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- //>/</ fierce
CHAPTER I.
GENERAL INSTRUCTIONS.
FIELD WORK.
Habitual Correctness. Habitual correctness is a duty.
Error should be looked upon as i>nib<il>h\ 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<j>'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 c1i<iir>n<in lines in flag
pole in hand of head chainman, then holds tape end to tack
on hub; flnymnn stands 50 feet or more from line opposite
middle of tape and directs head chainman in leveling front
end, then supports middle point of tape under direction of
head chainman; liead cJniirnmn, with spring balance at-
tached to tape and using pole as help to steady pull, brings
tension to 12 pounds; recorder plumbs down front end, and
sets pin slanting sidewise. After checking the pin, proceed
with the next 100 feet. In chaining up hill, follow same
general method, using plumb bob at rear end. In
leveling the tape the tendency will be to get the down hill
end too low. Chain the line in duplicate, retaining the same
organization. (3) Chain the line again in duplicate, tape
lying on the ground, pull 12 pounds, pins set plumb, frac-
tion direct to nearest 0.01 foot. Set temporary pegs flush
with ground every 100 feet and also at intermediate sudden
changes of slope, for levels. Determine differences of eleva-
tion between successive pegs, unless the leveling data are
supplied to the party. Record data and make reductions
and comparisons as in form.
PROBLEMS.
31
32 THE CHAIN AND TAPE.
PROBLEM A10. ANGLES OF A TRIANGLE WITH TAPE.
(a) Equipment. 100-foot steel tape, 50-foot metallic tape,
set of chaining pins, 2 plumb bobs, 2 flag poles, five-place
tables of trigonometric functions (each member of party
to have tables).
(b) Problem. Measure the angles of an assigned triangle
with the steel tape and also with the metallic tape, the error
of closure not to exceed 3 minutes.
(c) ^f('t1i<>(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) E<iiiii>iiiciit. 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) E<iitii)i>i<'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
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CO
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Si
TION
(s-bJ
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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+
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Z .2/369
7 \
CA.l
!"*+
76 Jt
i.aetse
^ e ^
2 1
i
tOO++4
z ^S
+O65O
^
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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
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z et/,f
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+9J7^
22860
t 3SSZ3
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1_066J_
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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
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o-t
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e7.7i
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-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<nie of
the plate level lines. With one sight removed and the instru-
ment leveled, range in with the remaining sight two points
as far apart vertically as possible, say on the side of a build- -
ing. Reverse in azimuth and bring the bottom of the sight
in range with the lower point; if the upper point is then in
range, the sight is in adjustment. If not, correct one-half
the error by putting paper under one side, or by filing off
the other side. Repeat process for the other sight.
PROBLEMS. 51
The Pivot. To mljuxt tlie pivot to the center of ilic i/railn-
uteiJ circle Set the south end of the needle to read zero, and
read the north end of the needle; reverse the compass box
in azimuth, repeat the observations, and correct one -half
the difference between the two readings of the north end
of the needle by bending the pivot, using the special wrench
for the purpose. Turn the compass box 90 and repeat.
See (b), Fig. 13.
The Needle. To *lrii/hten the needle. Having adjusted
the pivot, set the north end of the needle to read zero and
bend the needle so that the south end reads zero also. Turn
the compass box and test for other graduations.
PROBLEMS WITH THE COMPASS.
PROBLEM Bl.
DECLINATION OF THE MAGNETIC
NEEDLE.
(a) Equipment. Surveyors' compass, flag pole, reading
V L
WITH SURVE
Mr* fr/ry C**, f
.V.. **-r oit
=<S' COMPA<
I A'a 2O (Atttctt
52 THE COMPASS.
(b) Problem. At a point on the true meridian determine
the mean magnetic declination with the surveyors' compass.
(c) Methods. (1) Set the compass over one point and a
flag pole at another on the true meridian. (2) Lower the
needle and sight at the flag pole carefully with the north
end of the compass box to the front. (3) When the vibra-
tions of the needle have ceased, move the vernier by means
of the tangent screw so that the north end of the needle
reads zero, and check the sighting of the compass. (4)
Read the declination on the vernier to the nearest minute.
(5) Lift the needle, verify the zero needle reading and the
sighting, read the vernier and record; repeat the process
until ten satisfactory consecutive values of tl ? declination
are obtained. Observe the time of each reading xo the near-
est minute. (6) Correct the mean of the ten values for
daily variation by reference to the diagram, Fig. 11, using
the mean time. Record and reduce the data as in form.
(Note that the values in the form were obtained by estimat-
ing the nearest five minutes. Which is better? Try both
if time allows.)
PROBLEM B2. ANGLES OF TRIANGLE WITH COMPASS.
(a) Equipment. Surveyors' compass, two flag poles, read-
ing glass.
(b) Problem. Measure the angles of a given triangle with
the surveyors' compass.
(c) Methods (1) Set the compass over one of the vertices
of the triangle and a flag pole behind each of the other two.
(2) Lower the needle and sight at one of the flag poles care-
fully, with the north end of the box to the front. (3) When
the vibrations have ceased, read the north end of the needle
to the nearest five minutes by estimation. (4) Lift the
needle, verify the sighting and also the reading. (5) Turn
the compass box to the other point and determine the bear-
'ing, as before. The required angle is the difference between
the two bearings. (6) Measure the other two angles in like
manner. The error of closure must not exceed 5 minutes.
v ollow the prescribed form.
PROBLEMS.
f
.Station
e.*;.^
S'-KC
WITH SURVE
S 4 THE COMPASS.
PROBLEM B3. TRAVERSE OF FIELD WITH COMPASS.
(a) Equipment. Surveyors' compass, 2 flag poles, engi-
neers' chain, set of chaining pins.
(b) Problem. Determine the bearings of the sides of an
assigned field with the surveyors' compass and measure the
lengths of the sides with an engineers' chain.
(c) .Vrt/iorf*. (1) Set the compass over one of the corners
of the field which is free from local attraction, and set off
the declination with the vernier. '(2) Take back sight on
the last point to the left and fere sight to the next point
to the right, following the methods used in Problem B2.
(3) Repeat this process for the remaining corners of the
polygon taken in succession to the right. (4) Chain the
sides of the field to the nearest 0.1 foot by estimation. (5)
Compare the chain with standard. (6) From the observed
bearings compute the interior angles of the field, and the
true bearings of the sides. The angular error of closure
must not exceed 10 minutes for a five-sided fielrt . Record
and reduce data as in prescribed form.
PROBLEM B4. AREA OF FIELD WITH COMPASS.
(a) Equipment. Five-place table of logarithms.
(b) Problem. Compute the ar^a of the assigned field by
means of latitudes and departures.
(c) Methods. (1) Prepare forms for calculation; tran-
scribe data, and carefully verify copy. (2) Compute lati-
tudes and departures by contracted multiplication, preserv-
ing results to the nearest 0.1 foot. (3) Make the same cal-
culations by logarithms, as a check. (4) Determine the ac-
tual linear error of closure. (5) Determine the permissible
error of closure (see chapter on errors of surveying). (6)
If consistent, distribute the errors in proportion to the sev-
eral latitudes and departures, respectively, repeating the
additions as a check. (7) Transcribe field notes and ad-
justed latitudes and departures, and verify transcript. (8)
Calculate the meridian distances of the several stations and
lines. (9) Calculate the latitude coordinates. (10) Calcu-
late the partial trapezoidal areas by multiplying the meri-
dian distances of the lines by the respective latitudes, pre-
PROBLEMS.
56 THE COMPASS.
serving consistent accuracy, and observing algebraic signs.
(11) Determine the area by taking the algebraic sum of the
partial areas. Reduce to acres, and correct for standard.
Follow the prescribed form.
PROBLEM B5. ADJUSTMENT OF THE COMPASS.
(a) Equipment Surveyors' compass, adjusting pin, small
screw driver.
(b) Problem. Make the necessary tests and adjustments
of the surveyors' compass.
(c) Methods. Observe the following program: (1) test
the magnetism of the needle; (2) test the metal of the com-
pass box; (3) test and adjust the plate levels; (4) test the
sights; (5) test the pivot; (6) test the needle.
PROBLEM B6. COMPARISON OF DIFFERENT MAKES
AND TYPES OF COMPASSES.
(a) Equipment. Department equipment, catalogs of rep-
resentative makers of compasses.
(b) Problem. Make a critical comparison of the several
types of compasses.
(c) Methods. Examine the department equipment and
study the several catalogs carefully, noting the character-
istic features, prices, etc. The following items, at least,
should be included in the tabulated report: name of instru-
ment, length of needle, length of alidade, vernier, tripod,
weight, price, etc.
CHAPTER IV.
THE LEVEL.
Description. The engineers' level consists of a line of
sight attached to a bubble vial and a vertical axis. Two
types of level, the wye and dumpy, Fig. 14, are used by engi-
neers. In the former the telescope rests in Y-shaped sup-
ports, from which it may be removed. In the dumpy level
the telescope is fixed. The dumpy is a favorite with British
engineers and the wye level with Americans. The two types
differ chiefly in the methods of adjustment. A third type,
not shown in the cuts, is called the level of precision be-
cause of its use solely for work of extreme refinement.
DUMPY LEVEL.
Fig. 14.
58
THE LEVEL,
In Fig. 15 are shown: (a) an architects' or builders' level
of the wye type; (b) a roadbuilders level of the dumpy
type; (c) a reconnaissance level with a decimal scale for
reading horizontal distances direct; (d) a water level some-
times used in locating contours; (e) a Locke hand level; (f)
a clinometer; (g) a binocular hand level.
Fig. 15.
THE TELESCOPE.
Principles. The telescope used in the engineers' level
and transit, shown in section in Fig. 16 and 22, consists
of an objective or object glass which collects the light and
forms an image in the plane of the cross-hairs, and an ocular
or eyepiece which magnifies the image and cross-hairs. The
cross-hairs are thus at the common focus of the objective
and eyepiece. The principle of this type of telescope, both
optically and mechanically, may be illustrated by the photo-
graphic camera if cross lines be ruled on the ground giass
focusing plate and a microscope be used in viewing the
image formed by the lens. Telescopes of the above class are
called measuring telescopes, while those of the opera glass
type are termed seeing telescopes. The latter have no real
image formed between the object glass and eyepiece.
Line of Collimation. The telescope of the level or tran-
sit may be represented by a line, called the line of coUiiua-
tion, which joins the optical center of the objective and the
THE TELESCOPE.
Mfft.f-j
Jo/e. Tav g eni-_ Li_ne_oj
- - -* M&ay^rvjK -_- - - (-Say 4OO') -7!
< 2nd Method.
Two -Peg Test.
Fig. 16.
60 THE LEVEL.
intersection of the cross-hairs. The optical center is a point
such that a ray of light passing through it emerges from
the lens parallel to its original direction. The line of colli-
mation is independent of the eyepiece.
Objective. The objective is a double convex or plano-
convex lens. In all good telescopes the objective is com-
pound, that is, made up of two lenses, with the view to cor-
rect two serious optical defects to which a simple lens is
subject. These defects are called chromatic aberration end
spherical aberration.
Chromatic aberration' is the separation by the objective of
white light into its component colors. A lens which is free
from this defect is called achromatic. A telescope is tested
for the chromatic defect by focusing on a bright obj ^ct, such
as a piece of paper with the sun shining on it, and noting
the colors on the edge of the object and especially at the
edge of the field of view as the focus is slightly deranged.
Yellow and purple are the characteristic colors indicating
good qualities in the lens.
Spherical aberration is a defect which prevails to a serious
extent in a simple lens having spherical surfaces. It is due
to a difference in the focal distance for different concentric
or annular spaces of the objective, so that the plane of focus
for rays passing through the outer edges of the lens is dif-
ferent from that of the middle portion. A telescope is test-
ed for this defect by focusing on a well defined object, such
as a printed page, with the rays of light cut off alternately
from the middle and the edge of the lens. This is best done
by means of a circular piece of paper with a small round
hole in it.
As a rule, the object glass in good levels and transits con-
sists of a double convex lens of crown glass fitted to a con-
cavo-convex or a plano-concave lens of flint glass, the
former to the front. The defects described above are avoid-
ed through the different dispersive and refractive powers of
the two kinds of glass, and by grinding the surfaces of the
two lenses to the proper curvatures.
Eyepiece. As in the camera, the image formed by the
objective is inverted, so that if a simple microscope be used
as an eyepiece, the observer sees objects inverted. Such
THE TELESCOPE. 61
an eyepiece Is commonly used on the dumpy level, as shown
in Pig. 14. This form of eyepiece consists of two plano-
convex lenses with their convex sides facing each other.
The form of eyepiece most used in American instruments is
the erecting eyepiece in which two plano-convex lenses re-
place each of the two in the simpler form. The erecting
eyepiece is much longer than the simple one, as may be
seen at a glance in Fig. 14. While the simple eyepiece causes
a little confusion at first, owing to the inversion of objects,
it is much superior to the erecting eyepiece in the matter of
clearness and illumination.
The chief inherent defect in the eyepiece is a lack of
flatness of the field. A single lens usually causes a distor-
tion or curving of straight lines in the image, especially to-
wards the edge of the field. A telescope is tested for this
defect by observing a series of parallel right lines, prefer-
ably a series of concentric squares, which fill the entire field
of view.
In the best achromatic eyepieces, one or more of the sep-
arate lenses may be compounded, the curvatures being such
as to eliminate the color defect and give rectilinear qualities
to the lens or combination of lenses.
Definition. The definition of a telescope depend upon
the finish and also the accuracy of the grinding of the
curved surfaces of the lenses. It may be tested by reading
the time on a watch or a finely printed page at some dis-
tance from the instrument.
Illumination. Illumination and definition are apt to
be confused. Poor definition causes indefinite details, while
poor illumination causes faintness in the image. The latter
may be tested about dusk, or in a room which can be grad-
ually darkened, and can be best appreciated if two telescopes
of different illuminating qualities be compared.
Aperture of Objective. The aperture or effective di-
ameter of the objective is determined by moving the end of
a pencil slowly into the field and noting the point where it
first appears to the eye when held say 8 or 10 inches back
from the eyepiece. The process should be repeated in the
reverse order. The annular space is deducted from the
actual diameter to obtain the real aperture.
Size of Field. The field of the telescope is determined by
noting the angle between the extreme rays of light which
62 THE LEVEL.
enter the effective aperture of the objective. With the tran-
sit telescope, the limiting points may be marked on the side
of a building and the angle measured directly with the
plates; or with either level or transit the angle may be cal-
culated from the measured spread in a given distance. For
simplicity, a distance of 57.3 feet may be taken, and the re-
sult reduced to minutes.
Magnifying Power. The magnifying power of a tele-
scope is expressed in diameters, or as the multiplication of
linear dimension. It is determined most readily by IP til? ing
an observation with both eyes open, one looking through
the telescope and the other by natural vision. The com-
parison may be made by means of a leveling rod, or the
courses of brick or weather-boarding on the side of a house
may be used in like manner.
Parallax. Parallax is the apparent movement of the
cross-hairs on the object with a slight movement of the eye,
and is due to imperfect focusing of the eyepiece on the
cross-hairs before focusing the objective. The eyepiece
should be focused irith tlie eye normal, the cross-hairs being
illuminated by holding the note book page or other white
object a few inches in front of the objective.
Cross-Hairs. The cress-hairs are attached to a ring or
reticule which is held by two pairs of capstan headed screws.
The hairs usually consist of spider lines, although some
makers use platinum wires for the purpose. To remove the
reticule the eyepiece is taken out, one pair of screws is re-
moved and a sharpened stick is inserted in a screw hole. The
best spider lines are obtained from the spider's egg nest.
In Fig. 17, (a) shows the usual arrangement of the : cross-
hair ring- and the method of attaching the hairs; (b) shows
THE BUBBLE VIAL. 63
the number and positions of hairs used, (1) being the most
common, (2) the form for stadia work with the transit and
also for estimating the lengths of sights with the level, (3)
a form used by some makers with the level, and (4) a style
found in English levels; (c) shows the egg pod or case of
the large brown spider (about half size) which yields the
best lines for engineering instruments; (d) illustrates a
convenient vest pocket outfit for replacing cross-hairs in
the field, consisting of a supply of spider lines and some
adhesive paper (bank note repair paper) each in a capsule
or tin tube, and several sharpened sticks for stretching the
hairs. Cross-hairs stretched in this manner may last indefi-
nitely, or they may be fastened on permanently with shel-
lac at the first opportunity.
THE BUBBLE VIAL.
Principle. The spirit level consists of a sealed glass
tube nearly filled with ether or other liquid, and bent or
ground so that the action of gravity on the liquid may indi-
cate a level line by means of the bubble. The delicacy of the
bubble depends upon the radius of the curvature in a verti-
cal plane, the greater the radius the more delicate the level.
Thus, for example, a perfectly straight tube could not be
used as a level.
Curvature of Bubble Vials. Good bubble vials are now
made by grinding or polishing the interior surface of a se-
lected glass tube by revolution, as indicated in exaggerated
form at (a) Fig. 18. As a general rule, only one side of the
vial is actually used, it being customary to encase it in a
brass tube having a slot or race on one side. However,
both sides of the vial may be utilized, as in (b) and (c). Fig.
18. which show the rcccrxioii Icrel adapted to the transit and
wye level, respectively. Bubble vials of several sizes are
shown in (d), Fig. 18. It was formerly customary to grind
out only a portion of the upper side of the glass tube, as
shown at (e). The cheap vial, consisting merely of a bent
tube, used mostly in carpenters' and masons' levels, is
shown at (f); and a method of increasing the precision of
the bent tube by lilting it is indicated at (g) Fig. 18. .
64
THE LEVEL.
Fig. 18.
Delicacy. The delicacy of the bubble vial is designated
cither by the radius, usually in feet, or by the central angle
in seconds corresponding to one division or one inch of the
bubble scale. Two methods are employed to determine the
delicacy of level vials, (1) by the optical method, as at (h),
Fig. 18, where the radius is calculated from an observed tar-
get movement at a given distance for an observed bubble
movement, the two triangles being similar; and (2) by the
level tester, as at (i), by means of which the angular move-
ment is read from the micrometer head for a given move-
ment of the bubble. The engineer usually employs the radial
designation, while the maker expresses the delicacy in an-
gular units. As shown at (h) and (i), Fig. 18, the radius in
feet is equal to 17,189 divided by seconds per inch of bubble.
Bubble Line. The relations of the bubble to the other
parts of the instrument are best understood by representing
LEVELING RODS.
65
the vial by a line. This line may be either the axis of the
surface of revolution in (a), Pig. 18, or to provide for either
of the three forms of vial shown, it may be taken as the
tangent line at the middle or top point. This tangent line
will be meant hereafter in referring to the bubble line.
(dt
Fig. 19.
th)
(I)
rg)
LEVELING RODS.
Types. There are two classes or types of leveling rods;
(1) target rods, having a sliding target which Is brought
into the line of sight by signals from the leveler; and (2)
self -read ing or speaking rods which are read directly by the
leveler.
66 THE LEVEL.
In Fig. 19, (a) is the Philadelphia rod; (b) the New York
rod; and (c) the Boston rod. The first is either a target
or self-reading rod; the second is a target rod, but may be
read from the instrument when the rod is "short"; the Bos-
ton rod is strictly a target rod. The Philadelphia rod is
perhaps the favorite for most purposes, and the Boston rod
is used least. A folding self-reading rod is shown at (d),
Fig. 19; (e) is a woven pocket device which may be tacked
to a strip of wood and used as a leveling rod; (f) is a rail-
road contouring rod with an adjustable base; (g) is a plain
rod graduated to feet, for use with the water level.
Targets. The targets shown on the Philadelphia and
New York rods, (a) and (b), Fig. 19, are called quadrant
targets. That on the Boston rod, (c), is a modified form of
the diamond target. A special form, called the corner tar-
get, is turned on two sides of the rod to assist in plumb-
ing the rod, and another target has two parallel planes for
the same purpose. A detachable rod level is shown at (h).
The target on rod (b), with the zero of the vernier 0.09 foot
below the center of the target, frequently causes blunders.
USE OF THE LEVEL.
Use. The engineers' level is used: (1) to determine dif-
ferences of elevation; (2) to make profile surveys; (3) to
locate contours; (4) to establish grade lines; (5) to cross-
section; (6) to run lines.
Differential Leveling. Differential leveling consists
of finding the difference of elevation between two or more
points. In the simplest case the difference of elevation be-
tween two points may be found from a single setting of
the level, the leveling rod being used to determine the
vertical distance from the plane of the instrument to each
of the two points, and the difference between the rod read-
ings taken. When the distance between the two points is
too great, either vertically or horizontally, or both, to ad-
mit of this simple process, two or more settings of the level
are taken so as to secure a connected series of rod read-
ings, the algebraic sum of which gives the desired differ-
ence of elevation. This difference may be expressed either
by the numerical result of the algebraic sum of the rod
readings, or by assuming an elevation for the beginning
USE OF THE LEVEL. 67
point and calculating the elevation of the closing point by
means of the observed rod readings.
A back sight is a rod reading taken to determine the height
of the instrument. A fore sight is a rod reading taken to de-
termine the height of a point. A bench mark is a point se-
lected or established for permanent reference in leveling
operations. A turning point is a temporary reference point
used in moving the instrument ahead to a new setting. The
same point is often both a turning point and bench mark.
