule, but it is better to take from the notes the largest even number of equal segments, assuming the re- maining portion to be a trapezoid or triangle. (4) Give signs to the several results by reference to the field sketch, and combine them algebraically to get the net area, as shown in the accompanying form. PROBLEM A18. AREA OF FIELD WITH CURVED BOUNDARY FROM PLAT. (a) Equipment. Drafting instruments, paper, etc., pla- nimeter (as assigned). (b) Problem. Determine the area of the field with curved boundary directly from the plat. (c) Methods. (1) Make an accurate plat of the field from the notes obtained in A16, using a prescribed scale. (2) Determine its area directly from plat by two methods men- tioned in (3) of A15, other than those used in that problem. (3) Prepare on the plat a tabulated comparison oi' the re- sults by the several methods. (4) Finish the plat, as re- quired. PROBLEM A19. PASSING AN OBSTACLE WITH TAPE. (a) Equipment. 100-foot steel tape, set of chaining pins, plumb bobs, 4 flag poles. (b) Problem. Prolong an assigned line through an as- sumed obstacle by one method and prove by another, finally checking on a precise point previously established. (c) Methods. Given two hubs, A and B, 200 feet apart, prolong line and establish C 200 feet from B: (1) by con- structing a 200-foot square in one direction; and (2) by lay- ing off a 200-foot equilateral triangle on the opposite side, using pins to mark points thus established. (3) Prolong the PROBLEMS. e/Ktea point C rX'Oj* from A ana B, G , ff., and 6/Jtcted CA of O and C3 at . Caainea OE. Tnen calculated AS ot.rt/a/ meaj'/nt 40 THE CHAIN AND TAPE line by each method to the hub D, 200 feet from C, and record discrepancies in line. (4) Interpolate a point at C on tme line between B and D, and note errors of prolonga- tion at C. Record as in form. PROBLEM A20. OBSTRUCTED DISTANCE WITH TAPE. (a) Equipment. 100-foot steel tape, set of chaining pins, 2 plumb bobs, 4 flag poles. (b) Problem. Determine the distance between two as- signed points through an assumed obstruction to both vis- ion and measurement, using two independent methods, and finally chaining the actual distance. (c) Methods. (1) Standardize the tape. (2) Determine the distance between the assigned points by constructing a line parallel to the given line, and equal or bearing a known relation to it. (3) Secure a second result by running a random line from one hub past the other so that a per- pendicular less than 100 feet long may be let fall, measur- ing the two sides and calculating the hypothenuse. (4) After securing two results differing by not more than 1:1,000, chain the actual distance. Follow form. PROBLEM A21. RUNNING IN CURVE WITH TAPE. (a) Equipment. 100-foot steel tape, 50-foot metallic tape, set of chaining pins, 2 plumb bobs, 3 hubs, 6 flat stakes, marking crayon, tacks, five-place table of functions. (b) Problem. Lay out two lines making an assigned angle with each other, and connect them with a prescribed curve by the "chord offset" method. (c) Methods. (1) Calculate the radius, R, for the given degree of curve, D. (2) Calculate the tangent distance, T, for the given radius, R, and angle of intersection, I. (3) Calcu- late the chord offset, d, and tangent offset, t, for the known radius, R, chord, c and degree, D. (4) At the given point intersection (P. I.), A, lay off the given angle, /, by the chord method. (5) From the P. I. lay off T along the two tangent lines and locate point tangent (P. T.) and point curve (P. C.), setting hubs at P. C. and P. T., with guard stake at each hub. (6) Run in the curve, by chord offsets, PROBLEMS. 41 LOCATION OF CURVE <,. (incur,.) C/.ar and <. 100-FrStrtl Toft /Va.Jfl, Lot/Mr 3S - /OO.'OO Gf'vtft flub at A and a dis tant rtvb ff, to /ay off a lint AC maHing an ano/f I of SO" uH, BA preHmjtd, and et^tcf Mt jubrinatd Ay a lOO-ft Chora*, c. Ihard of on arc it r,ct tnr tint of naif tat art, c/>trt>= i r**X Smf D 7 ~" = - fane fit of '/j fane 9 (f.rj. Bryan at PC ana ran i j/m,a M sxttn. frrer of P.T waj i //. l/n, and ai m a u* c 1 :.;:. : DISCU SION or EI a.., RORS Cuf.oT WITH nwi. TATC; rt tHSI <'V- ( .11 CJ FT. Dl'ton t fe, jita^ JE. C-/( a-c suits s,,,.. { >- -rtf.il -C 3l7f7t "-e 'Mt ,,,,l, / B-0 IfClll , e -D /Z8\63 X-^ _+t4.5O A-C 1 003. 