The datum is the plane or surface of reference from which
the elevations are reckoned; it may be sea level, or an arbi-
trary local datum. A level line is a line parallel to the sur-
face of a smooth body of water. A horizontal line is tangent
to a level line at any point. The curvature varies as the
square of the distance from the point of tangeiicy, and is
0.001 foot in 204 feet, or 8 inches in one mile.
In Fig. 19, (i) shows a metal and also a wooden peg com-
monly used for turning points. Several forms of bench
marks are shown in Fig. 19; (j) is a mark on the corner
of a stone water-table; (k) a rivet leaded into a hole
drilled in a stone slab, (1) a railroad spike driven into a
wooden post or telegraph pole; (m) a projection cut on the
root of a tree, preferably with a spike driven vertically into-
the top of the bench, and usually with a blaze alsove
marked "B. M. No.." All bench marks and also turning
points should be clearly described in the notes.
Two chief essentials in correct differential leveling are.
(1) that the bubble be in exactly the same position (usu-
ally the middle) on both back and fore sight; and (2) that
the length of back sight and fore sight, horizontally, shall
be balanced. It is seen at (e), Fig. 16, that with the bubble
always in the middle, the line of collimation generates a
horizontal plane when in perfect adjustment, but a cone with
axis vertical when out of adjustment; so that ir. taking
equal distances in the opposite directions, the base of the
con" is used, this base being parallel to the true collima-
tion plane. In the best leveling practice the instru-
ment is adjusted as perfectly as possible and then used so that
the residual errors balance each other.
The three common styles of leveling rod may be read to
0.001 foot by vernier or by estimation on a scale of 0.005
foot. However, for most kinds of leveling, it is an absurd
68 THE LEVEL.
refinement to read the rod closer than 0.01 foot, especially
with the usual maximum length of sight of 350 to 400 feet,
and with the more or less sluggish bubbles supplied in the
general run of leveling instruments. Furthermore, the
horizontal hair usually covers 0.01 foot or so of the target
at the maximum length of sight, that is, the target can move
that amount without being noticed by the observer.
Profile Leveling. Profile leveling consists of finding
the relative elevations of a series of representative points
along a surveyed line, for the purpose of constructing a pro-
file or vertical section. The skeleton of profile leveling, that
is, the precise bench marks and turning points with the
successive heights of instrument, is identical with differen-
tial leveling, already described. Having determined the
height of instrument by taking a back sight on a bench
mark of known or assumed elevation, rod readings are
taken at proper intervals along the measured and staked
line. These readings are fore sights, but they are usually
termed intermediate sights to distinguish them from the
more precise rod readings taken on turning points and
bench marks. On railroad surveys intermediate sights are
taken usually to the nearest 0.1 foot on the ground; but in
other cases, such as tile and sewer surveys, intermediates
are often read to the nearest 0.01 foot on small pegs driven
beside the station stakes flus'h with the surface of the
ground. In railroad work, the benches, turning points,
and intermediates of special importance are commonly read
to 0.01 foot, although some engineers persist in the ques-
tionable practice of taking the nearest 0.001. In drainage
surveys the nearest 0.01 foot is usually taken on bench
marks, although more carefully than on the intermediate
peg points, and the nearest 0.1 foot is read on ground points.
The errors of profile leveling are balanced on turning
points by equal back and fore sights, as in differential lev-
eling. If the instrument is seriously out of adjustment, an
error is made in the case of odd bench marks with unbal-
anced sights, and also on all intermediate sights. However,
the error is usually unimportant when ground readings are
taken to the nearest 0.1 foot. In important leveling, such
as canal and drainage work, it is customary to run a line of
check levels to prove the benches, before construction be-
gins.
USE OF' THE LEVEL. 6d
The profile is plotted to an exaggerated scale vertically
on a special paper, called profile paper. Three kinds, known
as plates A, B and C, are in general use. The most common
is plate A, which is ruled in i/i-inch squares with a further
subdivision to 1-20 inch vertically. In railroad profiles the
scales most used are 400 feet to the inch horizontally and
20 feet vertically. A still greater exaggeration is generally
used in drainage profiles.
Contour Leveling. Contour leveling is an application
of the methods of profile leveling to the location of contour
lines, that is, lines having the same elevation. Two methods
are employed: either (1) actually establishing points on
the adopted contour planes on the ground and then locat-
ing these points; or (2) taking random elevations at rep-
resentative points and interpolating the contour lines from
the plotted data. The latter is the more common. The
chief purpose of contour leveling is to make a contour map,
and the process is essentially a part of topographic survey-
ing, where it will be more fully considered.
Grade Lines. The establishment of grade lines is usti-
ally the concluding part of profile leveling. After making
the profile, the grade line is established by stretching a fine
thread through the ruling points, taking into account the
controlling conditions, such as maximum gradient or earth-
work quantities on a railroad profile, the carrying capacity
or the scour in the case of a ditch, etc. After laying the
grade line on the profile, notes are made of the data, and
the actual grade line is established. Two methods are used:
(1) the height of instrument is determined as usual, and
stakes are driven at measured intervals with their tops to
match calculated rod readings; and (2) a limited number
of ruling points are established by the first method or
otherwise, and the remaining stakes are "shot in" by con-
structing a line parallel to the ruling line used. The latter
is more rapid, since a constant rod reading is used; how-
ever, the method is unreliable unless the fore sight be
checked frequently on a fixed target.
Cross-Sectioning. Cross-sectioning consists of staking
out the limits of the transverse section of an excavation or
embankment for the purpose of construction, and usually
includes the collection of data for the calculation of the
quantities. This may be done either with the engineers'
70 THE LEVEL.
level, rod and tape line, or with special rods called cross-
section rods. The notes are taken as rectangular coordi-
nates, usually with reference to the center of the finished
roadbed. The slope stakes are set where the side slope lines
pierce the surface of the ground.
Running Lines. Lines are sometimes run with the en-
gineers' level, provision being made in most good levels for
the attachment of a plumb bob. A line may be prolonged
by sighting in two points ahead. A clamp and tangent
movement are necessary. Some builders' levels have a
needle and also a roughly divided horizontal circle for use
in staking out buildings.
Practical Hints. The following practical suggestions
apply more or less directly to all kinds of leveling, and also
in a general sense to transit work.
Speed. Cultivate the habit of briskness in all the de-
tails of the work. While undue haste lowers the standard
of the results, an effort should be made to gain speed
steadily without sacrificing precision. Gain time for the
more important details by moving rapidly from point to
point. On rapid surveys both leveler and rodman often move
in a trot. Neither rodman nor leveler should delay the
other needlessly.
Care of Instruments. Do not carry the level on the shoul-
der in climbing fences. Clamp the telescope slightly when
hanging down. Keep the tripod legs at the proper tight-
ness, and avoid looseness in the tripod shoes. Avoid undue
exposure to the elements, and guard the level from injury.
Do not leave the instrument standing on the tripod in a
room over night.
Setting Up. In choosing a place to set the level up, con-
sider visibility and elevation of back point and probable
fore sight. Set up with plates about level. On side-hill
ground place one leg up hill. In general, place two tripod
shoes parallel to the general line of the levels.
Leveling Up. A pair of foot screws should be shifted to
the general direction of the back or fore sight before level-
ing up. Set the foot screws up just to a snug bearing and
no tighter. If either pair of screws binds, loosen the other
pair a little. The bubble moves with the left thumb. Level
up more precisely in the direction of the sight than trans-
verse to it, but do not neglect the latter. Inspect the bubble
USE OF THE LEVEL. 71
squarely to avoid parallax, and also to prevent such blun-
ders as reading the bubble five spaces off center.
OUscrcationn. Adjust the eyepiece for parallax with the
eye unstrained. It is much easier on the eyes to observe
with both eyes open. Read at the intersection of the cross-
hairs, since the horizontal hair may be inclined. Set the
target approximately, check the bubble, and repeat the pro-
cess several times before approving the sight. Be certain
that the bubble is exactly in the middle at the instant of
approving the target. If the level has horizontal stadia
lines, beware of reading the wrong hair (the reticule may be
rotated one-quarter so as to have the extra hairs vertical,
or a filament may be attached to the middle horizontal hair
to assist in identifying it). Avoid disturbance of the tripod
by stepping about the instrument. Assist the rodman in
plumbing the rod. Let signals be perfectly definite both as
to direction and amount, using the left hand for "up" and
the right for "down", or vice versa.
The leveler can work much more intelligently if he knows
the space covered on the rod by one division of the bubble
scale at the maximum length of sight, and also the space
on the rod hidden by the cross-hair.
Balancing Sights. Balance the length of back sight and
fore sight, and record the approximate distances. The dis-
tances in the two directions may be made equal roughly by
equality of focus, but it is better on careful work to pace
the distances or determine them by means of the stadia
lines in the level. If necessary to unbalance the sights,
they should be balanced up at the first opportunity, and in
general they should be in balance when closing on import-
ant benches. When leveling up or down steep slopes, fol-
low a zigzag course to avoid short sights. Take no sights
longer than 350 or 400 feet.
Leveling Rod. The rod should be carefully plumbed, to
accomplish which the rodman should stand squarely behind
the rod and support it symmetrically between the tips of
the extended fingers of the two hands. With "short" rods
avoid the somewhat common blunder of 0.09 foot when the
vernier slot is below the center of the target. With "long"
rods, see that the target has not slipped from its true set-
ting before reading the rod. Read the rod at least twice,
and avoid blunders of 1 foot, 0.1 foot, etc. Careless rodmen
72 THE LEVEL.
sometimes invert the rod. Each rod reading on turning
points and bench marks should, when practicable, be read
independently by both rodman and leveler.
Bench Marks and Turnlinj Points. Wooden pegs or other
substantial points should be used to turn the instrument
on. Select bench marks with reference to ease of identifica-
tion, the balancing of sights, freedom from disturbance, etc.
As a rule, each bench mark should be used as a turning
point so that the final closure of the circuit may prove the
bench.
Record and Calculations. Describe bench marks and turn-
ing points clearly. It is good practice to apply algebraic
signs to the back and fore sight rod readings. The eleva-
tions should be calculated as fast as the rod readings are
taken, and calculations on turning points should be made
independently by leveler and rodman, and results compared
at each point. The rodman may keef) turning point notes
in the form of a single column. The calculations should be
further verified by adding up the columns of back sights
and fore sights for each circuit, or page, or day's work, and
the algebraic sum of the two compared with the difference
between the initial and last calculated elevation.
Error of Closure. A circuit of levels run with a good
level by careful men, observing all the foregoing pre-
cautions, should check within 0.05 foot into the square root
of the length of the circuit in miles (equivalent to 0.007 foot
into the square root of the length of the circuit in 100-foot
stations.) In closing a circuit, the error should be care-
fully determined, as above indicated, and the value of the
coefficient of precision found. (See discussion of errors of
leveling and precision diagrams in the chapter on errors of
surveying.)
ADJUSTMENT OF THE WYE LEVEL.
Elementary Lines. The principal elementary lines of
the wye level, as shown in Fig. 16, are: (1) the line of col-
limation; (2) the bubble line; (3) the vertical axis. For
the purpose of adjustment there should be added to these:
(4) the axis of the rings; (5) the bottom element of the
rings. The following relations should exist between these
lines; (a) the line of collimation and bubble line should be
ADJUSTMENT OF THE LEVEL. 73
parallel; (b) the bubble line should be perpendicular to the
vertical axis. The first of these relations involves two
steps, viz., (1) to make the bubble line parallel to the bot-
tom element of the rings, and (2) to make the line of col-
limation coincide with the axis of the rings. The other
relation involves the wye adjustment, and is similar to the
plate level adjustment described in the chapter on the com-
pass.
Bubble. To make the bubble line parallel to the bottom
element of the rinyx. Two steps are involved, (a) to place
the bubble line I'M the same plane with the bottom element,
and (b) to make the two lines parallel.
Azimuth Xereirx. To make the bubble line in the same plane
iritJt tlie bottom element of the rinyx. Clamp the level over a
pair of foot screws, loosen the wye clips, and level up; ro-
tate the telescope through a small angle, and if the bubble
moves away from the middle, bring it back by means of the
azimuth adjusting screws. Test by rotating in the opposite
direction. Leave the screws snug.
Altitude Screirs To make the bubble line and tlie bottom ele-
ment of the rinyx parallel Make the element level
with the foot screws and bring the bubble to the middle by
means of the <iltitud< adjusting screws. The element is
made level by the method of reversions as follows: With
the level clamped over a pair of foot screws, as above, lift
the clips and level up precisely; cautiously lift the tele-
scope out of the wyes, turn it end for end, and rrry yentlii
replace it in the wyes; if the bubble moves, bring it half
way back by means of the foot screirx. Before disturbing
adjusting screws make several reversals, and conclude the
adjustment with screws snug. This end for end reversal
is similar to that made with the carpenter's level, the
straight edge of the level corresponding to the element of
the rings. The lines involved are shown in Fig. 16.
Line of Collimation To make the line of coll imat Ion
rninr-ide icith the a.cis of the rinys. Loosen clips, sight on a
point, say a nail head or the level target, more distant than
the longest sight used in leveling; rotate the telescope half
way and note the movement of the hair, if any. The line
of collimation generates a cone, the axis of which is that
of the rings, and the apex of which is at the optical center
of the objective. Correct one-half the observed error by
74 THE LEVEL.
means of the capstan headed screws which hold the cross-
hair ring. Gradually perfect the adjustment until the in-
tersection of the oross-hairs remains fixed on the same
point when reversed by rotation with reference to either
hair. The adjustment should be concluded with the screws
at a snug bearing.
After collimating the instrument for a long distance, the
adjustment should be checked for a short distance, say 50
or 100 feet, so as to test the motion of the optical center
of the objective.
Rings. The theory of tlif wye lerel demands perfect equality
of the rings, that is, the parallelism of the axis and element,
as in (c), Fig. 16. Should the rings be unequal, either from
poor workmanship or uneven wear in service, they form a
cone instead of a cylinder, and the axis is not parallel to the
element, as in (d), Fig. 16. Under the latter conditions, the
principle of the wye level fails, and an independent test is
demanded. This is known as the two-peg test, the de-
tails of which are shown in (e) and (f), Fig. 16, and de-
scribed in the adjustments of the dumpy level. If, after
making the wye level adjustments above described, the two-
peg test shows that the line of collimation and bubble line
are not parallel, the rings are probably unequal and the in-
strument should thereafter be adjusted as a dumpy level.
However, hasty conclusions should be guarded against.
In case the instrument has a reversion level, shown
at (c), Fig. 18, the equality of the rings may be tested by
first adjusting the top tangent line of the bubble vial par-
allel to the bottom element of the rings, and then after ro-
tating the telescope half way round in the wyes, compare
the bottom (now above) tangent line of the vial with the
top (now below) element of the rings, all by the end for
end reversion. However, the exact parallelism of the top
and bottom tangent lines of the reversion level should first
be proven by the two-peg method.
Wyes. To make bubble line perpendicular to the rertical
a.ris. Make the vertical axis vertical and bring the bubble to
the middle by means of the tri/e mitx. The vertical axis is
made vertical by reversion thus: With clips pinned, level
up; reverse over the same pair of screws, and bring the
bubble half way back with the foot screws. When adjusted,
the bubble will remain in the middle during a complete rev-
ADJUSTMENT OF THE LEVEL. 75
olution. This adjustment is identical in principle with the
plate level adjustment of the compass and transit, illus-
trated in (a), Fig. 13. The wye adjustment should follow
the adjustment of the bubble line parallel to the element
of the rings. The wye adjustment is a convenience, not
a necessity.
Centering the Eyepiece. After collimating the level,
the cross-hairs should appear in the center of the field. The
eyepiece is centered by moving its ring held by four screws.
This adjustment is desirable, but not essential.
ADJUSTMENT OF THE DUMPY LEVEL.
Elementary Lines. The principal elementary lines of
the dumpy level are identical with those of the wye level:
(1) the line of collimation; (2) the bubble line; (3) the ver-
tical axis. As in the wye level, the bubble line should be
(1) perpendicular to the vertical axis, and (2) parallel to
the line of collimation. However, owing to the difference
in the construction of the two types of instrument, the
auxiliary elementary lines are not recognized in the dumpy
level. The transit with its attached level is identical in
principle with the dumpy level.
Bubble. To make the bubble line perpendicular to the ver-
tical axix. Make the vertical axis vertical by the method of
reversions, and adjust the bubble to the middle. This adjust-
ment is identical in principle with the plate level adjust-
ment, shown in (a), Fig. 13. The bubble should remain in
the middle through a complete revolution.
Line of Collimation. To make the line of collimation
parallel to the bubble line. Construct a level line, and adjust
the cross-hairs to agree with, it. The level line is determined
either by using the surface of a pond of water, or by driv-
ing two pegs at equal distances in opposite directions from
the instrument, and taking careful rod readings on them
with the bubble precisely in the middle, as shown at (e),
Fig. 16. For simplicity, the two pegs may be driven to the
same level, or two spikes may be driven at the same level
in the sides of two fence posts, say 400 feet apart. Other-
wise, determine the precise difference of elevation, as indi-
cated in (e), Fig. 16. Then set the level almost over one of
the pegs, level up, and as in the first method of (f), Fig. 16,
76 THE LEVEL.
set the target of the leveling rod at the line of coliimation,
as indicated by the center of the object glass cr eyepiece,
(this can be done more precisely than most levels will set
the target at 400 feet distance); now with the rod on the
other peg, sight at the target (shifted to allow for the dif-
ference if the two pegs are not on the same level); adjust
the cross-hair to the level line so constructed. If preferred,
the second method shown in (f), Pig. 16, may be used; the
level is set back of one peg, rod readings are taken on both
pegs, allowance made for the difference in level of the two
pegs, if any, the inclination of the, line of coliimation deter-
mined, correction made for the small triangle from the
level to the first peg, and finally the level line constructed
by means of the calculated rod readings. The second
method is simplified and made practically equivalent to the
first by setting the level at minimum focusing distance from
the first peg. The small corrective triangle is thus practi-
cally eliminated. This process is called the two-peg ad-
justment.
The foregoing method ignores curvature of the earth
(equal to 0.001 foot in about 2CO feet, or 0.004 foot in 400
feet) which is less than the error of observation with most
levels.
Uprights.--In some dumpy levels the uprights which
connect the telescope with the level bar are adjustable,
similar to the wyes of the wye level. This adjustment is
designed to bring the bubble line perpendicular to the ver-
tical axis in case the bubble is first adjusted parallel to the
line of coliimation. However, the best order is that already
described, viz., first adjust the bubble line perpendicular
to the vertical axis, and then the line of coliimation par-
allel to the bubble line, in which case the adjustable up-
rights are unnecessary.
PROBLEMS WITH THE LEVEL.
PROBLEM Cl. DIFFERENTIAL LEVELING WITH THE
HAND LEVEL (OR WATER LEVEL.)
(a) Equipment. Hand level (or water level), rod gradu-
ated to feet.
(b) Problem. Run an assigned level circuit with the hand
PROBLEMS.
77
*
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78 THE LEVEL.
level (or water level), observing the nearest 0.1 foot by es-
timation, and closing back on the starting point.
(c) Methods. (1) Determine the correct position of the
bubble of the hand level by sighting along a water table,
or sill course of a building, or by the principles of the two-
peg test. (If the water level is used, fill the tube so as to
have a good exposure of the colored water in the glass up-
rights.) (2) Take sights of 100 feet or so (paced), estimat-
ing the rod reading to the nearest 0.1 foot; balance back
and fore sights; assume the elevation of the starting point,
and keep the notes in a single column by addition and sub-
traction. (3) Check back on the first point. Determine the
coefficient of precision.
PROBLEM C2. DIFFERENTIAL LEVELING WITH EN-
GINEERS' LEVEL (OR TRANSIT WITH ATTACHED
LEVEL).
I
(a) Equipment. Engineers' level (or transit with attached
level), leveling rod, hatchet, pegs, spikes.
(b) Problem. Run the assigned level circuit, observing
the nearest 0.01 foot, and closing back on the initial point.
(c) Methods. Follow the practical suggestions given at
the conclusion of the "Use of the Level," giving special at-
tention to the following points: (1) eliminate parallax of
tthe eyepiece; (2) balance back and fore sight distances; (3)
have the bubble precisely in the middle at the instant of
sighting; (4) both rodman and leveler read each rod and
also make the calculations independently; (5) calculate ele--
vations as rapidly as rod readings are obtained; (6) plumb
the rod; (7) avoid blunders; (8) determine coefficient of
precision; (9) no sights longer than 350 or 400 feet. Fol-
low the first form shown to begin with, the other after
several circuits have been run.
PROBLEM C3. PROFILE LEVELING FOR A DRAIN.
(a) Equipment. Engineers' leveling instrument, leveling
rod, 100-foot steel tape, stakes, pegs, axe.
(b) Problem. Make a survey, plat and profile, with esti-
mate of cuts and quantities for a drain under assigned con-
ditions.
PROBLEMS.
79
SURVEY FOB A DRAIN FROM
D..crlpti.n.
fffom pipm ///T* A> Cert-itrvotor-y.
*ai/* of main trvtK, t/.l C.St.Ay.
(Cutoff thro* i/n/'*crjSfy grounds.}
point 3'W.o>not 2'J. o/" /V.*K Cot-,
of no. Lab. Lin* runs tA+nce
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ftojh *v//A ^ot/nrf /<*> sfa/fes.
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THE LEVEL.
(c) Methods. (1) Examine the ground, determine the
head and outlet of the drain, and select the general route.
(2) Stake out the line, set stakes every 50 feet, or oftener
if required to get a good profile, and drive a ground peg
flush, say 2 feet to the right (or left) of each stake; record
data for mapping the line. (3) Starting with the assigned
datum or bench mark, run levels over the line of the pro-
posed drain, observing the nearest 0.01 foot both on turning
points and ground pegs, the former somewhat more care-
fully; take rough ground levels, as required, to the nearest
0.1 foot; locate and determine the depth of intersecting
drains or pipe lines, or other objects which may influence
the grade line of the drain, and secure full data for placing
the same on the profile; observe due care with the back and
fore sights, as in differential leveling, and conclude the
leveling work with a line of check levels back to the initial
bench mark; a permanent bench mark should be established
at each end of the drain, and if the length is considerable,
at one or more intermediate points as well. (4) Make plat
and profile of the drain line; lay the grade line, taking into
account all ruling points; calculate the cuts, both to the
nearest 0.01 foot, and also to the nearest %-inch; mark the
latter on the stakes for the information of the ditcher, using
waterproof keel and plain numerals; make estimate of the
quantity of drain pipe, and of the cost of the job. Follow
the accompanying forms.
PROBLEMS.
81
'
(PROF
LE LI
YZL H
ores,
GROUN:
ELEVATIOMS TO O.I FOOT.)
109
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Re_d- Grade line- elevations^ rates of grade.
Blue. Wafer level; notes fe/af,'ve to ^sarne.
BtocK. Syrface fine, stcrt/on numerals,
220
82 THE LEVEL
PROBLEM C4. RAILROAD PROFILE LEVELING.
(a) Equipment. Engineers' leveling instrument, leveling
rod, 100-foot steel tape, stakes, axe.
(b) Problem-. Run. levels over a short section of line
staked out after the manner of railroad surveys, for the
purpose of constructing a profile.
(c) Methods. Follow the general process outlined in the
preceding problem, taking rod readings to the nearest 0.01
foot on turning points and bench marks, and also on im-
portant profiling points, when consistent; but take ground
rod readings only to the nearest 0.1 foot. In calculating
elevations, preserve the same degree of exactness in the re-
sult as observed in the rod reading, that is, when the rod
readings are taken to the nearest 0.1 foot, use only the
nearest 0.1 foot in the height of instrument to determine
the elevations. When a hub or station stake is to be used
as a turning point, the notes should show the ground rod
and elevation to the nearest 0.1 foot on the line preceding
the precise turning point record. Bench marks should be
selected 1 with reference to their freedom from disturbance
during construction, and they should be located not more
than 1500 or 2000 feet apart along the line. Check levels by
the same parties should not differ more than 0.05 foot into
the square foot of the length of circuit in miles. Back and
fore sights shoula be balanced, and no sight longer than
350 or 400 feet should be taken. In order to secure a renre-
sentative profile, ground rods should be taken not only at
every station stake, but also at every important chanee of
slope between station points. Pluses may be determined
either by pacing, or when short, by means of the leveling
rod. The rodman should keen a record of the turning
points. The notes should be checked and the other safe-
guards taken, as outlined in the practical hints under the
"Use of the Level."
The profile is best plotted by having another nerson read
off the data. The horizontal scale on railroad profiles is
usually 400 feet to the inch and the vertical scale 20 feet to
the inch. Gradients are expressed to the nearest 0.01 per
cent. It is usual to give the aliuement notes and prominent
topography, as shown.
PROBLEMS.
S3
PROBLEM C5. VERTICAL CURVE.
(a) h'liiiiiiniciit. Drafting instruments, profile paper.
(b) Problem. Connect two grade lines by a parabolic
curve, as assigned.
(c) Methods. (1) Plot the given grade lines, station num-
*/.
i 07.00
Ffate, r= o.SO per *t
Length, L = = 10.
Chord Gradients.
9S
COMPARISON OF RESULTS.
of Grade
Tangent.
BY Tangent Correct
Tangent Cu
FT"
+ O.OO
i-0. fO
+ O.4O
-f-0. 90
f- / 60
+ 2. SO
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+ 0-00
Ft.
/ 07. OO
i06.ro
'OS. 40
'04.90
'04-60
/O4-50
f04.60
/ O4-00
By Chord Gradients.
Chord Gradient. Curve
Di-ff. Gradient. Elevation
Per Cent.
Per Cenf.
(-1.00)
-0.90
-O.7O
-Q.SO
-0.30
-0. I
-f-o./o
+ 0.30
i-0. SO
+ O.7O
+0.90
(+1.00)
/ OS. 00
I 07.OO
I 06 OO
tos.oo
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106. >0
107.00
84 THE LEVEL.
bers, etc., on the sheet of profile paper. (2) Determine the
grade angle, that is, the algebraic sum of the two rates of
grade. (3) Determine the length of the vertical curve by
dividing the grade angle by the assigned or adopted change
of grade per station (notice the analogy to simple circular
curves). (4) Calculate the apex correction. (5) Determine
the corrections at the several station or fractional stations
(as assigned), and tabulate the stations and elevations, (.fi)
Plot the vertical curve from the data so determined, as in
the example. (7) Also compute and plot the same curve by
the method of chord gradients.
PROBLEM C6. ESTABLISHING A GRADE LINE.
(a) Equipment. Leveling instrument, leveling rod, flag
pole, 100-foot steel tape, stakes, axe.
(b) Problem. Establish an assigned grade line, (1) by
measured distances and calculate rod readings, and (2) by
"shooting in" the same line, for comparison.
(c) Method* (I) Stake off the distance between ruling
points, and drive stakes to the required grade, or if desira-
ble, parallel to it, by dividing up the fall in proportion to
the distance, (2) Set the level over one ruling point and
determine the height from the point to the line of collima-
tion by means of the leveling rod; set the flag pole behind
the other ruling point and establish a target, consisting of a
rubber band holding a strip of paper wrapped about the
pole at a height equal to the rod reading; having thus con-
structed a line parallel to the d'esired grade line, direct the
telescope on the fore sight target, and with the same rod
reading, "shoot in" the same stakes. Make careful record
of data and comparative results.
PROBLEM 07. SURVEY OF LINE SHAFTING.
(a) Equipment Engineers' transit with attached bubble,
leveling rod (or instead of these engineers' instruments, a
16-foot metal-bound straight-edge with an adjustable bubble
of say 20-foot radius, a long braided fishing line, and 3 long
metal suspenders exactly alike (as shown in the form), to
suspend straight-edge from line of shafting). 2 good plumb
bobs, 50-foot etched steel tape, copper tacks, hatchet.
(b) Problem. Make a survey of a line of shafting in a
PROBLEMS.
machine shop, and establish a true alinement for it, both
vertically and transversely.
(c) Mftliwl*. (Assuming that the transit and rod are
not available), (1) Plan the survey carefully, and if possi-
ble find some well denned base line close to the line shaft-
ing, to which to refer its position transversely. (2) Stretch
the braided string from end to end of the shaft line (or from
end to end of the room in case the shafting passes through
the wall), and fix it taut on or parallel to the adopted base
of reference; upon finally fixing the location of the string,
at least three points, one at either end and one near the
middle of its length, should be carefully plumbed down and
marked temporarily with copper tacks in the wooden floor
of the shop for further reference; there should be as little
draft as possible during this and the following steps. (3)
Plumb down from the line shaft at each hanger and care-
fully measure the horizontal right angled distance to the
reference string, noting the nearest 1-16-inch; the hangers
should be numbered and the distances between them meas-
ured and recorded; the plumb bob should be suspended from
corresponding points at all the hangers; and the bob should
always hang from the same side of the shafting; likewise,
the shafting should be calibrated, and record made of any
changes of diameter found. (4) Determine the radius of
curvature of the bubble on the straight-edge, (the radius
should be at least 20 feet); test the parallelism of the edge
of the straight-edge and the bubble line after the manner
used with the carpenters' level, that is, by reversion, and
Resurve
j, Meta) Shop.
86 THE LEVEL.
adjust the bubble if found in error; or if there is no way to
adjust the bubble, find its mean position. (5) Prove the
equality of the suspenders in a similar manner, by hanging
them from the shafting and testing them with the adjusted
straight-edge. (6) Having verified the special instruments,
determine the relative elevations of the shafting at the suc-
cessive hangers, noting the nearest 1-16-inch of elevation;
the differences can be accurately measured by means of a
wedge scale; for greater precision, the level may be reversed
end for end each time, and the mean taken; reduce the
level notes by summing up the differences algebraically so
as to secure elevations relative to the first or any other
hanger as a reference or bench, or above or below any
datum plane desired; it is a good plan to adopt a marked
spot on a machine or engine foundation as zero datum. (7)
Plot the data on profile paper, so as to secure an exagger-
ated vertical and lateral profile; now inspect the several
hangers and note the margin of adjustment available in the
screws, making record of same on the profile; if the line of
shafting passes through into another room of the shop,
carry a line through a door or other opening on the pro-
longation of the reference line, using great care with the
parallels, if any be required; collect complete data rela-
tive to the alinement through the length of the entire
shafting, as described above for the first stretch of it; also
plot any definite lines such as jack shafting lines or axes of
long or important machines which may now or in the future
bear a relation to the shafting now under survey. (8)
Study the profiles very carefully with the aid of a fine
thread; and after due consideration of all ruling points and
conditions, lay a line on it with a view to secure the best
results with the least disturbance of the shafting; abrupt
turns or elbows are likely where shafting passes through
small openings in partition walls, and sudden swings often
occur near heavy machines; the ideal alineruent is a hori-
zontal right line; if only slight changes are required, they
may be made at once, but if the readjustments are con-
siderable in amount, it may be wise to check up the main
lines of the survey before disturbing the hangers; after es-
tablishing the lines, it is best to fix permanent reference
points for future use, and these points should be character-
istic (such as one copper tack surrounded by three others),
PROBLE. 13. 87
to avoid mistakes of identification; a line of tacks, one be-
neath the edge of each hanger, located say in a vertical
plane tangent to the same side of the shafting throughout,
establishes the element of the cylinder, which is more con-
venient to use than the axis of the shaft line. (9) Care-
fully preserve the record of the survey and changes of the
hangers, and in due time make a resurvey to discover loose
and shifting hangers, especially near belts under heavy
stress.
(Should the regular engineers' instruments be employed,
the general method 1 would be unchanged; the difference
would consist in the greater facility of securing the data,
in passing through difficult places from one room of the
shop to another, in reestablishing the alinement, and in
detecting changes subsequently. As a rule, the resurvey
should be made when the shafting is idle, and if a transit
or level is employed, it should, when possible, be set up on
a masonry foundation of an engine or machine to aA'oid dis-
turbance from the shaky wooden floors due to the vibration
of machinery elsewhere in the shop, or to the observer mov-
ing about the tripod legs.) Keep the record in tabular
form and make profile in the manner indicated in the ac-
companying diagram.
PROBLEM C8. CONTOUR LEVELING.
(a) Equipment. Engineers' leveling instrument, leveling
rod, 100-foot steel tape, stakes, axe.
(b) Problem. Make a rapid contour survey of an assigned
tract of ground with the level and chain.
(c) Method*. (1) Examine the tract and plan the system
of reference lines for locating the points at which levels
are to be taken; if the ground is comparatively regular, a
simple subdivision into squares of 100 feet may suffice; but
if much broken, special lines along gullies and ridges
should be included 1 in the survey plan. (2) Stake off the
tract according to the plan, and make a record of the same.
(3) Starting from an assigned bench, determine the eleva-
tions of the ground at the various stakes and at such other
points as may be required to give a correct basis for accu-
rate contouring. (4) Plot the data, and interpolate contours
at a specified interval, employing both numerical calcula-
88
THE LEVEL
Sully f.
*,*gt3
an, Y 3.
CONTOUR PLAT AND DEVICE FOR THE
RAPID INTERPOLATION OF CONTOURS.
PROBLEMS. 89
tions and geometrical methods. (5) Finish the plat, as re-
quired.
PROBLEM C9. USE OF CONTOUR MAP.
(a) Equipment. Contour map, drafting instruments, etc.
(b) Problem. From the given contour map: (1) construct
profiles on the assigned lines; (2) project a line of specified
grade through assigned points on the contour map; make
profile, lay grade line and estimate earthwork quantities
approximately; (3) calculate the earthwork quantities from
the map for given grade planes and limitations of area.
(The third step may, perhaps, best be taken with a different
map from the first two.)
(c) Method*. (1) Use profile paper for the profiles. (2)
To project the line on the map, set the dividers at the
horizontal distance in which the specified gradient will sur-
mount the vertical interval between successive contour
planes; then beginning at a specified point, locate points
on the successive contour lines up or down on the given
gradient, as required; sketch in the route roughly, and pro-
ject a series of connected curved and tangent lines approxi-
mating to it; construct a profile along the new line; lay
the required grade line on the profile, and estimate approxi-
mate earthwork quantities for specified dimensions and
slopes of roadbed. (3) By means of end area method calcu-
late the earthwork quantities required to establish the
specified grade planes on the designated contoured area.
PROBLEM CIO. TEST OF DELICACY OF BUBBLE VIAL.
(a) Equipment. Engineers' leveling instrument, leveling
rod, tape, level tester.
(b) Problem. Determine the radius of curvature of the
assigned bubble vial. (1) by means of the optical test, and
(2) by the level tester.
(c) Method*. (1) Measure off a base line say 100 feet long,
set level at one end and hold rod on a peg driven at the
other end; note the target movement corresponding to a
given bubble movement, both in the same linear unit; cal-
culate the radius by the method shown at (h), Fig. 18. (2)
Set the level tester on a solid base and place the instru-
90 THE LEVEL.
ment on it, as indicated at (i), Fig. 18; by means of the
micrometer head and known relations of the level tester,
determine the angular equivalent in seconds for one divis-
ion and also one inch movement of the bubble, from which
calculate the radius of curvature of the vial in feet. Follow
the form.
PROBLEM Gil. COMPARISON OF LEVEL TELESCOPES.
(a) Equipment. Five (or other specified number) engin-
eers' levels (both wye and dumpy), leveling rod, metallic
tape.
(b) Problem. Make a critical examination and compari-
son of the telescopes of the assigned instruments.
(c) Methods. Carefully read the discussion of the tele-
scope in the text. Then compare the telescopes with refer-
ence to: (1) magnifying power; (2) chromatic aberration;
(3) spherical aberration; (4) definition; (5) illumination;
(6) flatness of fields; (7) angular width of field; (8) effect-
ive aperture of objective. Make tabulated record of com-
parisons, giving in separate columns; (a) locker number;
(b) kind of level; (c) name of maker; (d 1 ) magnifying
power; and so on for the other points examined.
PROBLEM C12. TESTS OF THE WYE LEVEL.
(a) Equipment. Wye level, leveling rod, tape.
(b) Problem. Test the essential relations and adjustments
of the wye level.
(c) Methods. Carefully note the construction of the as-
signed level and the positions of the elementary lines. Then
following the methods outlined in the text, test the fol-
lowing adjustments ('but do not disturb the adjusting
screws): (1) The bubble, both as to the azimuth and alti-
tude movements; find the position of the bubble when par-
allel to the element of the rings. (2) The line of collima-
tion; its deviation from the axis in 400 feet. (3) The wyes;
finding the position of the bubble when the vertical axis is
vertical. Keep a neat and systematic tabulated record of
observed numerical data, with explanation of the several
adjustments.
PROBLEMS.
91
PROBLEM CIS. ADJUSTMENT OF THE WYE LEVEL.
(a) Equipment Wye level (reserved expressly for ad-
justment), leveling rod, tape, adjusting pin.
(b) Problem. Make the full series of adjustments of the
wye level.
(c) M cth mix Follow the methods detailed in the text ac-
cording to the following program: (1) Adjust the bubble
line (a) into the same plane with the bottom element of
the rings, and (b) parallel to that element. (2) Adjust the
line of collimation to coincide with the axis of the rings,
first on a long distance; and then, to test the object glass
slide, try it for a short distance; if necessary, shift the
reticule in rotation to make the horizontal hair horizontal,
and also center the eyepiece. (3) Adjust the bubble line
perpendicular to the vertical axis by means of the wye
nuts. (4) Test the rings of the wye level by the two-peg
test; if the level has a reversion bubble, first test the paral-
lelism of the top and bottom tangent lines, and then test
the rings. Keep a clear and systematic record. In each
case, state (a) the desired relation, (b) the test, and (c) the
adjustment.
92 THE LEVEL.
PROBLEM C14. SKETCHING THE WYE LEVEL.
(a) Equipment. Wye level.
(b) Problem. Make a first-class freehand sketch of the
assigned wye level.
(c) Methods. The sketch should be correct in proportion
and clear in detail. The essential parts should be desig-
nated in neat and draftsmanlike form, and the elementary
lines clearly indicated.
PROBLEM CIS. TESTS OF THE DUMPY LEVEL.
(a) Equipment. Dumpy level, leveling rod, tape.
(b) Problem. Test the essential relations and adjustments
of the dumpy level.
(c) Methods. Carefully note the construction of the as-
signed level and the position of the elementary lines. Then,
following the methods outlined in the text, test the follow-
ing adjustments: (1) the bubble line, whether perpendic-
ular to the vertical axis; and if not, what is the angular
inclination of the vertical axis when the bubble is in the
middle? (3) The line of collimation, whether parallel to
the bubble line. Record the errors and observations sys-
tematically.
PROBLEM C16. ADJUSTMENT OF THE DUMPY LEVEL.
(a) Equipment. Dumpy level (reserved expressly for ad-
justment), leveling rod, tape, pegs, axe, adjusting pin.
(b) Problem. Make the essential adjustments of the as-
signed dumpy level.
(c) Methods. (1) Adjust the bubble line perpendicular to
the vertical axis. (2) Adjust the line of collimation parallel
to the bubble line by the two-peg method. In describing
the adjustments, the record should state (a) the desired
relation, (b) the test, and (c) the adjustment.
PROBLEM C17. SKETCHING THE DUMPY LEVEL.
(See Problem C14.)
PROBLEMS. 93
PROBLEM C18. STRETCHING CROSS-HAIRS.
(a) Equipment. Engineers' level or transit (or cross-hair
reticule), pocket cross-hair outfit, reading glass.
(b) Problem. Renew the cross-hairs in a level or transit
instrument by a method applicable to field use.
(c) Methods. (It instrument is provided, follow the com-
plete program outlined below; otherwise, merely stretch
the lines on the reticule and test same.) (1) Remove the
eyepiece, carefully preserving the screws from loss. (2)
Remove one pair of the capstan headed reticule screws;
turn the -ring edgewise and insert a sharpened stick in the
exposed screw hole, take out the other two screws and re-
move reticule from telescope tube. (3) Clean the cross-hair
graduations, and support the reticule on a sharpened stick,
or (if a transit) place it on the object glass with a piece of
paper interposed to protect the lens. (4) Select from the
capsule (see (d), Fig. 17) two spider lines 2 inches or more
long, and fasten a stick to either end of each hair by means
of glue from the adhesive paper. (5) Put the hairs in place,
(with the bits of wood hanging loose), shifting them as
desired with a pin point or knife blade. (6) Apply a bit of
the moistened adhesive paper to the reticule over each hair,
and after a few minutes cut or break the sticks loose. (7)
Test the hairs by blowing on them full force. (8) If they
stand this test, replace the reticule, and adjust the instru-
ment. Make a record of the process.
PROBLEM C19. ERROR OF SETTING A LEVEL TARGET.
(a) Equipment. Engineers' leveling instrument, leveling
rod (perferably a New York or Boston rod), tape, pegs.
(b) Problem. Determine the probable error of setting the
level target at distances of 100 and 300 feet (or such other
distances as may be assigned.
(c) Method*. (I) Determine the magnifying power of the
telescope. (2) Determine the radius of curvature of the
level vial by the field method. (3) Determine the space on
the rod-covered by the diameter of the hair. (4) Drive a
peg at ICO feet from the level, level up, and secure ten satis-
factory consecutive rod readings with rod held truly plumb
on the peg; shift the target several inches between read-
94 THE LEVEL.
ings, and reset without bias; reject no readings; watch the
bubble closely, but work briskly. (4) Repeat the series at
300 feet. (5) Determine for each distance the mean rod,
the probable error of a single reading, and of the mean, as
indicated in the form,
PROBLEM C20. COMPARISON OF DIFFERENT MAKES
AND TYPES OF ENGINEERS' LEVELS.
(a) EtiniiniH'iit. Department equipment, catalogs of repre-
sentative engineering instrument makers.
(b) PrvMcin. Make a critical comparison of the several
types and makes of engineers' levels.
(c) MrtJiat]*. Examine the department equipment and
study the several catalogs carefully, noting the usual and
special features, prices, etc., and prepare a systematic sum-
mary or digest of the same. Prepare brief specifications for
a leveling instrument, and also suggest the preferred make.
CHAPTER V.
THE TRANSIT.