79 B-l e-g c-e + 7ff.9f -oot\ l*78ti*0 eeoeens -D /^*7tf/ Jt-C 1063.79^ A-O 3991.69 o-t w. Jlff.fi e7.7i too -ft- -003 ' -*.t+ f = e\ 1 49SCC L or D ., r f ff.Otf im- s-* Dttignaring E + and W- f-afh Co/vmn) if f's seen f/rar tfa rffarnma rttvfrs frxceff Ct>} are yrtaftr, Th* /'. - ffint, t r st.n..rd Twp, /en.thi, */*.. Effort = /OO.Otf f af-r?r*/OO.OO&, 'f. fne tapt grajv**// dcireaSHt in length, cauainj yrtfrrr attrrvfi/ ftngtha. ^/ 42 THE CHAIN AND TAPE. beginning at P. C. and checking at P. T. Calling P. C. Station 0, establish Station 1 by laying off tangent offset, t, and chord, c. Having one station on the curve, the next is located by prolonging the chord and forming an isosceles triangle having the chord offset as a base. Check on the P. T., noting the discrepancy of distance and line. Also establish the tangent again by tangent offset and observe the error of line. Follow form. PROBLEM A22. DISCUSSION OF ERRORS OF CHAINING. (a) Equipment. (No instrumental equipment, unless further data are desired, in which case Problems A6, A7 and A8 may be assigned again). (bj Problem. Investigate the errors of linear measure- ment with the several kinds of chains and tape, with the view to determine practical working tests or coefficients of precision for actual use. (c) Methods. Assume that the conditions in Problems A6, A7 and A8 are practically constant in the same problem, and that the actual differences between observed lengths of the several segments when chained in opposite direc- tions, represent the normal errors with the particular chain and chainmen; then tabulate: (1) the measured lengths of all rossible segments of the chaining course, either from direct observation or by subtraction; (2) the actual errors or dif- ferences between the two results, giving signs; (3) the chaining ratios, l:d, and the decimal expressions of the same to six places; (4) the "coefficients of precision" for each case, calculated by formula, or more quickly, taken from the diagram in the chapter on errors of surveying; (5) the mean decimal chaining ratio and its equivalent; and (6) the mean coefficient of precision. Follow the prescribed form. PROBLEM A23. TESTING (OR ESTABLISHING) AN OF- FICIAL STANDARD OF LENGTH. (a) Equipment. Standard tape (with certified length given), turnbuckle adjustments with bolts, spring balance, standard steel rule graduated to 0.01 inch, 2 thermometers, PROBLEMS. 2 microscopes, strips of wood, a watch. (b) P roll f HI Make a series of ten observations with a standardized steel tape for the purpose of testing (or estab- lishing) an official standard of length, observing the near- est 0.0001 foot. (c) UetJtods. (If a neir offical standard is being estab- lished, one standard mark may be made permanent, and the precise distance taken to an approximate temporary point on the other bolt, the exact correction being applied after a sufficient number of results have been obtained. If the sun is shining, the tape should be protected by a wooden box or other covering throughout its length. Cloudy days or night time give best results. The observations should be made briskly so as to have slight range of temperature. If isolated standard monuments are used, their foundation should go below frost line, and the monuments should be located so as to suffer as little as possible from heaving. If the standard marks are indoors, the conditions are less difficult to control). (1) Arrange "bucksaw" or turnbuckle adjustments, each held firmly by a bolt dropped into a piece of gaspipe driven 44 THE CHAIN AND TAPE. flush with surface of ground, with spring balance and tape lined up, as shown in sketch in accompanying form; place the two thermometers at the one-third points as nearly as possible under the actual conditions of the tape. (2) With four men in party, No. 1 sets end graduation precisely at one standard mark by means of screw adjustments and mi- croscope; No. 2 sets balance at 12 pounds; No. 3 obseives fraction at other standard mark by means of steel scale graduated to 0.01 inch, estimating to nearest 0.001 inch (say 0.0001 foot) by microscope; and No. 4 records all data, ob- serves time to nearest minute, and temperature to nearest 0.1 degree. Nos. 1, 2 and 3 should lie flat. Release the ten- sion between observations. Record and reduce as in form. PROBLEM A24. DETERMINATION OF CONSTANTS OF A STEEL TAPE. (a) Equipment. Steel tape and other articles named in preceding problem. (b) Problem. Determine coefficients of expansion and stretch of the assigned tape. (c) Metliods.