Description. The engineers' transit consists of an ali-
dade, carrying the line of sight, attached to an inner verti-
cal spindle (or upper motion) which turns in an cuter an-
nular spindle (or lower motion). The latter carries the
horizontal graduated circle or limb, and is supported by the
tripod head. The alidade includes the telescope, magnetic
needle with its graduated circle, and the vernier; it may be
revolved while the graduated limb remains stationary. The
horizontal limb is graduated to degrees and half degrees
and sometimes to twenty minutes, and is numbered prefer-
ably from zero to 360 in both directions.
The complete transit differs from the plain transit, Fig.
20, in having a vertical arc and level bubble attached to
the telescope.
COMPLETE TRANSIT. PLAIN TRANSIT.
Fig. 20.
96
THE TRANSIT.
In Fig. 21 are shown: (a) the English theodolite; (b)
the shifting plates and foot screws of a transit; (c) the
Saegmuller solar attachment to the transit; (d) the grad-
Fig. 21.
USE OF THE TRANSIT. 97
ienter; (e) tripods; (f) reflectors; (g) reading glass; (h)
flag poles; (i) plumb bobs; (j) the Brunton pocket tran&it.
The Vernier. The vernier is an auxiliary scale used to
read fractional parts of the main graduated scale or limb.
The least count of a direct vernier is found by dividing the
value of one division of the limb by the number of divisions
on the vernier. With a limb graduated to half degrees and
a direct vernier reading to single minutes, 30 divisions on
the vernier cover 29 divisions on the limb.
In read in <j a direct vernier observe the following rule:
Read from the zero of the limb to the zero of the vernier,
then along on the vernier until coincident lines are found.
Add the reading of the vernier to the reading of the limb.
In scttiny the vernier to a given reading, as for example
a zero reading for measuring an angle, the tangent move-
ment should be given a quick short motion to secure the
last refinement, since a slow movement is not noticed by
the eye. Notice adjacent and end graduations.
In Fig. 23, (c) is a vernier reading to single minutes, (d)
to half minutes (30"), and (e) to thirds of minutes (20").
The slant in the numerals on the limb corresponds with that
on the vernier.
USE OF THE TRANSIT.
Use. The complete transit is used: (1) to prolong lines;
(2) to measure horizontal angles; (3) to measure vertical
angles; (4) to run levels; (5) to establish grade lines. The
plain transit is confined to the first two uses, unless it has a
vertical clamp and tangent movement, when it may be used
to "shoot in" grade lines.
Prolongation of Lines. If the instrument is in adjust-
ment a line can be prolonged by sighting at the rear sta-
tion and reversing the telescope in altitude. It is, however,
not safe to depend on the adjustments of the transit, and
important lines should always be prolonged by the method
of "double sights," as given in Problem D2. Lines may be
prolonged with the- plates by sighting at the rear station
with the A vernier reading 180, reversing the alidade in
azimuth and locating stations ahead with the : A vernier
reading zero. A third method employs two points ahead
of the instrument.
98 THE TRANSIT.
Measurement of Horizontal Angles, -Horizontal
angles are measured as described in Problem Dl. If greater
accuracy is required, angles may be measured by series or
by repetition.
By Series. In measuring an angle by series all the
angles around the point are read to the right, both verniers
being read to eliminate eccentricity. The instrument is
then reversed in altitude and azimuth and all the angles
around the point are read to the left. The readings are
checked by sighting back on the first point in each case.
These observations constitute one "set." The vernier is
shifted between sets 360 divided by the number of sets.
The arithmetical mean of the observed values is taken as
the true value.
Bit Repetition. Angles are measured by repetition as
described in Problem DIG. This method is especially suited
to the accurate measurement of angles with an ordinary
transit and is to be preferred to the series method which is
a favorite where precise instruments are used. In the repe-
tition method all the instrumental errors are eliminated
and the error of reading is very much reduced. It is doubt-
ful if it is ever consistent to make more than 5 or 6 repe-
titions.
Azimnth. The azimuth of a line is the horizontal angle
which it makes with a line of reference through one of its
ends, the angles being measured to the right from to
360, as in (f) Fig. 23. It is usual to assume that the true
meridian is the line of reference, the north point being
taken as zero in common surveying.
Deflection. The deflection of a line is the angle that it
makes with the preceding line produced, and is called de-
flection right or left depending upon whether the angle is
on the right or left side of the line produced, as in (h) (
Fig. 23.
Vertical Angles. Vertical angles are referred to the
horizon determined by the plane of the level under the
telescope, and are angles of depression or elevation relative
to that plane. In measuring vertical angles/the instrument
should be leveled by means of the level under the telescope
and correction should be made for index error of the- ver-
nier. With a transit having a complete vertical circle, the
true vertical angle may be obtained by measuring the
USE OF THE TRANSIT. 99
angle with the telescope normal and reversed and taking
the mean.
Traversing. A traverse is a series of lines whose
lengths and relative directions are known. Traverses are
used in determining areas, locating highways, railroads, etc.
Azimuth Traverse. In an azimuth traverse the azi-
muths of the lines are determined, usually passing around
the field to the right. In <,r\ni1\n<i the transit at any station
the A vernier is set to read the azimuth of the preceding
course, the telescope is reversed, directed towards the pre-
ceding station and the lower motion clamped; the telescope
is then reversed in altitude. The reading of the A vernier
with telescope normal will then give the azimuth of any line
sighted on. If there is any error in collimation the transit
may be oriented by sighting back with the A vernier read-
ing the back azimuth of the preceding course. In a closed
traverse the last front azimuth should agree with the first
back azimuth. The azimuth traverse is especially adapted
to stadia and railroad work. Azimuths can be easily
changed to bearings, if desired.
Deflection Traverse. In a deflection traverse the de-
flection of each line is determined, usually passing around
the field to the right. To avoid discrepancies due to error
in collimation, the transit may be oriented by sighting at
the preceding station with the A vernier set at 180, the
telescope being in its normal position, and the lower mo-
tion clamped. The reading of tae A vernier will then give
the deflection of any line sighted on.
Compass Bearings. Compass bearings should always
be read on an extended traverse as a check against such
errors as using the wrong motion or an erroneous reading
of the vernier. To guard against errors due to local attrac-
tion, back and front bearings should always be read, and
the angle thus determined compared with the transit angle.
Leveling with the Transit. The transit with an at-
tached level is the complete equivalent for the engineers'
level. The instrument is leveled up with the plate levels
first, after which the position of the attached bubble is eon-
trolled by means of the vertical tangent 'movement.
Grade Lines. Grade lines may be established with the
transit either by means of known distances and calculated
rod readings, or by "shooting in" a parallel line by means
100 THE TRANSIT.
of the inclined telescope, as deserioed under the use of the
engineers' level. For the latter purpose the transit is rather
more convenient than the level.
Setting up the Transit. To set the transit over a point
spread the legs so that they will make an angle of about
30, place them symmetrically about the point with two logs
down hill. Bring one plate level parallel to two of the legs,
force these legs firmly into the ground and bring the plumb
bob over the point and the plates approximately level with
the third leg, changing the position of the plumb bob with
a radial motion and leveling the plates with a circular mo-
tion of the leg. Finish the centering with the shifting
plates. In leveling up the bubbles move with the left thumb.
Use care to bring the foot screws to a proper bearing.
Parallax. Before beginning the observations the eye-
piece should be carefully focused on the cross-hairs so as to
prevent parallax.
Back Sight With Transit. A hcays check the Itncl- xifiJtt
tefore moving the transit to see that the instrument has not
been disturbed or that a wrong motion has not been used.
Instrumental Errors. The transit should be kept in as
perfect adjustment as possible, and should be used habitual-
ly as though it were out of adjustment, that is, so that the
instrumental errors will balance. No opportunity should be
lost to test adjustments.
ADJUSTMENTS OF THE TRANSIT.
Elementary Lines. Fig. 22 shows the elementary lines
of the transit, viz., (1) line of collimation; (2) horizontal
axis; (3) vertical axis; (4) plate level lines; (5) attached
level line. These lines should,have the following relations:
(a) the plate levels should be perpendicular to the vertical
axis; (b) the line of collimation should be perpendicular to
the horizontal axis; (c) the horizontal axis should be per-
pendicular to the vertical axis; (d) the attached level line
should be parallel to the line of collimation. The following
additional relations should exist: (e) the vertical axes of
the upper and lower motions should be coincident; (f) the
optical center of the objective should be projected in the
line of collimation; (g) the center of the graduated circle
ADJUSTMENT CF THE TRANSIT
101
should be the center of rotation, i. e., there should be no
eccentricity.
Plate Levels. To make the ]>l<itc 7rn7.s- in'ri>ciidit-nlar to the
vertical axis. Make the vertical a.rlx vertical tni'l adjuxt tin 1
bubbles to the middle of their race. The vertical axis is made
vertical by leveling up, reversing in azimuth, and if the
bubbles move, bring them half way back with the foot
screws. The adjustment is the same as for the compass, and
the reasons are shown in (a), Fig. 13.
After adjusting the plate levels with reference to say the
upper motion, test them with the lower motion to prove
the coincidence of the vertical axes.
Line of Collimation. To make the line of collimation per-
pendicular to the horizontal axis. Construct a straight tine
Fig. 22.
102 THE TRANSIT.
and adjust the vertical liair so that the instrument Kill
in altitude on it. The straight line may be established either
by prolongation beyond a point in front, or preferably by
the methods of double sighting, described in Problem D2.
One-fourth the apparent error is corrected for the reasons
indicated in (a), Fig. 23. In deciding which way to move
the hair, notice that the optical center is the fulcrum. The
transit should be collimated first for equal back and fore
sights, say 100 feet or so, and then checked for a dis-
tant point in one direction and perhaps 50 feet in the other,
so as to test the motion of the optical center of the
objective. The points should all be as definite as possible.
Chaining pins may be used, or V-marks may be made on the
side of a stake driven securely. Each altitude reversal
should be checked back and forth to make sure of the pro-
longations, and the telescope should be handled very care-
fully. If the cross-hair reticule is removed from the instru-
ment or should be much disturbed, the foregoing adjustment
is made approximately and the hair is made vertical by sight-
ing on a plumb line, such as the corner of a building, or by
noting whether the hair continuously covers the same point
as the telescope is moved in altitude; the collimation ad-
justment is then made precisely.
Horizontal Axis. To make the horizontal axis perpen-
dicular to the vertical axis. Adjust the horizontal a.ris so
that the line of collimation icill follow a plumb line. An actual
plumb line may be used; or preferably a vertical line may be
constructed by first sighting on a high point, then depres-
sing the telescope and marking a low point; then reversing
in altitude and azimuth (turning the horizontal axis end for
end), sighting at the high point again and marking a second
low point beside the first one. The mean of the two low
points is vertically beneath the upper one. The transverse
plate level is especially important in this process. One end
of the horizontal axis is changed, as in (b), Fig. 23.
Attached Level. To make the attached level and the line
of collimation parallel to each other. Construct a level line and
adjust the instrument to agree with it. The level line may be
obtained either by using the surface of a still body of water,
as of a pond, or it may be constructed by equal back and
fore sights, as indicated in (e), Fig. 16. Either the horizon-
tal hair may be changed to bring the line of collimation
ADJUSTMENT OF THE TRANSIT. 103
(C)
(dr
Fig. 23.
parallel to the bubble line, or vice versa. The method is the
same as used for the dumpy level.
If the bubble vial is a reversion level, as shown at
(b), Fig. 18, tihe adjustment is much simpler. However, the
two-peg test should be applied at least once to the reversion
level to prove the parallelism of the top and bottom tangent
lines of the bubble vial.
Vertical Arc. After the last preceding adjustment, the
vernier of the vertical circle should be made to read zero
when the bubble is at the center of the tube. Bring the
bubble to the center and shift the vernier to read zero. If
the vernier is fixed, an index correction may be applied to
all vertical angles; or the bubble may be made to agree
with the vernier and the horizontal hair then adjusted by
the two-peg method.
104 THE TRANSIT.
Eccentricity. Read the two verniers at intervals around
the circle; if the verniers have changed the same amount in
each case the circle is well centered. If the two verniers
have not changed the same amount, the mean of the angles
passed over by the verniers is the actual angle through
which the instrument has turned. The error cannot be ad-
justed.
Centering the Eyepiece. If the intersection of the
cross-hairs is not in the center of the field of view, move the
inner ring of the eyepiece slide by means of the screws
which hold it.
PROBLEMS WITH THE TRANSIT.
PROBLEM Dl. ANGLES OF A TRIANGLE WITH TRAN-
SIT.
(a) Equipment. Transit, 2 flag poles, reading-glass.
(b) Problem. Measure the angles of a given triangle vith
the transit.
(c) Methods. (1) Set the transit over one of the vertices
of the triangle and plumb a transit pole over each of the
other two. (2) Set the A vernier to read zero, sight at the
left hand point approximately, clamp the lower motion and
make an exact bisection with the lower tangent movement.
(3) Unclamp the upper motion, sight at the right hand
point approximately and make an exact bisection with the
upper tangent movement. (4) Read the A vernier to the
nearest single minute. This reading is the angle sought. (5)
With the A vernier set to read zero repeat the measurement,
sighting first at the right hand station and then at the left.
The recorded value of the angle is to be the mean of these
two determinations which must not differ by more than
one minute. (6) Measure the other angles in like n:anner.
The error of closure must not exceed one minute. Follow
the prescribed form.
PROBLEM D2. PROLONGATION OF A LINE WITH
TRANSIT.
(a) Equipment. Transit, 2 flag poles, axe, 6 hubs, 6 flat
stakes, tacks.
PROBLEMS.
105
Station
' >
(b) Problem. Prolong a EOD-foot base line successively
with the transit by the method of "double sights" about
1500 feet, and check on a hub previously established.
(c) Methods. (1) Drive two hubs, A and B, about 1500 feet
apart. (2) Set the transit over tack in hub A, sight at flag
pole plumbed over tack in hub B, drive hub C about SCO
feet from the transit and locate, a tack in line very care-
fully. Remove the flag pole from hub B. (3) Set the tran-
sit over hub C, back sight on hub A and clamp the vertical
axis. (4) Reverse the telescope, drive hub D at a distance
of about 300 feet and mark line very carefully with a pen-
cil. (5) Reverse the transit in azimuth, sight on hub A; re-
verse the telescope and locate a second point on hub D.
Drive a tack midway between these two points. (6) Set the
transit over the mean point on hub D, back sight on hub
C, prolong 300 feet and set hub E by double sights. (7) Set
over hub E, back sight on hub D, prolong 300 feet and set
hub P, as before. (8) Finally prolong from hub F, with
back sight on E, and establish mean tack at terminal hub
B. Record the collimation errors at D, E, and the final
error at B. Follow the form.
106. THE TRANSIT.
PROBLEM D3. INTERSECTION OF TWO LINES WITH
TRANSIT.
(a) Equipment. Transit, 2 flag poles, plumb line string,
axe, 6 hubs, 6 flat stakes, tacks.
(b) Problem Determine the intersection of two lines with
the transit.
(c) Methods. (1) Set the transit over a hub and tight at a
second point on line. (2) Set and tack a hub on line a short
distance on each side of the intersection. (3) Set the trans-
sit over a hub on the second line and sight at a point on
line. (4) Locate a hub at the intersection by sighting with
the transit and stretching a string between the two hubs
located on the first line. (5) Measure the angle of inter-
section. Record the data.
PROBLEM D4. TRIANGULATION ACROSS A RIVER.
(a) Equipment. Transit, 2 flag poles, 100-foot steel
tape, axe, 4 hubs, 4 flat stakes, tacks.
(b) Problem. Determine the distance across an imaginary
-river by triangulating with the transit and check by direct
measurement.
(c) Methods. (1) Set the transit over a hub on line on one
bank, and set a hub on the opposite bank of an imaginary
river about 800 feet wide by "double sigths". (2) Turn off
90 and lay off a base line very carefully with the steel tape.
(3) Set the transit over the hub at the farther end of the
base line and measure the angle between the lines joining
it and the other points. (4) Compute the distance across
the river. (5) Measure the distance across the rive." and
compare with the computed distance. The difference should
not be greater than 1:1000. Follow the prescribed form.
PROBLEM D5. PASSING AN OBSTACLE WITH TRAN-
SIT.
(a) Equipment. Transit, 100-foot steel tape, 2 flag poles,
axe, hubs, flat stakes, tacks.
(b) Problem. Prolong a line beyond an imaginary ob-
stacle by three methods and check by direct measurement.
(c) Methods. (1) Pass the obstacle to the right by means
PROBLEMS
107
IJO:
sjo'ooh
3F DOJJBLE SI6HTS
H ENGINEE
Jforrts." (Sff
et nubs QD on* i
using >r,e so*,
Note. It ts very
f lunar trlesccfe
5' TRANSIT.
tJ, Cool an* Cloudy.
about 300ft. frctnAA.
'Oft. by">ou6/e
X
a^j/yiwj/-^
Ooe. ^\
TRI,
^NGUL
ATI ON
ACRO
S A R
VER
SVITH ENGINEE
M' TRANS IT.
5 fat. 'on
Distance
Ancj
t
fVov.27, 133$. fff riot.
**), Cold ondC/eor.
Ft.
Value
tjjeof routh Transit,
ocAerryoei and
a
/so. oo
o-a-c
to'oo-
Ctia/niny iocrre
Mo 33.
c
e-c-o
fOJO
M'tr, Tram it over
9 set nub at D by
ttie'rtrtno * of D,
ub/e Sights* with
6D
t6/. as
A as a oacSrs/gri,
Stf rtvb at C, mease.
ing BC Mirh cart,
c
olcula
ion oj
^0..
and measvreof
CBCO
BO =
0CX7,
distance by c/Mtlnirto&a.
*o^
O-Lei,
/SO.O+
^c^To,
rfBt/0-
Lenytn of 7a/te &6
Iff. Observed eft's -
^ 0^ ,
0= Z.,
7C00+
ro.oess
fonces rrcor-a-ed.
t-
~* 2.
1SS9SI
i
0=1
i.sefi
*m /
A4MM4
BO-
ac x
-an. SO
30'
Surer-
eo
^^RY.
= /a/.,
>S ft.
/fftaf/naify
fkvvi
Colr, f
rsulf -
IS/SI
ft
-^
1
Chair,
eat o>i
fane 6
181. 4f
c y '~~\$
^
*.
/;*/.
'":.
t.'/eso
/SO.OO'
v
103 THE TRANSIT.
of the 'equilateral triangle method" with sights of not less
than 2(TO feet. (2) Pass the obstacle to the right by means of
the "right angle off-set method" and check on the same hub
as before. (3) Pass the obstacle to the left by means of the
"deflection method", turning off an angle that vrill just
pass the obstruction. Check the three methods by direct
measurement. Follow the prescribed form,
PROBLEM D6. TRAVERSE OF FIELD WITH TRANSIT.
(a) Equipment. Transit, 2 Hag poles, 100-foot steel tape.
(b) Prubh-m Determine the deflections of the sides of an
assigned field with the transit, check angles by observing
the magnetic bearings, and measure the lengths of the sides
with a steel tape.
(c) Methods. (1) Set the ti-ansit over one corner of the
field, set the A vernier to read 180, and sight at a flag
pole plumbed over the point to the left with the telescope
normal. Read and record the magnetic bearing. (2) Keep
the telescope normal and sight at the next point to the right.
The reading of the A vernier will be the deflection of the
second line. (3) Read and record the magnetic bearing
and compare the transit and magnetic deflections. (4) Re-
peat this process for the remaining corners of the polygon
taken in succession to the right. Deflections will be based
on duplicate readings agreeing within one minute. (5)
Measure the sides to the nearest 0.01 foot with the tape.
Compare the tape with the standard at the beginning and
conclusion of the chaining. (6) From the observed deflec-
tions determine the bearings of the field assuming one side
as a true meridian. The angular error of closure must not
exceed one minute. Record and reduce data as in the pre-
scribed form.
PROBLEM D7. AREA OF FIELD WITH TRANSIT.
(a) Equipment. Five-place table of logarithms.
(b) Proft/em. Compute the area of the assigned field by
means of latitudes and departures.
(c) Methods. (I) Prepare forms for calculation; tran-
scribe data, and carefully verify copy. (2) Compute lati-
tudes and departures by contracted multiplication, preserv-
PROBLEMS.
109
110 THE TRANSIT.
ing results to the nearest 0.01 foot. (3) Make the same cal-
culations by logarithms as a check. (4) Determine the ac-
tual linear error of closure. (4) Determine the permissible
error of closure .(see chapter on errors of suveying). (6) If
consistent, distribute the errors in proportion to the several
latitudes and departures, respectively, repeating the addi-
tions as a check. (7) Copy the field notes and adjusted lati-
tudes and departures, and verify transcript. (8) Calculate
the meridian distances of the several stations and lines. (9)
Calculate the latitude coordinates. (10) Calculate the par-
tial trapezoidal areas by multiplying the meridian dis-
tances of the lines by the respective latitudes, preserving
consistent accuracy, and' observing algebraic signs. (11)
Determine the area by taking the algebraic sum of the
partial areas. Reduce to acres, preserving results to the
nearest 0.001 acre. Follow the prescribed forms.
PROBLEM D8. STAKING OUT A BUILDING.
(a) Equipment. Transit, 100-foot steel tape, 2 flag poles,
axe, hubs, tacks, plan of building.
(b) Probltm. On an assigned plot of ground stake out
the assigned building.
(c) Methods. (1) Orient one side of the enclosing rec-
tangle with reference to a true meridian or a street line. (2)
Locate and check up the corners of the rectangle, by set-
ting over each corner in turn, passing around to the right,
back-sighting on the corner to the left, turning off 90
and locating the corner to the right. (3) Locate the corners
of the building by setting stakes on the side lines of the
building produced, using the rectangle as a base line. (4)
Check all stakes by additional measurements. The rectangle
should close to the nearest minute, the linear error should
not exceed 1:50,000. Follow the prescribed form.
PROBLEM D9. HEIGHT OF TOWER WITH TRANSIT.
(a) Equipment. Complete transit, 2 flag poles, leveling
rod, 100-foot steel tape, axe. hubs, tacks.
(b) Problem. Determine the height of an assigned tower
with the transit and steel tape.
(c) Methods. (1) Set the transit over a hub located a little
PROBLEMS.
Ill
112 THE TRANSIT.
further from the base than the height of the lower. (2)
Level the instrument very carefully with the attached level
and determine the index error of the vertical circle. (3)
Bring the bubble of the attached level to the center and read
a level rod held on the base of the tower. (4) Sight at the
top of the tower, read the vertical angle, correct for index
error and record. (5) Reverse the telescope and locate a
second point at least as far from the first as the height of
the tower, check by "double sights." (6) Set the transit
over the second hub, sight at the top of the tower and read
the vertical angle, as before. (7) Read the level rod on the
base of the tower as before. Each angle and rod reading
is to be based on duplicate readings. Follow the prescribed
form.
PROBLEM DID. ANGLES OF TRIANGLE BY REPETI-
TION.
(a) Equipment. Transit, reading glass, 2 chaining pins,
2 tripods with plumb bobs (if necessary).
(b) Problem-. Measure the angles of a prescribed triangle
with transit by repetition.
(c) .l/r/7/of/s. (l)Set the transit over one of the vertices of
the triangle and set chaining pins in the tops of the monu-
ments at the other two. (2) Set the A vernier to read zero,
(3) Sight at the left hand station with the bubble down,
and clamp the lower motion. (4) Unclamp the upper mo-
tion, sight at the right hand station, read both verniers and
record. (5) Unclamp the lower motion, sight at the left
hand station, and check the verniers to see that they have
not moved. (6) Unclamp the upper motion and sight at the
right hand station but do not read verniers. Repeat until
five repetitions of the angle are secured, and read both ver-
niers to eliminate errors of eccentricity. (7) Divide the
arithmetrical mean of the two vernier readings by five and
compare with the value obtained by single measurement. (8)
Reverse the instrument in altitude, and set the A vernier to
read zero. (9) Sight at the right hand station with the
bubble up, and clamp the lower motion. (10) Unclamp the
upper motion,- sight art- the left hand station, read both ver-
niers and record. (11) Unclamp the lower motion, sight at
the right hand station, and check the verniers to see that
PROBLEMS.
113
ANCLfS OF
TRIAN iLE S
114. THE TRANSIT.
they have not moved. (12) Unclamp the upper motion and
sight at the left hand station, but do not read the verniers.
Repeat until five repetitions of the angle are secured, and
read both verniers to eliminate errors of eccentricity. (13)
Divide the mean of the two vernier readings by five and
compare with the value obtained by single measurement
(14) Take the mean of the two sets as the most probable
value. (15) Measure the other angles in the same manner.
The angular error of closure should not exceed 15". Follow
the prescribed form.
PROBLEM Dll. DETERMINATION OF TRUE MERIDIAN
BY OBSERVATION ON POLARIS AT ELONGATION.
(a) Equipment. Complete transit, reading glass, hub, 2
flat stakes, plank 18"x 4"x 2", 4 8d nails, axe, 2 lanterns,
good watch set and regulated to keep railroad time.
(b) Problem. Determine a true meridian by an observa-
tion on Polaris at elongation.
(c) Methods. (1) Calculate the time of elongation of
Polaris, and regulate and set a good reliable watch to keep
railroad time (mean solar time for the 90th meridian.) (2)
Set the transit over a hub about 40 minutes before the time
of elongation. (3)Level the instrument very carefully, and
set the vernier of the vertical circle to read the latitude of
the place. (2) Focus the objective on a bright star; sight
at Polaris which will be found by following the pointers of
the Great Dipper at an elevation equal to the latitude of the
place. (3) With a reflector or a piece of white paper re-
flect light into the telescope so that the cross-hairs and the
image of Polaris will be visible at the same time. (4) De-
press the telescope and establish a target at a distance of
about 500 feet; place the plank on the ground and nail it
firmly to a flat stake driving one at each end. (5) Level up
again and follow Polaris with the telescope by means of the
tangent movement; at elongation it will appear to traverse
the vertical hair for several minutes. (6) Depress the tele-
scope, sight at a pencil held on the target and mark the
n oint very carefully. (7) As a check make three observa-
tions within half an hour after elongation, noting the time
of sighting on the star. Reverse the instrument in altitude
nnd azimuth after the first check observation. (8) Reduce
the check observations to observations at elongation by the
PROBLEMS.
115
following rule: Multiply the square of the time since
elongation in minutes by 0.058, and the product will be the
correction to the azimuth of Polaris in seconds of arc, for
latitude 40. (9) The next morning lay off the azimuth of
Polaris for each observation to the east or west depending
upon whether the observation was made at western or east-
ern elongation. (10) Check the observed meridian with the
standard meridian. The error of the mean of the four ob-
servation should not exceed one minute. Record and re-
duce the data as in the prescribed form.
PROBLEM D12. DETERMINATION OF TRUE MERIDIAN
BY OBSERVATION ON POLARIS AT ANY TIME.
(a) Equipment. The same as in Dll.
(b) Problem. Determine a true meridian by observing
Polaris at any time.
(c) MethndK. (l) Make the observations in the manner
described in Dll. (2) Compute the azimuth of Polaris at
the time of each observation, using the tables given in the
U. S. Land Survey Manual, pp. 118-119; Johnsons' Survey-
ing, pp. 814-815; Wilsons' Topographic Surveying, pp. 716-
116
THE TRANSIT.
AZIMUTHS OF POLARIS AT ELONGATION
Between 1900 and 1910 and Latitudes 3O and6oNorth.
(From U. S. Land Survey Manvil.)
Latitde.
1900.
1901.
1902.
1903.
1904.
95-
30
I 24.9
i 24.6
i 24.2
i 23.9
i 23.5
I 23.1
31
25.8
25-5
25-1
24-7
24.4
24.0
32
26.7
26.4
26.0
25.6
25-3
24.9
33
27-7
27.3
27.0
26.6
26.2
25.9
34
28.7
28.4
27.6
27.2
26.9
35
i 29.8
i 29.4
I 29.0
l 28.7
i 28.3
I 27-9
36
30.9
30.5
30.1
29.8
29.4
29.0
37
32.1
3i-7
31-3
30,9
30.5
30.1
38
33-4
33-0
32.6
32.2
31. s
31.4
39
34-7
34-3
33-9
33-5
33-1
32.7
40
i 36.0
i 35-6
i 35.2
I 34.8
i 34-4
I 34-0
41
37-5
37-1
36.7
36.2
35-8 ; 35-4
42
43
39-o
40.6
38/6
40.2
38.2
39-8
37-7
39-3
37-3 36.9
38-9 38.5
44
42.3
41-8
41.4
41.0
40.5 40.1
45
I 44.0
I 43-6
I 43-2
i 42-7
I 42.3 i 41.8
46
45-9
45-5
45.0
44-6
44.2 43.7
47
47-9
47-4
46.9
46.5
46.0 ; 45.6
48
49-9
49-5
49-o
48.6
48.1 47.7
49
52.1
51-7
51.2
50.7
50.2 49.8
50
I 54-4
I 54.0
i 53-5
i 53-0
1 52.5 I 52.0
Latitude.
1906.
1907.
1908.
1909.
,9,0.
3
I 22.8
i 22.4
I 22.1
I 21-7
I 21.3
31
2 3 .6
23.2
22.9
22.5
22.2
32
24-5
24.1
23.8
23-4
23.1
33
25-5
25-1
24-7
24.3
24.0
34
26.5
26.1
25-7
25-3
25.0
35
I 27.5
i 27.1
I 26.8
I 26.4
I 26.0
36
28.6
28.2
27.9
27-5
27.1
37
29.7
29.3
29-0
28.6
28.2
38
31.0
30.6
30.2
29.8
29.4
39-
32.3
31-8
31-4
31-0
30.6
40
I 33-6
I 33-2
I 32-8
I 32.4
I 32.0
41
35-0
34.6
34-2
33-8
33-4
42
36.5
36.0
35-6
35-2
34-8
43
38.
37-6
37-2
36.8
36.3
44
39-
39-2
38.8
33.4
37-9
45
I 41.
I 40.9
I 40.5
I 40.1
I 39-6
46
43-
42.7
42.3
41.9
41.4
47
45-
44-6
44-2
43-7
43-3
48
47-
46.7
46.3
45-8
45-3
49
49-
48.4
47 -9
47-4
50
i 51-
I 51-0
i 50.6
i 50.1
I 49-6
PROBLEMS.
117
CORRECTION TO AZIMUTHS OF POLARIS FOR EACH MONTH.
(From U. S. Land Surrey Manual.)
Latitude.
Latitude.
f.
40.
55-
35.
40*.
55.
January....
'
- 0.4
-0.5
July
, Q
+ 0.3
+ -4
February . . .
-3
0.3
- 0.4
August
~\~ -
-4- o. I
+ -2
March
April
O.I
0.2
0.2
September. .
0.
0.
0. I
- o-3
-4
May
June
+ 0.2
+ 0.3
+ 0.4
December.. .
0.
- o.S
- -7
LOCAL MEAN TIME-OF UPPER CULMINATION OF POLARIS.
Computed for Longitude 6 hours or 90 W. of Greenwich.
(From U. S. Land Survey Manual.)
Date.
1900
,,0,
190*.
,.
.904.
1903.
Dift. for
i Day.
Jan.
Feb.
I
Mar.
Apr.
636.3
5 4i-o
433-9
3 38.6
2 43.4
148.2
6 37.4
5 42-1
4 35-o
3 39-7
2 44.5
i 49-3
638.5
5 43-2
436.1
340.8
2 45-6
i 50.4
039.6
5 44-3
4 37-2
341-9
246-7
I 51-5
6 40.7
545-4
438.3
3 43-0
2 47-8
I 52.6
641.8
546.5
4 39-4
344-1
2 48.9
i 53-7
046.8
3-95
3-95
3-95
3-95
3 94
3-94
3-94
May'
3 42-4
239-5
22 40.6
22 41.7
242.8
346.8
2 43.9
23 47-9
22 44.0
3-93
3-93
June
I
July
Aug.
i
Sept.
Oct.
i
o 38.0
943-2
8405
7 45-7
6 39.1
5 44-3
4 37-6
342.7
2 39.9
i 44 9
20 39.1
9 44-3
8 41.6
746.8
6 40.2
545-4
4 38.7
343-8
2 41.0
I 46.0
20 40.2
9 45-4
8 42.7
7 47-9
641-3
5 46-5
4 39-8
3 44-9
2 42.1
I 47-1
041.3
946.5
843.8
7 49-0
6 42.4
547.6
4 0.9
3 6.0
2 3.2
I 8.2
042.4
9 476
8 44.9
7 50.1
6 43.5
5 48-7
4 42.0
3 47-1
2 44-3
I 49-3
2043-5
19 48.7
1 8 46.0
17 5L2
16 44.6
15 49-8
I443.I
13 48.2
12 45.4
II 50.4
3 92
3-92
3-92
3-92
3 9 1
3-92
3-92
3.92
3-93
3-93
I
Dec.
15
9 42-9
8 399
7 44-7
9 44-0
8 41.0
7 45-8
9 45-1
842.1
7 46.9
9 6.2
8 3.2
7 48.0
9 47-3
844.3
7 49-1
948.4
8 45-4
7 502
3-94
3-94
3.94
118 THE TRANSIT.
717. (3) The next morning lay off the computed azimuth
for each observation. (4) Check the observed meridian
with the standard meridian. The error of the mean of the
five observations should not exceed one minute. Record
the data.
PROBLEM D13. COMPARISON OF TRANSIT TELE-
SCOPES.
(a) Equipment. Five engineers' transits.
(b) Problem. .Make a critical comparison of the telescopes
of five engineers' transits.
(c) Methods. Follow the methods outlined in the com-
parison of level telescopes.
PROBLEM D14. TEST OF A TRANSIT.
(a) Equipment. Transit, reading glass, leveling rod,
chaining pins, foot rule.
(b) Problem. Test the following adjustments of an as-
signed transit: (1) Test the graduation for eccentricity
(2) Test the plate levels to see if they are perpendicular to
the vertical axis. (3) Test the line of collimation to see if
it is perpendicular to the horizontal axis. (4) Test the
horizontal axis to see if it is perpendicular to the vertical
axis. (5) Test the level under the telescope to see if the
tangent to the tube at the center is parallel to the line of
collimation. (6) Test the vertical circle to see if the vernier
reads zero when the line of sight is horizontal.
(c) Methods. Make the tests as described in the first part
of this chapter but do not make any of the adjustments or
tamper with any of the parts of the instrument. Check each
test. Make a careful record of the methods and errors, in-
cluding a statement of the manner of doing correct work
with each adjustment out.
PROBLEM D15. ADJUSTMENT OF A TRANSIT.
(a) Equipment. Transit, reading glass, leveling rod,
chaining pins, adjusting pin, small screw driver.
(c) Methods. Make the following tests and adjustments
of an assigned transit that has been thrown out of adjust-
ment by the instructor: (1) Test the graduation for eccen-
PROBLEMS.
119
tricity. (2) Adjust the plate levels perpendicular to the
vertical axis. (3) Adjust the line of collimation perpendicu-
lar to the vertical axis. (4) Adjust the horizontal axis per-
pendicular to the vertical axis. (5) Adjust the level under
the telescope parallel to the line of collimation. (6) Ad-
just the zero of the vertical circle to read zero when the
line of sight is horizontal. (7) Center the eyepiece.
(c) Methnds.Ma.'ke the tests and adjustments as de-
scribed in the first part of this chapter. Use extreme care
in manipulating the screws and if any of the parts
stick or work harshly, call the instructor's attention before
proceeding. Repeat the tests and adjustments. Make a
careful record of methods and errors.
PROBLEM D16. SKETCHING A TRANSIT.
(a) I-'<ii(iimcnt. Engineers' transit.
(b) Problem. Make a first-class sketch of an engineers'
transit.
(c) Methods. (See similar problem with the level.)
The floff iv<a
'rpf&feat /vsf
Error
'ftfof eacn fr'fnt.
TO ft.
00 Ft.
+r-^3j ,0,103 *>.
4/0?- 0.031 In-aoon ft
-10. 006J-
120 THE TRANSIT.
PROBLEM D17. ERROR OF SETTING FLAG POLE WITH
TRANSIT.
(a) Equipment. Transit, iron flag pole, flat stake l"x 2"x
15", foot rule.
(to) Problem. Determine the probable error of setting a
flag pole with the transit at a distance of 300 feet. Repeat
for 600 feet.
(c) Methods (1) Set the transit up and sight at the flag
pole plumbed near the middle of the stake at a distance of
about 300 feet. (2) Measure the distance from the point of
the flag pole to a mark on the stake. (3) Keep the vertical
axis clamped, and move the pole to one side. (4) Set the
pole with the transit, and measure the distance from the
first line. (5) Repeat until at least ten consecutive satis-
factory results are obtained. (6) Compute the probable
error of a single observation and of the mean of all the
observations (see chapter on errors of surveying), and re-
duce the mean error to its angular value. (7) Repeat for 600
feet. Determine distances by pacing. Follow the prescribed
form.
PROBLEM D18. REPORT ON DIFFERENT MAKES AND
AND TYPES OF TRANSITS.
(a) Equipment. Department equipment, catalogs of the
principal makers of engineers' transits.
(b) Problem. Make a critical comparison of the several
types of transits made by the different makers.
(c) Methods. (See similar problem with the level.)
CHAPTER VI.
TOPOGRAPHIC SURVEYING.
Topographic Map. A topographic map is one which
shows with practical accuracy all the drainage, culture, and
relief features that the scale of the map will permit. These
features may be grouped under three heads as follows: (1)
the culture, or features constructed by man, as cities,, vil-
lages, roads; (2) the hypsography, or relief of surface forms,
as hills, valleys, plains; (3) the hydrography, or water
features, as ponds, streams, lakes. The culture is usually
represented by conventional symbols. The surface forms
are shown by contours (lines of equal height), (a) Fig. 24,
or hachures, (b) Fig. 24. The water features are shown by
soundings, conventional signs for bars, etc.
Topographic maps may be divided into two classes de-
pending upon the scale of the map. Small scale topographic
maps are made by the U. S. Coast and Geodetic Survey and
the U. S. Geological Survey, and are drawn to a scale of
1:62,500, 1:125,000 or 1:250,000 with corresponding contour
intervals of 5 to 50, 10 to 100, and 200 to 250 feet. These
maps show the streams, highways, railroads, canals, etc., in
outline but do not show any features of a temporary char-
acter.
Fig. 24.
122 TOPOGRAPHIC SURVEYING.
Large scale topographic maps are drawn to a scale of 400
feet to 1 inch (1:4800), or greater, with contour intervals
from 1 to 10 feet depending upon whether the ground is flat
or hilly. Roads, streets, dwellings, streams, etc., are drawn
to scale. Features too small to be properly represented
when drawn to scale are drawn out of proportion to the
scale of the map.
Topographic Survey. The object of a topographic sur-
vey is the production of a topographic map, and hence
neither time nor money should be wastefully expended in
obtaining field data more refined than the needs of the map-
ping demand.
METHODS. A topographic survey may be dividied into
three parts: (1) the reconnaissance; (2) the skeleton of
the survey; (3) filling in the details.
Reconnaissance. The reconnaissance is a rapid prelim-
inary survey to determine the best methods to use in mak-
ing the survey and the location of the principal points of
control. A careful reconnaissance enables the topographer
to choose methods that are certain to result in a better map
and a distinct saving of time.
Skeleton. There are three general methods of locating
the skeleton of a topographic survey: (1) tie line survey
with chain only; (2) traverse method with transit or com-
pass; (3) triangulation system, (f), Fig. 30. The first
method is used for the survey of small tracts. The second
method, in which the distances are measured with the chain,
tape or stadia, is used on railroad and similar surveys. The
third method, in which triangulation stations are connect-
ed with each ether and with a carefully measured base line
and base of verificatio'n, is used on surveys for small scale
maps and on detailed or special surveys, such as surveys
of cities and reservoir sites.
Filling in Details. There are three general methods
employed for filling in details: (1) with transit or compass
and chain; (2) with transit and stadia; (3) with plane table
and stadia. The transit and stadia are used by the Missis-
sippi and Missouri River Commissions. The plane table
and stadia are used by the U. S. Coast and Geodetic and the
U. S. Geological Surveys.
Topographic City Survey. A topographic city survey is
one of the best examples of a survey for a large scale map.
HYDROGRAPHIC SURVEY. 123
It is usually based on a system of triangulation executed
with precision and connected with carefully measured base
lines. The details of the survey are usually taken up in the
following order: (1) reconnaissance and location of trian-
gulation stations; (2) measurement of base line and base of
verification; (3) measurement of angles by repetition; (4)
establishment of bench marks by running duplicate levels,
(5) adjustment of angles of triangulation system; (6) com-
putation of sides, azimuths and coordinates; (7) filling in
details, usually with transit and stadia; (8) plotting of
triangulation and other important points on the map by
rectangular coordinates; (9) plotting the details and com-
pleting the map. The instructions given on the succeeding
pages are for a survey of this type.
HYDROGRAPHIC SURVEY.
Classes. Hydrographic surveying may be divided into
river and marine. The first includes the determination of
depths, location of bars, and obstructions to navigation,
determination of area of cross-section, discharge, sediment
carried, etc. The second includes the making of soundings,
location of bars, ledges, buoys, etc. The depth of the water
is determined by making soundings with a lead or rod,
and the velocity is gaged by means of floats or a current
meter, (d), Fig. 31.
Soundings are located: (1) by two angles read simulta-
neously from both ends of a line on the shore, (f), Fig. 31;
(2) by keeping the boat in line with two flags on shore, and
determining the position on the line by means of an angle
read on the shore, or by a time interval; (3) by intersecting
ranges, (g), Fig. 31; (4) by stretching a rope or wire across
the stream; (5) by measuring with a sextant in the boat
at the instant that the sounding is taken two angles to three
known points on the shore, (c), Fig. 31; the point is located
by solving the three point problem graphically with the
three arm protroctor, (e), Fig. 31; (6) by locating the posi-
tion of the boat at the instant that the soundings are taken
with transit and stadia. The first three methods are used
on small river or lake surveys. The fourth method is used
where soundings are taken at frequent intervals. The fifth
method has been used almost exclusively in locating sound-
124
TOPOGRAPHIC SURVEYING.
ings in harbors, lakes, and large rivers. The sixth method
is rapidly coming into general use and promises to be the
favorite method.