^(To be devised by the student.) PROBLEM A25. COMPARISON OF DIFFERENT MAKES AND TYPES OF CHAINS AND TAPES. (a) Equipment. Department equipment and collection of catalogs of representative instrument makers. (b) Problem. Make a critical comparison of the several types of chains and tapes made by different makers. (c) Methods. Study the different catalogs and prepare a systematic and concise report. CHAPTER III. THE COMPASS. Description. The magnetic compass consists of a line of sight attached to a graduated circular box, at the center of which is a magnetic needle supported on a steel pivot. The compass box is attached to a tripod or Jacob staff by a ball and socket joint, and is leveled by means of the plate levels. The needle should be strongly magnetized and have an agate cap to receive the point of the hardened steel pivot. The dip of the needle is counter-balanced by a small coil of wire, which can be shifted as desired. The E and W points are reversed. In Fig. 10 are shown the usual types of magnetic com- passes: (a) the vernier compass; (b) the plain compass; (c) the vernier pocket compass with folding sights; (d) the ordinary pocket compass; (e) the prismatic compass. Fig. 10. 46 THE COMPASS. Declination of the Needle. If the needle is allowed to swing freely, its magnetic axis will come to rest in the magnetic meridian. The horizontal angle between the mag- netic meridian and the true meridian at any point is called the magnetic declination for that point. Imaginary lines joining points on the earth's surface having the same declination are called isoyonic lines. The isogonic line join- ing the points of zero declination is called the (ninnic line. Fig. 12 is an isogonic chart of the entire earth's surface. Of the three isogonic lines, one passes through Michigan, Ohio, etc. Diagram of Secular Variation of the MAGNETIC DECLINATION IN UNITED STATES. Diagram or DAILY VARIATION of the MAGNETIC DECLINATION, Northern United States DECLINATION OF THE NEEDLE. 47 Variation of the Declination. The declination of the needle is not a constant at any place. The change or fluctuation is called the rarkitiun of the declination. The variations of the magnetic needle are of several kinds: secular, daily, annual, lunar, and irregular variations due to magnetic storms. The most important of these is the secular variation which is illustrated in the uppsr diagram 48 THE COMPASS. of Fig. 11 for a series of representative points in the United States. This diagram shows that the extreme range or swing of the needle is roughly 6 or T , and that the period of time between extreme positions is about a century and a half. Also that the wave of magnetic influence progresses across the continent alike in successive cycles. At present (1900) the needle is at its extreme western position at East- port, Me., and at its extreme eastern pointing at San Diego, Cal. The 3" East isogonic line now passes through western Indiana, and is moving westward at the rate of about 4' per year. This rate of change is general throughout the central part of the United States, and is represented by the straight sections of the curve in the upper diagram of Fig. 11. The daily variation of the magnetic declination is shown graphically in the lower part of Fig. 11, the scale being greatly magnified laterally. It is seen that the needle un- dergoes each day a vibration similar in a general way to the grand swing of three centuries or so shown in the upper diagram. The magnitude of the daily movement in north- ern United States ranges from 5' in winter to neany 12' in summer time. The needle is in its mean daily position between 10 and 11 a. m. for all seasons. The diagram rep- resents the normal magnetic day, of which there are per- haps five or six per month. Local Attraction. The pointing of the needle is af- fected by the close proximity of magnetic substances, such Fig. 13. USE OF THE COMPASS. 