THE STADIA.
Description. The stadia is a device for measuring dis-
tances by reading an intercept on a graduated rod. The
stadia-hairs, shown in (g), Fig. 27, are carried on the same
reticule as the cross-hairs and are placed equidistant
from the horizontal hair. The stadia-hairs are sometimes
placed on a separate reticule and made adjustable. It is,
however, considered better practice by most engineers to
have the stadia-hairs fixed and use an interval factor,
rather than try to space the hairs to suit a rod or to gradu-
ate a rod to suit an interval factor.
Stadia Rods. Stadia rods are always of the self reading
type. In Fig. 27, (a) a-nd (b) are the kind used on the U. S.
Coast Survey; (c) on the U. S. Lake Survey; (d) and (c) by
the U. S. Engineers. A target for marking on the rod the
height of the horizontal axis of the transit above the sta-
tion occupied is shown in (f), Fig. 27.
Theory of the Stadia. In Fig. 25, by the principles of
optics, rays of light passing from points A and B on the
rod through the objective so as to emerge parallel and pass
through the stadia-hairs a and b, respectively, must inter-
sect at the principal focal point d in front of the objective;
therefore the rod intercept, s is proportional to the dis-
tance, g from the principal focal point in front of the ob-
jective.
THE STADIA.
125
Stadia Formula For Horizontal Line of Sight and Ver-
tical Rod. In Fig. 25, from similar triangles we have
From which
and
s :g :: i : f
g = -p s = ks
D = k s + (c -f f)
(1)
(2)
(3)
Stadia Formula For Inclined Line of Sight and Ver-
tical Rod In Fig. 26 we have
and
but
also
BD = AE cos a (approx. ) (4)
D = k s cos a + (c + f) (5)
H = D cos a (6)
= k s cos 2 a + (c + f ) cos a (7 )
= k s kssin 2 a + (c -f f) cos a (8)
V = D sin a . (9)
= k s sin a cos a -f (c + f) sin a (10)
, ikssin2a + (c + f) sin a (11)
126
TOPOGRAPHIC SURVEYING.
USE OF THE STADIA. The transit is set up over a
station of known elevation and with a given direction or
azimuth to another visible station; the height of the line of
collimation above the top of the station is determined either
by holding the rod beside the instrument and setting the
target, or preferably by graduating one leg of the tripod
and using the plumb bcb; then with the transit oriented on
a given line, "Phots" are taken to representative points, and
record made of the rod intercept, vertical angle and azi-
muth. In reading the intercept the middle hair is first set
roughly on the target, then one stadia-hair is set at the
nearest foot-mark on the rod and the intercept read with
the other stad'ia-hair, after which the precise vertical angle
is taken, and the azimuth is read.
Reducing the Notes. The notes may be reduced by
means of tables, diagrams, or a special slide rule. The slide
rule is the most rapid but has the disadvantage that it can-
not well be taken into the field.
Hi
(0)
<>
'hi (C) (d)
Fig. 27.
<!
THE PLANE TABLE. 127
1 1
COMPLETE PLANE TABLES
THE PLANE TABLE.
Description. The plane table consists of an alidade,
carrying a line of sight and a ruler with a fiducial edge. The
alidade is free to move on a drawing board mounted on a
tripod. The drawing board is leveled by means of plate
levels. The line of sight should make a fixed horizontal
angle with the fiducial edge of the ruler. The complete
plane table is a transit in which the horizontal limb has
been replaced by a drawing board.
There are three general types of plane tables: (1) the
Coast Survey plane table, (a) Fig. 28; (2) the Johnson plane
table, (b), Fig. 28: (3) the Gannet plams table, (d), Fig. 29.
USE OF THE PLANE TABLE. In making a survey
with a plane table the angles are measured graphically and
the lines and points are plotted in the field. The principal
methods of making a survey with a plane table are: (1)
radiation; (2) traversing; (3) intersection; (4) resection.
Radiation. In this method a convenient point on the
paper is set over a selected point in the field, and the table
clamped. The line of sight is then directed towards each
point to be located in turn and a line is drawn along the
fiducial edge of the ruler. The distances, which may be de-
termined -by measuring with chain, tape or stadia, are
plotted to a convenient scale, (a), Fig. 30.
Trarrring. This method is practically the same as trav-
128
TOPOGRAPHIC SURVEYING.
Fig. 29.
ersing with a transit,, (b), Fig. 30. Care should be used
in orienting the plane table to get the point on the paper
over the corresponding point on the ground as nearly as the
character of the work requires.
Intersection. In this method the points are located by in-
tersecting lines drawn from the ends of a measured base
line, (c), Fig. 30.
Resection. In the resection method the plane table is set
up at a random point and oriented with respect to either
three or two given points, which gives rise to two methods
known respectively as the three-point and two-point prob-
lems.
Three Point Problem. "Where three points are located on
the map and are visible but inaccessible, the plane table is
oriented by solving the "three point problem". There are
several solutions, the 'best known of which are: (1) the
mechanical solution; (2) the Coast Survey solution; (3)
Bessel's solution; (4) analytical solution. The problem is
indeterminate if a circle can be passed through the four
points.
In the mechanical solution the two angles subtended by
the three points are plotted graphically on a piece of trac-
ing paper and the point is located by placing the tracing
paper over the plotted points.
THE PLANE TABLE.
129
In Bessell's solution, (d), Pig. 30, a, b, c are three points
on the map corresponding to the three points, A, B, C on
the ground, and D is the randlom point at the instrument
whose location, d, it is desired to find on the map. Con-
struct the angle 1 with vertex at point c as follows: Sight
along the line ca at the point C, and clamp the vertical axis.
Then center the alidade on c and sight at B by moving the
alidade, and diraw a. line along the edge of the ruler. Con-
struct the angle 2 with vertex at a in the siame manner. The
Fig. 30.
130 TOPOGRAPHIC SURVEYING.
line joining b and e will pass through the point d required.
Orient the board by sighting at B with the line of sight
along the line e b, and locate d by resection.
Two Point Problem. To orient the board whon only two
points are plotted, proceed as follows: Select a fourth
point, c, that is visible, and with these two points as the
ends of a base line, (e), Fig. 30, laid off to a convenient
scale, locate two points a' and b' on the map by intersec-
tion. The error of orienting the board will be the angle
between the lines a, b and a' b'. The table can now be
oriented and the desired point located on the board by re-
section.
Adjustments. The adjustments of the plane table are:
(1) the plate levels; (2) the line of collimation; (3) the
horizontal axis; (4) the attached level. These adjustments
are practically the same as those for the transit.
THE SEXTANT.
Description. The sextant consists of an arc of 60,
with each half degree numbered as a whole degree, (a), Fig.
31, combined with mirrors so arranged that angles can be
measured to 120.
Theory. The principle upon which the sextant is con-
structed is that if a ray of light is reflected successively be-
tween two plane mirrors, the angle between the first and
last direction of the ray is twice the angle of the mirrors.
In (b), Fig. 31, the angles of incidence and reflection
are equal,
i = r and i l = r 1 , and
E= (i + r) (i 1 + r')= 2 (r-r>)
C l = (90 i 1 ) (90 r) = (r r 1 )
and therefore E = 2 C 1
but C 1 = angle CIC 1 , by Geometry, since the
mirrors are parallel for a zero reading.
USE OF THE SEXTANT. To measure an angle be-
tween two objects with a sextant bring its plane into the
plane of the two objects; sight at the fainter object with the
telescope and bring the two images into coincidence. The
THE SEXTANT.
131
Fig. 31.
reading is the angle sought. The angle will not be the true
horizontal angle between the objects unless the objects are
in the same level with the observer. Since the true vertex
of the measured angle shifts for different angles the sextant
should not be used for measuring small angles between ob-
jects near at hand.
ADJUSTMENTS. Index Glass, To make the index,
glass, I, perpendicular to the plane of the -limb, 'bring -the
vernier to about the middle of the arc and examine the arc
132 TOPOGRAPHIC SURVEYING.
and its image in the index glass. If the glass is perpendicu-
lar to 'the plane of the limb, the image of the reflected and
direct portions will form a continuous curve. Adjust the
glass by means of the screws at the base.
Horizon Glass. To make the horizon glass, II, parallel
to the index glass, I, for a zero reading. With the vernier
set to read zero, sight at a star and note if the two images
are in exact coincidence. If not, adjust the horizon glass
until they are. If the horizon glass cannot be adjusted,
bring the images into coincidence by moving the arm and
read the vernier. This reading is the index error which
must be applied with its proper sign to all the angles
measured.
Line of Collimation. To make the line of collimation
parallel to the limb. Place the sextant on a plane surface
and sight at a point about 20 feet away. Place two objects
of equal height on the extreme ends of the limb and note
whether both lines of sight are parallel. If not, adjust the
telescope by means of the screws in "the ring that carry it.
PROBLEMS IN TOPOGRAPHIC SURVEYING.
PROBLEM El. DETERMINATION OF STADIA CON-
STANTS OF TRANSIT WITH FIXED STADIA-HAIRS.
(a) Equipment. Complete transit, stadia rod. steel tape,
set chaining pins, foot rule.
(b) Problem. Det ermine the stadia constants c, f and k
for an assigned transit.
(c) Methods. (1) Set up the transit and set ten chaining
pins in line about 100 feet apart on level ground. (2) Plumb
the stadia rod by the side of the first pin. (3) Set the lower
hair on an even foot or half foot mark keeping the telescope
nearly level, and read the upper stadia-hair. (4) Record
the intercept. (5) Read the intercept on the rod at the re-
maining pins. (6) Measure the distance from the center of
the transit to each pin with the steel tape. (7) Focus the
objective on a distant object, measure f (the distance from
the plane of the cross-hairs to the center of the objective),
and c( the distance from the center of the objective to the
center of the instrument). (8) Calculate the value of the
stadia ratio, k, for each distance by substituting in the
PROBLEMS.
m
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134 TOPOGRAPHIC SURVEYING.
fundamental stadia formula. (9) Take the arithmetical
mean of the ten determinations as the true value. (10) Com-
pute the probable error of a single observation and of the
mean of all the observations. The interval factor should
be determined by the instrument man under the conditions
of actual work. The determination should be checked at
frequent intervals during the progress of the field work.
Follow the prescribed form.
PROBLEM E2. STADIA REDUCTION TABLE.
(a) Equipment. (No instrumental equipment required.)
(b) Problem. Compute a stadia reduction table giving the
horizontal distances from a point in front of the objective
equal to the principal focal distance for the stadia intervals
from 0.01 feet to 10 feet, for the transit used in Problem El.
(c) Methods. (1) Prepare form for calculation. (2) Com-
pute the horizontal distances by substituting the different
values of s in the stadia formula. Compute D' for values of
s varying from 0.01 foot to 0.1 foot varying by 0.01 foot;
from 0.1 foot to 1 foot varying by 0.1 foot; and from 1 foot
to 10 feet varying by 1 foot.
(To use the table, take the sum of the values of D' cor-
responding to the units, tenths and hundredths of s as given
in the table. To the value of D' thus obtained add c plus f.)
PROBLEM E3. AZIMUTH TRAVERSE WITH TRANSIT
AND STADIA.
(a) Equipment. Complete transit, stadia rod, steel pocket
tape.
(b) Problem. Make a traverse of the perimeter of an as-
signed field with a transit and stadia.
(c) Methods. (1) Set the transit over one corner of the.
field and set the A vernier to read the azimuth of the pre-
ceding course. (2) Sight at a stadia rod held edgewise on
the last station to the left with the telescope normal and
clamp the lower motion. (3) Read the intercept on the rod
to the nearest 0.01 foot. (4) Sight at the target set at the
first station and read the vertical angle to the nearest min-
PROBLEMS. 135
ute. (The observer should measure the height of the hori-
zontal axis above the station with the steel pocket tape, or
one tripod leg may be graduated and the instrument height
determined by swinging the plumb bob out against the leg.)
(5) Unclamp the upper motion, sight at the next station to
the right and clamp the upper motion. (6) Read the A ver-
nier, which will be the azimuth of the course. (7) Read the
intercept on the rod. (8) Measure the vertical angle by
sighting at the target set at the height of the horizontal
axis as before. (9) Set the transit over the next station to
the right and determine the intercepts and vertical angles as
at the first station. (10) Determine the stadia intercepts and
vertical angles at the remaining stations, passing around the
field to the right. (11) Reduce the intercepts to horizontal
distances before recording. (12) Compute the vertical dif-
ferences in elevation using mean distances and vertical
angles, (13) Compute latitudes and departures to the near-
est foot using a traverse diagram or traverse table. Follow
form B4. The angular error of closure for a six-sided
field should not exceed 2' Follow the prescribed form for
the field notes.
PROBLEM E4. SURVEY OF FIELD WITH PLANE
TABLE BY RADIATION.
(a) Equipment Plane table, stadia rod, 2 flag poles, engin-
eers' divided scale, drawing paper, 6H pencil.
(b) Problem Make a survey of an assigned field by radi-
ation with the plane table.
(c) Met'hods. (1) Set the plane table up at some conven-
ient point in the field and select a point on the drawing
board that will allow the entire field to be plotted on the
paper. (2) Sight at one of the stations with the ruler cen-
tered on the point on the paper. (3) Draw a line along the
fiducial edge of the ruler towards the point. (4) Measure
the distance to the point with the stadia. (5) Lay off the
distance on the paper to the prescribed scale. (6) Locate
the remaining points in the same manner. (7) Complete
the map in pencil. The map should have a neat title, scale,
meridian, etc. (8) Trace the map on tracing linen. (9)
Compute the area by the perpendicular method, scaling the
dimensions from the map.
136 TOPOGRAPHIC SURVEYING.
PROBLEM E5. SURVEY OF A FIELD WITH PLANE
TABLE BY TRAVERSING.
(a) Equipment Plane table, stadia rod, 2 flag poles, engin-
eers' divided scale, drawing paper, 6H pencil.
(b) Problem. Make a survey of an assigned field by tra-
versing with the plane table.
(c) Methods: Follow the same general methods as those
given for traversing with the transit. Adjust the plane
table before beginning the problem. Complete the map and
compute the area as in Problem E4.
PROBLEM E6. SURVEY OF FIELD WV^H PLANE
TABLE BY INTERSECTION.
(a) Equipment. Plane table, 2 flag poles, engineers divid-
ed scale, drawing paper, 6H pencil.
(b) Problem. Make a survey of an assigned field with tfc.3
plane table by intersection.
(c) Methods. (1) Select and measure -a base line having
both ends visible from all the stations in the field. (2) Set
the plane 'table over one end of the base line and sight at
the other end of the base line and at each one of the
stations of the field. (3) Set the plane table over the other
end of the base line, orient the instrument by sighting at
the station first occupied and sight at all the stations in the
field. (4) Complete the map and compute the area as in
Problem E4.
PROBLEM E7. THREE POINT PROBLEM WITH PLANE
TABLE.
(a) Equipment Plane table, 2 flag poles, engineers' divid-
ed scale, 6H pencil.
(b) Problem. Having three points plotted on the map, re-
quired to locate a fourth point on the map by solving the
"three point problem" with the plane table.
(c) Methods. (1) Use Bessell's solution. (2) Check by
using the mechanical solution.
PROBLEM E8. ANGLES OF TRIANGLE WITH SEX-
TANT.
(a) Equipment. Sextant, 2 flag poles.
PROBLEMS. 137
(b) Problem. Measure the angles of an assigned triangle
with the sextant.
(c) Method*. -(I) Set the flag poles behind the monuments
at two of the vertices of the triangle and stand on the
monument at the third. (2) Hold the plane of the sextant
horizontal, sight at one flag pole directly with the tele-
scope and bring the image of the other flag pole into coin-
cidence by moving the arm. (3) Read the vernier. This
reading is the angle sought. (4) Repeat the measurement
with the sextant inverted. Take the mean of the two read-
ings, which should not differ more than 2' as the true value
of the angle. (5) Measure the other angles in the same
manner. The error of closure should not exceed 3'. Record
the data in a suitable form.
PROBLEM E9. DETERMINATION OF COEFFICIENTS
OF A TAPE.
(a) Equipment. Steel tape, spring balance, 2 thermom-
eters, steel rule, 2 stout stakes, axe, 2 pieces sheet zinc 2 by
2 inches.
(b) Problem. Determine the coefficients of expansion,
stretch and sag for an assigned tape. Make three deter-
minations of each and take the arithmetrical mean as the
true value.
(Standard Tape*. In laying off a standard or measuring
a base line where a high degree of precision is required it
is important that all measurements be referred to the same
standard 1 . The Bureau of Weights and Measures of the U.
S. Coast and Geodetic Survey, Washington, D. C., will com-
pare a tape with the government standard for a small fee.
The tape tested is certified to be of a given length for a
given temperature and pull. For example the standard tape
marked "U. S. W. & M. 215" used in laying off the 100-ft.
standard in Problem A. 23, was certified to be 99.9967 feet
long at a temperature of 62 F. and a pull of 12 pounds when
tested on a plane surface. The coefficient of expansion of
this tape was 0.0000061 per degree F.)
(c) Methods. (1) Correction for Expansion. Measure the
length of the tape on a plane surface at two different tem-
peratures but with a constant pull determined by a spring
balance. Then substitute the lengths, 1 and L, and tem-
peratures, t and T in the formula
138 TOPOGRAP1HC SURVEYING.
1 L = e ( t T ) 1
where e is the coefficient of expansion. Repeat the test
and obtain three values of the coefficient e. As large a
range of temperatures as possible should be secured. Take
the arithmetrical mean of the three determinations as the
true value.
(2) Correction for Stretch. Measure the length of the tape
on a plane surface with two different pulls but at a constant
temperature. Determine the pull with a spring balance.
Then substitute the lengths 1 and L and the pu,lls p and P
in the formula
1 L = s ( p P ) 1
where s is the coefficient of stretch. Repeat the test and
obtain three values of the coefficient s. The pulls should
range from 10 to 40 pounds. Take the arithmetical mean
of the three determinations as the true value.
(3) Correction for Sag. Remove the handles from the taps
and determine its weight very carefully. Divide the weight
by the length to obtain the weight per foot, w. Drive two
stout hubs a little less than 100 feet apart and fasten a piece
of sheet zinc with a line ruled at right angles to the line on
the top of each stake. With a pull of 10 pounds, as deter-
mined by the spring balance, measure the distance between
the stakes. Calculate the correction for sag by substituting
the lengths 1 and L, pull p, and weight per foot w, in the
formula.
1 - L= 2 1 4 (y) 2
Repeat the measurements using a pull of 20 and 30 pounds,
respectively. Add the corrections for sag to each measure-
ment and compare the results. The temperature should re-
main constant during the tests. To remove the possibility
of an error due to temperature, observe the temperature at
the time of each observation and correct the observed
length for expansion before substituting in the formula.
Report the methods, data, computations and results on a
suitable form.
(a) Equipment. Standard tape, transit or level, stakes
PROBLEMS. 139
PROBLEM E10. MEASUREMENT OP BASE LINE.
i
(number and size to be specified by instructor), axe, spring
balance, 2 thermometers, lath stakes, 8-d nails, steel rule,
pieces sheet zinc 2 by 2 inches.
(b) Problem. Measure an assigned base line with a stan-
dard tape. Support the tape at intervals of 20 feet and note
the pull and temperature. Make at least three determin-
ations of the length of the base line. Reduce the observed
results to the standard by making corrections for standard,
expansion, sag, stretch and slope. Take the arithmetical
mean of all the determinations as the true value.
(c) Methods. (1) Set the transit over one end of the base
line, sight at the other end and determine the difference
in elevation and grade. (2) Drive stout square stakes to
grade by "shooting" them in with the instrument in true
line a little less than a full tiape length apart. The
tops of the lowest stake should not be less than 6 inches
above the ground. (3) Fasten a piece of sheet zinc with a
fine line ruled at right angles to the direction of the base
line on the top of each stake. (4) Drive lath stakes in line
about 20 feet apart. (5) Drive an 8-d nail through
each lath stake at grade to support the tape. (6) Measure
from stake to stake, the men working as follows: No. 1
plumbs up from the rear monument or holds the zero on
the mark on the rear stake; No. 2 takes the spring balance
and puts a pull of 16 pounds on the tape; No. 3 reads the
tape and measures the fraction of a tenth with a steel
rule to 0.001 feet; No. 4 records the reading of the tape and
reads the two thermometers placed at the quarter points
of the tape. (7) Obtain at least three determinations of the
length of the base line. (8) Correct each measurement of
the base for standard, expansion, sag, stretch, and slope
(see problem on coefficients of a tape). The three measure-
ments should not differ more than 1:100,000. Report
methods, computations and results on a suitable form.
PROBLEM Ell. CALCULATION OF TRIANGULATION
SYSTEM.
(a) Equipment Seven-place table of logarithms.
(b) Problem. Adjust and calculate an assigned triangula-
tion system and plot the skeleton.
140 TOPOGRAPHIC SURVEYING.
(c) Methods. Observe the following program: (1)
prepare forms for calculation and transcribe data; (2) ad-
just the angles of the triangulation system (see chapter on
errors of surveying) ; (3) calculate the front and back azi-
muths of each line; (4) beginning with the base line com-
pute the sides, to the nearest 0.001 foot; (5) calculate the
latitudes and departures to the nearest 0.001 foot. (6) cal-
culate the coordinates of the triangulation stations to the
nearest 0.001 foot. In computing the coordinates of the
stations take the mean of the values found by taking the
different routes from the base line as the true value. (7)
Plot the skeleton of the triangulation system to the pre-
scribed scale by means of the coordinates of the points.
The plotting sheet should be ruled off into squares very
carefully before beginning the plotting. For this purpose
use a steel straight edge and beam compass.
PROBLEM E12. SKETCHING TOPOGRAPHY.
(a) Equipment. Small drawing board or plane table, plat
of assigned field, 4H pencil.
(b) Problem. Sketch in the roads, walks, buildings and
five foot contours on the plat of the assigned field by eye
having given the elevations of the ruling points.
(c) Methods (1) Transfer from the level notes to the plat
the elevations of the ruling points of the field. (2) Locate
the roads, buildings, etc., on the map as nearly as possible
in their relative positions (the topographers' estimate of
distances should be frequently checked by pacing.) (3)
Estimate the slopes and locate the contour points between
the points of known elevation. (4) Join these points by
smooth curved lines. (5) Finish the map in pencil, putting
on a neat title, the scale of the map and a meridian. (6)
Compare the finished map with a contour map furnished by
the instructor.
PROBLEM E13. FILLING IN DETAILS WITH TRANSIT
AND STADIA.
(a) Equipment. Complete transit, 2 stadia rods, pocket
tape.
(b) Problem. Locate the topographic details of an as-
signed area with the transit and stadia.
PROBLEMS.
141
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(c) Methods (1) Set the transit over one corner of the
field and set the A vernier to read the azimuth of a triangu-
lation line. (2) Sight at the s'tadia rod held sidewise on the
triangulation station at the other end of the given line, with
the telescope normal and clamp the lower motion. (3)
Read the intercept on the rod to the nearest 0.01 foot. Re-
duce this reading and check the ratio k by comparing the
observed with the known distance. (4) Sight at target of
the stadia rod or a rubber band at the height of the hori-
zontal axis of the instrument above the first station and
read the vertical angle to the nearest minute. (5) Unclamp
the upper motion and take side shots to locate the topo-
graphic details. In taking the side shots read the intercept
first, then set the middle cross-hair on the target and signal
the rod man all right. The vertical angle and azimuth
can then be read. Enough side shots should be taken to lo-
cate representative points, ridges, gullies, etc., on the sur-
face that can be shown on the finished map. The scale of
the map should therefore be known before beginning the
field work. It is usually best to run along the top of a ridge
and take side shots on both sides. (6) After all the side
shots have been taken at the first triangnlqtion station
142 TOPOGRAPHIC SURVEYING.
select a stadia station at a convenient point. (7) Sight at
the edge of the stadia rod held on the stadia station and
clamp the upper motion. (8) Read the A vernier which
will be the azimuth of the course. (9) Read the intercept
on the rod. (10) Measure the vertical angle as before. Set
the transit over the stadia station and orient as at the first
station. Take side shots as at the first station. Continue
around the field, connecting the stadia stations by a closed
traverse as in Problem E3. Record the field notes in the
prescribed form. (11) Reduce the field notes by using either
the slide rule, tables, or diagrams, and check in part by
using one of the remaining methods. (12) Plot the stadia
traverse and sid<e shots using a protractor. Number each
point plotted on the map and write its elevation just below
the number in the form of a fraction. (13) Locate the con-
tours by interpolating between the plotted points and com-
plete the map in pencil on manila paper. (14) Trace the
map if required.
PROBLEM E14. FILLING IN DETAILS WITH PLANE
TABLE AND STADIA.
(a) Equipment. Complete plane table (preferably with
prismatic eyepiece), 2 stadia rods, engineers' divided scale,
drawing paper, 6H pencil, pocket tape.
(b) Problem. Locate the topographic details of an as-
signed area with the plane table and stadia.
(c) Methods Follow the same methods as in Problem E13
except that the notes are to be plotted on the drawing paper
in place of being recorded in the field book. Mark the point
by number and write the elevation of each point under the
number in the form of a fraction. Locate the contour points
by interpolation on the map and connect the points by
smooth curves. Complete the map in pencil and make a
tracing if required.
PROBLEM E15. TOPOGRAPHIC SURVEY.
(a) Equipment. Complete transit, 2 stadia rods, stakes,
hubs, spring balance, pocket tape, stadia slide rule, seven-
place logarithm table, (extra tripods, stadia reduction table
stadia reduction diagrams, etc., as required).
PROBLEMS. 143
(b) Problem. Make a Complete topographic survey of an
assigned area and make a topographic map.
(c) Methods (1) Make a reconnaissance and locate the
triangulation stations. Care should be used to select the
triangulation stations so that the sights will be clear and
the triangles well formed. A system composed of quad-
rilaterals or more complicated figures will give more con-
ditions and checks than a simple string of triangles. A
system composed of simple triangles is sufficient for this
survey. (2) Mark the triangulation stations with gas pipe
monuments about 4 feet long, the exact point being marked
by a hole drilled in a bolt .screwed into a cap on the top of
the gas pipe. (3) Measure the base line and base of veri-
fication as described in Problem E10. (4) Measure the
angles by repetition as depcribed in Problem DIG. (5) Cal-
culate the skeleton as described in Problem Ell. (6) Estab-
lish permanent bench marks and determine their elevations
and the elevation of the stations of the triangulation sys-
tem by running duplicate levels with the engineers' level
reading the rod *o 0.001 foot. (7) Fill in the details with
either the transit and stadia or the plane table and stadia,
or both, as described in Problems E13 and E14. (8) Com-
plete the map in pencil on manila paper, and after- it has
been approved by the instructor trace it on tracing linen.
The title, meridian, scale, lettering and border should re-
ceive careful attention.
PROBLEM E16. LEVELS FOR PROFILE AND QUANTI-
TIES FOR PAVING A STREET.
(a) Equipment. Level, level rod, 4 flag poles. 100-foot steel
tape, chaining pfns, 50-foot metallic tape, hubs, axe.
(b) Problem. Take level rod readings on the center line,
right and left curb lines, right and left sidewalk lines, and
right and left property lines to determine profiles and quan-
tities for paving 1 street. Plot profiles on Plate A profile
paper to a scale of 40 feet to 1 inch horizontal and 4 feet to
1 inch vertical. Estimate the quantities of cut and fill and
paving materials.
(c) Vetfi od. * (1) Locate the center line of the street and
set flag poles on line about 400 feet apart by ranging in
with the eye. (2) Drive a hub at one end of the street and call
144
TOPOGRAPHIC SURVEYING.
this point station zero. (3) Run a line of differential levels
from the Standard B. M. to the zero end of the line. Read
the rod to 0.01 fort. (4) Read the level rod to 0.1 foot on the
ground at center hub. (5) Measure the distance out to the
right curb line, right sidewalk and right property lines
with the metallic tape and read the rod to 0.1 foot on the
ground. (6) Repeat for the left side. (7) Chain along the
center line to station 1. (8) Measure to the right and left
from the chaining pin the required distances with the
metallic tape and take rod readings as at station zero. (9)
Repeat the process at each station and at abrupt changes
intermediate. (10) Check the level circuit. (11) Make pro-
file on Plate A paper, scales 40 feet to the inch horizontal
and 4 feet vertical, indicating the several lines by conven-
tional lines or cclors. (12) Lay grade line as directed. (13)
Show plat at bottom of profile. (14) Plot sections at scale
of 20 feet to the inch and determine areas. (15) Compute
quantities of earthwork, paving, etc. Follow form.
12.09
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CHAPTER VII.
LAND SURVEYING.
Kinds of Surveys. Surveys of land are of two kinds:
(a) original surveys; (b) resurveys.
Original Surveys. An original survey is made for the
purpose of establishing monuments, corners, lines, bound-
aries, dividing land, etc. The survey of a townsite and the
government survey of a section are examples of original
surveys.
Resurveys. A resurvey is made for the purpose of iden-
tifying and locating corners, monuments, lines and bound-
aries that have been previously established. The resurvey of
a city block, or a survey to relocate a section corner are
examples of resurveys.
Functions of a Surveyor. In an original survey it is
the function of the surveyor to make a perfect survey, es-
tablish permanent monuments and true markings, and make
a correct record of his work in the form of field notes and
a plat.
In a resurvey it is the function of the surveyor to find
where the monuments, courses, lines and boundaries orig-
inally were, and not where they ought to have been. Fail-
ing in this it is his business to reestablish them as nearly as
possible in the same place they were. No reestablished
monument, no matter how carefully relocated will have the
same weight as the original monument if the latter can be
found. In making resurveys the surveyor has no official
power to decide disputed points. He can only act as an
expert witness. If the interested parties do not agree to
accept his decision the question must be settled in the
courts.
Rules for Resurveys. The following rules may be safe-
ly observed in making resurveys.
(1) The descriptions of boundaries in a deed are to be
taken as most strongly against the grantor.
(2) A deed is to be construed so as to make it effectual
rather than void.
(3) The certain parts of a description are to prevail over
the uncertain.
146 LAND SURVEYING.
(4) A conveyance by metes and bounds will convey all
the land included within.
(5) Monuments determine boundaries and transfer all
the land included.
(6) When a survey and a map disagree the survey pre-
vails.
(7) Marked lines and courses control courses and dis-
tances.
(8) The usual order of calls in a deed is: natural ob-
jects, artificial objects, course, distance, quantity.
(9) A long established fence line is better evidence of
actual boundaries than any survey made after the monu-
ments of the original survey have disappeared.
(10) A resurvey made after the monuments have disap-
peared is to determine where they were and not where they
ought to have been.
(11) All distances measured between known monuments
are to be pro rata or proportional distances.
If the above rules do not cover the case in question spe-
cial court decisions on that particular point should be con-
sulted.
THE UNITED STATES RECTANGULAR SYSTEM OF
PUBLIC LAND SURVEYS.
Historical. The United States rectangular system of
subdividing lands was adopted by congress May 20, 1785.
The first public land surveys were made in the eastern part
of the present state of Ohio under the direction of Capt.
Thomas Hutchins,* Geographer of the United States, and
were known as the "Seven Ranges". The tov/r: ships were
six miles square, and were laid out in ranges extending
northward from the Ohio river; the townships were num-
bered from south to north, the ranges from east to west.
In these initial surveys only the exterior lines of the town-
*The earliest published reference to the rectangular sys-
tem of land surveys is found in an appendix to "Bouquet's
Mardh," published in Philadelphia, 1764. Hutchins was
engineer with this expedition to the forks of the Muskingum
river, and wrote the appendix. (See reprint by Robt.
Clarke, Cincinnati.)
UNITED STATES LAND SURVEYS. 147
were run, but mile corners were established on the
township lines, and sections one mile square were marked
on the plat and numbered from 1 to 36, commencing with
section 1 in the southeast corner and running from
south to north in each tier to 36 in the northwest section.
The act of congress approved May 18, 1796, provided for
the appointment of a surveyor general and changed the law
relating to the surveys of public lands. Under this law the
townships were subdivided into sections by running paral-
lel lines two miles apart each v/ay and setting a corner at
the end of each mile. This law also provided that the sec-
tions be numbered beginning with section 1 in the north-
east corner of 'the (township, thence west and east alter-
nately to 36 in the southeast section. This is the method
of numbering still in use, shown in Figs. 33 and 34.
The act of congress approved May 10, 1800, required that
townships be subdivided by running parallel lines through
the same from east to west and from south to north at a
distance of one mile from each other. Section corners and
half section corners on the lines running from east to west
were required to be set. The excess or deficiency was to be
thrown into the north and west tiers of sections in the
townships.
The act of congress approved February 11, 1805, required
that interior section lines be run every mile; that corners
be established every half mile on both townships and sec-
tion lines; that discrepancies be thrown on the north and
west sides of the township. This act of congress further
provided "that all corners marked in the original surveys
shall be established as the proper corners of sections, or
subdivisions of sections; and that corners of half and
quarter sections not marked shall be placed as nearly as
possible "equidistant" from those two corners which stand
on the same line. The boundary lines actually run and
marked shall be established as the proper boundary lines
of the sections or subdivisions for which they were intend-
ed; and the length of such lines as returned by the surveyor
shall be held and considered as the true length thereof, and
the boundary lines which shall not have been actually run
and marked as aforesaid shall be ascertained by running
straight lines from the established corners to the opposite
corresponding corners." Under this law, which is still the
148
LAND SURVEYING.
FIRST v
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INITIAL/
POINT.
BASE LINE,
Fig. 32.
established rule of procedure, each reported distance be-
tween established monuments is an independent unit of
measure.
The revised instructions issued in 1855 required that the
sections be subdivided as shown in Fig. 33, the full lines,
representing "true" lines, are parallel to the east exterior
line of the township, and the dotted lines, representing
"random" lines, close on corners previously established.
The order of the survey of the interior section lines is in-
dicated by the small numerals. Double corners on the
north and west township lines, which were common in the
earlier surveys, were thus avoided in the revised practice.
Laws Inconsistent. It is obviously impossible to pre-
serve a true rectangular system on a spherical surface, ow-
UNITED STATES LAND SURVEYS. 149
ing to the convergency of meridians.* To harmonize the
methods of making surveys, the General Land Office has
issued instructions for the survey of public lands from time
to time.
DETAILS OF SURVEY. The details of the survey are
taken up in the following order: (1) selection of initial
points; (2) establishment of the base line; (3) establish-
ment of the principal meridian; (4) running standard paral-
lels; (5) running the guide meridians; (6) running the
township exteriors; (7) sirbdividing the township; (8)
meandering lakes, rivers, streams, etc. See Figs. 32 and 33.
Initial Points. Initial points from which to start the
survey are established whenever necessary iinder special
instructions prescribed by the Commissioner of the General
Land Office.
Base Line. The base line is extended east and west
from the initial point on a parallel of latitude. The proper
township, section and quarter corners are established and
meander corners at the intersection of the line with all
meanderable streams, lakes, or bayous. Two sets of chain-
men are employed and the mean of the two measurements
is taken as the true value. When the transit is used, the
base line which is a small circle parallel to the equator
is run by making offsets from a tangent or secant line, the
direction of the line being frequently checked by an observ-
ation of Polaris.
Principal Meridian. The principal meridian is extend-
ed either north or south, or in both directions from the
initial point on a true meridian. The same precautions are
observed as in the measurement of the base line.
Standard Parallels. Standard parallels, which are also
called correction lines, are extended east and west from the
principal meridian, at intervals of 24 miles north and
south of the base line. They are surveyed like the base line.
Guide Meridians. Guide meridians are extended north
*The angular convergency, a, of two meridians is m sin L,
where m is the angular difference of longitude of meridians
and L is the mean latitude of the two positions. The linear
convergency, c, for a length, t, is t sin a. For latitude 40,
the difference between the north and south sides of a town-
ship is 0.60 chains.
150
LAND SURVEYING.
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TI
ffondorn
t
H7 I
igrJ^
I6 1
t
* 15 i
25 ^- x
! 14 !
; 13
6- >
{.9l
| 20 !
t
5 2I 1
t
; 22^1
-t
23 i
24|
30 I
46- -p
* ZQ l
t
, 27 )
, 26 1
* 25
2 V
31 ]
32]
33 I
<M
"i
35 1
36
Fig. 33.
from the base line, and standard parallels, at intervals of
24 miles east and west from the principal meridian, in the
manner prescribed for running the principal meridian.
When existing conditions require that guide meridians shall
be run south from the base or correction lines, they are
initiated at properly established closing corners on such
lines.
Township Exteriors. The township exteriors in a tract
24 miles square, bounded by standard lines, are surveyed
successively through the block, beginning with the south--
western township. The meridional boundaries are run first
form south to north on true meridians with permanent cor-
ners at lawful distances; the latitudinal boundaries are run
from east to west on random or trial lines and corrected
UNITED STATES LAND SURVEYS.
151
First t'ian^a I' Parallel \ North I T
.f" I Sec.k I sZc.S* ^c!^ I Sec. 1 '
aftow ;>ta ivprwnfc a theoretical township with perfect tvbdMtion*,
cmttyiu>u to the north side of a Standard Parallel; in assumed Latitude
42 15' N.. and Longitude 10000' W. of Cr. Area M024.J6 A,
Fig. 34.
back on true lines. Allowance for the convergency of
meridians is made whenever necessary.
Township Subdivision. A true meridian is established
at the southeast corner of the township and the east and
south boundaries of section 36 are retraced. Then begin-
ning at the corner to sections 35 and 36 on the southern
boundary, a line is run north parallel to the range line,
corners are established at a distance of 40 and 80 chains;
from the last named corner a random line is run eastward,
parallel to the south boundary line of section 36, to its
intersection with the east boundary of the township. A
temporary corner is set at a distance of 40 chains, and a
permanent corner is afterwards established midway be-
52
LAND
39.94
T 39.94 '
1
Aifl
o
o
8
1 6
j 39.82
I
| 39.8
(G)
Fig. 35.
tween the two permanent corners. The other corners are
located in a similar manner, as shown in Pig. 33. The lines
closing on the north and west boundary lines of the town-
Ship are made to close on the section corners already es-
tablished. A theoretical township with perfect subdivisions
is shown in Fig. 34.
Meandering. Navigable rivers and other streams hav-
ing a width of three chains and upwards are meandered on
both banks, at the ordinary hig'h water line by taking the
general courses and distances of their sinuosities. The
meanders of all lakes, navigable bayous, and deep ponds of
the area of twenty-five acres and upwards are surveyed as
UNITED STATES LAND SURVEYS.
153
11
****
10 Ac.
40 A< - nE.%
i:,
w 2 I6O Ac.
640 Ac.
w.i
E -~L 5 -
QO Ac.
s.w.~
dO Ai,. 160 Ac.
\
\
Fig. 36.
directed for navigable streams. Meander corners are estab-
lished where meander lines cross base lines, township lines,
or section lines.
Subdivision of Sections. In Fig. 35, (a) gives the sub-
division of an interior section, (b) of section 2 on the north
side, (c) of section 7 in the west tier, and (d) of section 6
in the northwest corner.
Description of Land. Land is described in the rectan-
gular system by giving its Location in a civil township; for
example, in Fig. 36, the northwest quarter, containing
160 acres, would be described as: N E 14, Sec. 8, T 19 N,
R 9 E, 3 P. M. The ten acre lot indicated in tlhe northwest
quarter would be described as: S E y, N W %, N W *4,
Sete. 8, T 19 N, R 9 E, 3 P. M.
Corners. The corner monuments may be as follows:
(a) stone with pits and. earthen mound; (b) stone with
mound of stone; (c) stone with bearing trees; (e) post in
mound! of earth; (f) post in mound of stone; (g) post with
bearing trees; (h) simple mound of earth or stone; (i) tree
without bearing trees; (j) tree with bearing trees; (k) rock
in place, etc. The trees on line are required to be blazed.
The size, markings and proper corners to be used in any
154 LAND SURVEYING.
particular case and all other details are given in the
"Manual of Surveying Instructions for the Survey of Pub-
lic Lands of the United States," issued by the General Land
Office, Washington, D. C.
Restoration of Lost or Obliterated Corners.* An
obliterated corner is one where no visible evidence remains
of the work of the original surveyor in establishing it. Its
location may, however, have been preserved beyond all
question by acts of landowners, and by the memory of those
who knew and recollect the true position of the original
monument. In such cases it is not a lost corner.
A lost corner is one whose position can not be determined
beyond reasonable doubt, either from original marks or re-
liable external evidence.
General Rules. The following rules are derived from a
brief synopsis of congressional legislation relating to sur-
veys.
(1) The boundaries of the public lands established and
returned by the duly apponted government surveyors, when
approved by the surveyors general and accepted by the gov-
ernment, are unchangeable.
(2) The original township, section, and quarter-section
corners established by the government surveyors must stand
as the true corners which they were intended to represent,
whether the corners be in place or not.
(3) Quarter-quarter corners not established by the gov-
ernment surveyors shall be placed on the straight lines
joining the section and quarter-section corners and mid-
way between them, except on the last half mile of section
lines closing on the north and west boundaries of the
townships, or on other lines between fractional sections.
(4) All subdivisional lines of a section running between
corners established in the original survey of a township
must be straight lines, running from the proper corner in
one section line to its corresponding corner in the opposite
section line.
(5) That in a fractional section where no opposite corre-
sponding corner has been or can be established, any re-
*Circular on the "Restoration of Lost and Obliterated
Corners and Subdivision of Sections," General Land Office,
Washington, D. C.
UNITED STATES LAND SURVEYS.
s
155
Fig. 37.
quired subdivision line of such section must be run from the
proper original corner in the boundary line due east and
west, or north and south, as the case may be, to the water
course, Indian reservation, or other boundary of such sec-
tion, with due parallelism to section lines.
Locations of Principal Meridians. Principal merid-
ians have been established as the needs of the surveys
warranted. The surveys in the state of Indiana were made
with reference to the 2nd Principal Meridian, and those of
Illinois with reference to the 2nd, 3rd and 4th Principal
Meridians. See Pig. 37. There are twenty-four principal
meridians in all, the locations of which are given in the
"Manual of Instructions," mentioned above.