49 as iron ore, wire fences, railroad rails, etc. However, local attraction does not prevent correct work, provided back and fore sights are taken without change of magnetic condi- tions. It is therefore especially important to avoid disturb- ances of the needle by the chain, axe, passing vehicles, elec- tric wires, etc., or by articles on the person of the observer, such as keys, knife, spectacle frame, wire in the hat rim, reading glass case, etc. Also the glass cover may become electrified by friction and attract the needle, in which case it may be discharged with the moistened finger, or by breathing on it. The Vernier. The vernier is. an auxiliary scale used to read fractional parts of the divisions of the main scale or 1'mb . Verniers are retrograde or direct, according as the divisions on the vernier are larger or smaller than those on the limb. The vernier used on compasses for the setting off of the declination is direct, and is usually of the type shown in (c) of Fig. 13. In reading a vernier of any kind, blunders may be avoided by first estimating the fraction by eye be- fore noting the matched lines on the two scales. USE- OF THE COMPASS. Use. The compass is used: (1) to determine the bear- ings of lines; (2) to measure the angle formed by two lines; (3) to retrace old lines. The bearing of a line is the hori- zontal angle between the line and a meridian through one end of it. Bearings are measured from the north or south point 90 each way. The angle between two lines is th* difference in their directions as indicated by the bearings Having the true bearings of one side of a polygon, the tru, 1. tarings of the others may be obtained by algebraic addi- t'on of the angles; or by using the declination vernier so a# lo read the true bearing direct on the fore sights. Practical Hints. Point the north end of the compass box along the line and read the north end of the needle. Protect the pivot from needless wear by turning the needle in about the proper direction before releasing it. Always lift the needle before disturbing the compass. Habitually obtain duplicate needle readings on each sighting. Read the needle by estimation to the nearest five minutes, that is, to the one-sixth part of one-half degree, which is the CO THE COMPASS. usual subdivision of the compass box. Care should be taken to avoid parallax in reading the needle. ADJUSTMENTS AND TESTS. Elementary Lines. The elem<"ntarn lines of the compass, shown in (a) of Fig. 10, are: (1) the line of sight; (2) the vertical axis; (3) the plate level lines. The maker should see: (1) that the needle is strongly magnetized; (2) that the magnetic axis corresponds with the line joining the two ends; (3) that the metal in the com- pass box is non-magnetic; (4) that the line of sights passes through the center of graduation; (5) that the plates are perpendicular to the vertical axis; (6) that the zero of the vernier coincides with the line of sights. The needle may be magnetized with a bar magnet or by putting it into the magnetic field of a dynamo. The metal of the compass box may be tested by reading the needle, then moving the vernier and noting if the needle has moved the same amount, this process being repeated at. intervals around the full circle. The Principle of Reversion. In adjusting surveying instruments, the presence, direction 'and amount of the er- ror are made evident by the method of rcrerfionx which doubles the apparent error. If there is no difference after reversion, there is no error. Plate Levels. To make the plane of flic plate lerel line* Iterpemlieiilar to tlte vertical axis. Level up the instrument by means of the plate levels and reverse the compass box in azimuth, that is, turn it through a horizontal angle of 180. Correct one-half the error, if any, by means of the adjusting screws at the end of the level tube, and bring the bubble to the center by the ball and socket joint. The rea- sons for this process are shown in (a) of Fig. 13. Sights. To make the. plane of sigJits normal to tin- pl