Abridging Field Notes. The government surveyors use
156
LAND SURVEYING.
the method of abridging field notes shown in Fig. 38. Cor-
ners in the township boundary are referred to by letter;
interior section corners are referred to by giving the num-
bers of the sections meeting at the corner; interior quarter
section corners are referred to by giving the number on the
section lines produced.
Ed
CbBaA
1
i
i
i
i
!
D -
\e
i
15
!*
\3
i
\z
/
I
1
1
1
S ,'Q
1
5 10
!
15
1
k
IU
1
B
1
12
i
\G
1
i
I
i
i
13
-14-
b
MS-
1
19
\G
l- Q--
\5
HJK-
1-4
1
I
13
, 2 ; 3 _.
-24-
1
\6
\S
*-Z8--
1
13
i ,
12
Us-
1
--3 1 !--
1
I
'--33-
1-4
1
13
1
1
12
^-36--
/V n O oPpQyffrS s T
Fig. 38.
SURVEYS BY METES AND BOUNDS.
That portion of the United States settled before the adop-
tion of the rectangular system was surveyed by the method
of metes and bounds. For the most part these surveys were
very irregular and often involved complex and conflicting
conditions. The entire eastern portion of the United States,
and the state of Kentucky, were surveyed in this manner,
and further examples are found in the French surveys in the
states of Michigan, Indiana, Illinois, Missouri, Louisiana,
PROBLEMS.
1R7
etc . and the Spanish surveys of Texas, California, etc. The
general principles underlying the questions of ownership,
priority of survey, the restoration of lost corners, etc., are
identical whatever the system of survey used.
PROBLEMS IN LAND SURVEYING.
PROBLEM Fl. INVESTIGATION OF A LAND CORNER
(a) Equipment. Digging outfit, tape, etc, as required.
(b) Problem. Collect complete evidence relative to an as-
signed land corner, and after giving due weight to the same,
make a decision as to the true corner.
(c) Metlwds. (1) Make careful examination of the official
field notes and records pertaining to the land corner in
question and make extracts from the same for further ref-
erence. (2) Seek oral evidence from those acquainted with
the history of the corner. (3) Make a survey of fence lines
and other physical evidence, such as witness trees or their
stumps, etc., near the corner under investigation. (4) Make
careful examination of the site of the corner with the dig-
ging outfit; the digging should be done cautiously so as to
INVESTIGATION OF S.W. CORNER
""* """ f""">
*M//of
' Busty soyj rttaf A*j fuffitr
ty a mvtH f-jir ,r,~< w>,,~
Tfn't sfOHt Ifoca /f 0' Jc oho*i M
If ~OJ tr+ft,//y /a^t'fcj Ay ff
that tf,,
!* *,., timtfr
E., 30 PJ.
'/., Jrscr.ti
""" *""3
A* ~oj > toy, Mr Camp**//, ~Ae
of a joilafras jra*f mfliclt unqvlifier*-
,n f*evna ' Htmtllltra le~,t IS yffrt V
C*t itaiy J/j M/ fir A,~,,ttf cvrrft*
no* far ~,o~y yfon. Alovt /Oft
158
LAND SURVEYING.
avoid disturbance of existing stakes or other monuments.
(5) If more than one monument be found, make due record
of their character and positions, and make further inquiry
respecting them. (6) If no monument of any sort be found
at first, continue the search diligently and do not give up
finding the true corner as long as there is a remote chance
of locating it. In any event, avoid wanton disturbance of
any object or evidence that may have a bearing on the same.
Keep clear and concise record.
PROBLEM F2. PERPETUATION OF A LAND CORNER.
(a) Equipment. Digging outfit, a large boulder or other
permanent monument, cold chisel, hatchet, plumb bob,
string, stakes.
(b) Problem. Replace a temporary land corner by a per-
manent monument.
(c) Methods. (1) Uncover the identified temporary monu-
ment and carefully determine the true point with consist-
ent exactness. (2) Reference out the point by driving two
pairs of stakes with strings stretched so as intersect
squarely over the corner. . (3) After carefully checking the
ON sec-n, ns..
~tl,ct, Htyl> Snafttr My, At Hn,M ft AM
tot ctr ftr over 3O ytari . MarHtd!
n*f/f, tfra.aiifm, S-ffw., 7r /Hi. ,
turr-ffH,!!. . ft+JW., I2J .
ptfary stoXa evrry 10 cAt. in /int.
J R COMINOS AND H. ROWLAND.
r traflt ot corrrLt point,
f frtt ef OJ. Jvrvt}, timir.g
flftet of T r&l 4 ins. forty art fop
M.C.KH. norm ao~r.
rt sfmf.t
PROBLEMS. 159
referencing, dig out the old monument to a depth sufficient
to receive the boulder and permit its top to set several
inches beneath the natural siirface if located in a road or
where disturbance is probable. (4) Cut a plain cross mark
on the top of the stone, and set it in place in the hole,
packing the earth about it, and testing the position of the
mark by means of the reference stakes and strings and
plumb bob; finally leave the boulder set firmly in the correct
position. (5) Make reference measurements to suitable per-
manent points such as marks on curbing, gas pipes, witness
trees, etc., selected with respect to good intersections, and
make reliable record of the witness notes after checking
the same. (Other forms of permanent monuments are:
gas pipe; fish plate; section of T-rail; farm tile or vitri-
fied pipe filled with cement mortar; post hole filled with
mortar; special solid monument burned like farm tile;
special casting similar to a gas main valve box, with hole
in top to receive flag pole; etc.)
PROBLEM F3. REESTABLISHING A QUARTER-SEC-
TION CORNER.
(a) Eq ii ivnirnt Transit party outfit, digging tools, etc.
(b) TVoWfw?. Reestablish a quarter-section corner that
has been obliterated or lost.
(c) MrtJind .<?.(!) Collect and record all the available evi-
dence which may assist in the discovery and identification
of the corner. Examine the field notes of the original sur-
vey, the surveyors' plat book and the county atlas on file
at the court house, and make diligent inquiry for credible
and competent information, either written or oral as to the
location of the corner. (2) Make a careful search for the
monument. Trace all the lines of the original survev. nav-
ing particular attention to bearing and sight trees. Dig in
all the places indicated by the different lines and give un
the search only after you have exhausted every possible
flue. (3) If the corner cannot be found, reestablish it, giv-
ing due weight to all the evidence. The surveyor should
remembpr -fhat the corner should be reestablished where it
originally was and not where it ought to be. After having
located a stake at the supposed location of the original
monument .reference it out and renew the search. (4)
160 LAND SURVEYING.
After the monument has been relocated , mark it in a per-
manent manner as indicated in Problem F2, by a stone
with a cross cut in its top or with a gas pipe well driven
into the ground. Reference it out to at least two permanent
ofbjeets selected with a view to securing a first class inter-
section. Make a careful record and preserve consistent ac-
curacy in the work.
PROBLEM F4. REESTABLISHING A SECTION CORNER.
(a) Equipment. Transit party outfit, digging tools, etc.
(b; Problem. Reestablish an obliterated or lost section
corner.
(c) Method*. Follow the various methods described in
Problem F3, giving special attention to the search for the
original corner; upon failing to find trace of it, run out lines
with reference to the section, quarter, and quarter-quarter
corners in the four directions, with linear measurements
from the same and finally reach the most consistent de-
cision with reference to such survey lines, ownership lines,
fences, hedges, road centers, etc. (A fruitful cause of dis-
turbance of section 'and other corners is careless use of
road graders, or the failure to lower the corner sufficiently
below the surface of the road.)
PROBLEM F5. RESURVEY OF A SECTION.
(a) Equipment. Transit party outfit, digging tools, etc.
(b) Problem. Make a resurvey of an assigned section.
(c) ^fetllods.'(l) Make extracts from the field notes of
the original survey and of all resurveys on file at the court
house, and other notes that may be of value. Make dili-
gent inquiry among the property owners fpr evidence as to
the location of corners. (2) Retrace the lines, recording the
location of old fences, timber markings and other evidences
as to prior recognition of lines and corners. Use consistent
accuracy. Record the original notes as given in the forms.
Record the field notes in narrative style using the designa-
tion of corners as given in the resurvey plat in the form.
Make a plat of the section in the manner prescribed by state
law for a resurvey.
PROBLEMS.
161
9gf
^ y*
e...T,on OP evlB .Hc e .
April IS, 1133.
Off, te at Vrbana, ttl, the "Svrviyori ftaf BoqH '
lif ,.n,.*^r^,n,
rwo
^^^^^
MM.J
catti or var.oui r<svv,yi Float th, M-
low.nj c>tr,<ft r.W-y to Sec 9, T/9 //,
:::;\%:' f " "i
~f
rwttn itc Sara 6
*""
Sfonc
of ,.~. /-, / f~* a iron. f,.,;.ui,y
,..r;*f <*i-e ,i
*""'
M*r 'E i*eVMr'" y "
sec 5-
,. * / ./ , K , B.n*S B,,,nn,; f
" *""'"
162
LAND SURVEYING.
RESUfVEY or SECJ7, T.\IH., R. *Vi,3RaRM.
tyon afr Feu** IfaHf *i f/o<t and oefti
Vfarvtf rrfrl Jtonotoy. P/a*r*& J/tX7
t 9*011 arvvxr
n-rJKfta m.Ant teHu.Mafi.
-if 1 fevna rarrnrn ffit in corrf
FOR THE ESTATE OF JOHN VM. SMITH.
RESUBvey 6EC 27, SMITH
1 of Z0on*<
t ftttmna Bearing
e. *~ ,
fj
rur.
STATE (CONTINUED)
PROBLEMS. 163
PROBLEM F6. RESURVEY OF A CITY BLOCK.
(a) Equipment. Transit, 100-foot steel tape, chaining
pins, axe, hubs, stakes, 4 pieces one-inch gas pipe 2 feet
long, notes of previous surveys, etc.
(b) Problem. Make a resurvey of an assigned city block.
(c) Method*. (1) Procure full notes of all the surveys and
resurveys of the assigned block from the records at the
court house and from any other source available. (2) Make
a resurvey of the block, using the notes, and' drive hubs for
temporary corners. (3) Compute the latitudes and depart-
ures of the courses, and if consistent, balance the survey.
(4) If the corners of the block as located are consistent with
the existing property and street lines, drive gas pipes as
permanent corners. (5) Subdivide the block into lots as
shown in the notes. (6) Make a plat of the block on manila
paper to the prescribed scale, showing block and lot lines,
distances and angles obtained in making the survey, the
names of the owners of the property and the names of the
streets. Prepare a surveyors' certificate as provided by law.
Trace the map if required. (The accuracy attained should
be based on the valuation and other local conditions.
Before beginning the survey use every possible care to find
the corners with reference to which the original survey was
made. When lots are sold by number, the excess or de-
ficiency should be divided pro rata. However, when lot lines
have been long acquiesced in, it is doubtful if the courts will
uphold the surveyor in interfering with the ancient lines of
ownership. It then becomes necessary either to make a
compromise survey that will be satisfactory to the owners,
or to make a survey that is strictly according to the letter
of the law, and submit the map and certificate to the courts
for settlement. The surveyor should remember that he is
simply an expert witness and that he has no final judicial
powers.)
PROBLEM F7. RESURVEY BY METES AND BOUNDS.
(a) Equipment. Transit party outfit, digging tools, etc.
(b) Problem. Make a resurvey of an assigned tract whose
original survey was made by metes and bounds.
164 LAND SURVEYING.
(c) Methods. (1) Collect full notes and data relating to
the monuments, magnetic bearings, magnetic variation,
date of survey, lengths of lines, etc. (2) Make a careful
investigation of the lines and corners on the ground and
make notes of any evidence there found. (3) Locate and
identify with certainty as many as possible of the original
monuments; where double or contested corners exist, locate
each definitely for further reference; if corners are general-
ly lacking or doubtful, concentrate attention on at least two
which give most promise of definite relocation, and reestab-
lish these corners as carefully as possible. (4) Having at
least two corners, retrace by random line the perimeter of
the tract according to the original description, beginning
at one and closing on the other corner; set temporary cor-
ner stakes at the several points; note the linear and angular
error of closure of the random traverse on the" last monu-
ment. (5) Calculate the latitudes and departures of the
random survey, and determine the angular and linear re-
lations between the random and the original survey; also
fix the position of the several random stakes relative
to the supposed true positions of the respective corners. (6)
Set stakes in the true positions, as calculated, reference
them out, and renew the search for the original monu-
ments. (7) Finally reestablish each corner in the most
consistent position, put permanent corners in place, and
take witness notes for each, making complete notes of the
proceedings. Follow form.
PROBLEM F8. PARTITION OF LAND.
(a) Equipment. Transit party and digging outfits, etc.
(b) Problem. Make a partition of an assigned tract of
land in accordance with instructions.
(c) Methods. (1) Make the necessary resurveys of the as-
signed tract, identifying original monuments, and reestab-
lishing lost corners as required. (2) Make a plat of the
partition. (3) Subdivide the land and set permanent cor-
ners; carefully establish witnesses to the corners and secure
witness notes. (4) Prepare and file plat and description as
required by law.
PROBLEMS.
165
RESUKVE.Y OF "MISSION RlDGE
f'gr>**tty eta e/escr-fcfef
J-Pot, Surveyor. Mar /O, /S9Z.
PUBLIC ROAD FOR J D CLARK.
corners occortJ/ng /
<f -Search
f r*/rh */?'. as maynef-tc e/es-
vach cJ
cvrrft,/
point 6a f/nfts
3t*arT9 of rando
JJf c<rr f ft,/ ca&
st af fas
of notes -
'f
CALC1
LATlC
Dist.
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Tot Lot.
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Line Difference.
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166 LAND SURVEYING.
PROBLEM F9. DESIGN AND SURVEY OF A TOWN SITE
(OR ADDITION.)
(a) Equipment. Equipment for topographic survey for
both field and office.
(b) Problem. Make a preliminary topographic survey of
the proposed town site (or addition) design the plat, and
make the surveys for blocks, lots, etc.
(c) Methods. (1) Make a careful resurvey of the entire
tract. Reference the existing monuments and carefully re-
locate all mis-sing corners. (2) After the monuments have
been carefully located, remeasure the distances and angles
very carefully. Before beginning the chaining, a standard
should be established as described' in Problem A23.
(3) Fill in the topographic details with the transit and
stadia, unless directed otherwise, using consistent accuracy.
(4) Make a complete topographic map of the tract. (5) De-
sign the townsite and sketch it in on the map. The ques-
tions of surface drainage, sewerage, possible overflow,
street gradients, principal thoroughfares, diagonal streets,
alleys, etc., should be carefully considered. The streets
should be of ample width and laid out with reference to ease
of grading both the Street and the adjacent property. Resi-
dences should face desirable streets and the cross streets in
the residence district should not be too numerous. The
principal thoroughfare should pass through the business
portion and have minimum gradients. The system of sew-
erage and drainage Should be worked out roughly before
the design is completed. Much expensive construction can
be avoided by using care in designing the town site. (6)
Make preliminary profiles of all the streets on Plate A
profile paper to the prescribed scale. (7) Carefully locate
the block and other important corners and mark them by
permanent monuments of stone, gas pipe, tiling, etc. (8)
Subdivide the blocks into lots and mark the lot corners by
means of gas pipes or hubs. (9) After the streets have been
located carefully, take levels on the same, make profiles,
and lay grade lines for all streets, sidewalks, and improve-
ments.
Use accuracy consistent with the value of the property
throughout the problem. Make a careful record of the notes.
Complete the maps and profiles.
CHAPTER VIII,
RAILROAD SURVEYING,
Classification For the purpose of class instruction,
railroad surveying will be discussed under the following
heads: (1) curve practice, (2) reconnaissance, (3) prelim-
inary survey, (4) location survey, (5) construction, (6)
maintenance.
Curve practice is designed to give the student familiarity
with the methods of running curves so that the location
survey may be made without needless delay. It consists of
a series of typical problems covering the usual range of
conditions found in such surveys.
The reconnaissance is a rapid preliminary examination
of a district or area for the purpose of selecting ruling
points to control the general routes of the preliminary sur-
vey lines. The distances are paced or scaled from a map;
elevations are determined by means of the barometer or
hand level.
The preliminary survey is designed to obtain information
and to obtain it rapidly, as a guide in making the location
survey. A rapid deflection angle traverse is run, following
the general route of the proposed line, but keeping in clear
ground as far as may be to gain time; levels are run, topog-
raphy including contours taken, the map made, and one or
more location lines projected on the map.
The location survey fixes the exact lines, including the
curves, preparatory to building the proposed railroad. Some
engineers prefer to run one or more trial location lines, but
it is best practice to locate the line as projected on a reliable
contour map.
Construction surveys are made for the purpose of fixing
the roadbed limits and other constructive details, and esti-
mating earthwork and other quantities.
Maintenance surveys and resurveys are made after the
line is built, for ballasting, yard construction or other pur-
pose.
168 RAILROAD SURVEYING.
Field Organization of Class. In order to carry out the
foregoing steps, the following field parties are required:
(a) transit party, (b) leveling party, (c) topography party,
(d) land-line party, (e) cross-sectioning party, (f) bridge
and masonry party, (g) resurvey party.
General Requirements, Each party should work with
snap and vigor and accomplish the best results practicable,
both as to quality and quantity. To this end each member
of the party should not only be careful, exact, and rapid in
the discharge of his own duties, but avoid interfering with
the work of others, such as obstructing the view of the
transitman. In order to give each student practice in all
the positions, the posts will be shifted daily, progressing to
the higher positions in the party. The student should not
underrate his practice in the subordinate positions, nor fail
to make proper use of his more responsible duties. The
usual decorum of field parties will be observed.
TRANSIT PARTY. It is the duty of the transit party to
establish the traverse line upon which to base the levels and
topography. The student transit party will consist of the
following members: (1) chief of party, (2) transitman, (3)
head chainman, (4) rear chainman, (5) stakeman, (6) axe-
man, (7) front flagman, (8) rear flagman. The duties and
equipment of the respective members are stated below.
Chief of Party. (Party list, map of line, 50-foot metallic
tape, railroad curve text book.) The chief of party is re-
sponsible for the general progress and quality of the work.
It is his duty to direct the survey; see that each man does
his work properly and with sufficient accuracy and
despatch; check the transitman's work when necessary;
keep the transit notes if the transitman is pushed; and make
himself generally useful. He should be thoroughly ac-
quainted, before going to the field, with the situation and
with the data applicable to the work of the day. In requir-
ing subordinate members of the party to perform their work
properly, he should carefully preserve the dignity of his
own position. Should there be no chief, these duties will be
shared by the transitman and head chainman under the
former's directions.
Transitman. (Transit, reading glass, adjusting pin,
transit note book, railroad curve text book, figuring pad.)
The transitman runs the transit, keeps the notes, and in
TRANSIT PARTY. 169
the absence of the chief, directs the work of the party. He
should do careful and exact as well as rapid work, since the
progress and character of the survey are usually controlled
chiefly by the skill of the transitman.
In leveling up, keep the lower parallel plate about level.
Avoid undue tightness of foot screws. In setting the ver-
nier to zero, use a quick converging motion with the tangent
movement and note the adjacent graduations. If the (tran-
sit has lost motion, learn which way to get the slack on the
tangent screws. As a rule, use the lower motion by prefer-
ence. Habitually back sight to the rear with telescope re-
versed, then plunge the telescope on prolongation and read
the deflection right or left. If practicable, base tfhe cal-
culated bearings on a true meridian; otherwise, allow for
the magnetic declination at a station which seems to be free
from local attraction and thus obtain a reference meridian.
Check all deflection angles by needle reading, both as to
amount and direction. Lack of proper adjustment is no
excuse for error. Always prolong a tangent line by double
sightings. Also check deflection angles from time to time,
by double sightings. Check on back sight before finally
approving any precise point; likewise never fail to conclude
the observations at each transit station by checking on the
back sight. In such check it is usually best to sight hack
precisely on the point and then note whether the vernier has
the proper reading. Assist the flagman in plumbing the
pole, and always sight as near the bottom of the pole as
possible. The traisitman should admonish the chainmen,
etc., to keep clear of the line.
On preliminary surveys, usually let the rear chainman
line in the head ohainman by eye, at least for short
stretches. Do not hesitate to offset or zig-zag more or less
along open ground to gain time. A rapid method for pass-
ing through heavy timber is to zig-zag on slight deflection
angles right and left, tabulate the lengths in stations and
deflections in minutes, and the products of the two in sep-
arate columns on the right hand page. The original line is
regained by making the algebraic sum of the products zero,
and the original direction is resumed by turning off a de-
flection which balances the deflection angle columns.
On location, each stake should be lined in carefully by
transit. Small obstructions, such as trees, may be passed
170 RAILROAD SURVEYING.
by parallel lines, using offsets of one foot or so at two hubs
a few stations apart; the line is resumed in like manner.
Where plate readings are used in rectangular or other offset
methods, no sights shorter than 50 feet should be used. The
equilateral triangle one station or more on a side is often
used. Obstructions on curves may usually be passed readily
with the aid of tables of long chords and mid-ordinates.
Curve index-readings should be calculated as though the
entire curve were to be run in from the P. C.; starting with
the index-reading of P. C. always equal to zero, check the
calculations by noting that the index of M. C. is *4 I, and of
P. T. is % I. In using the notes, remember that with the
transit at any point whatever on the curve the following
rules apply: (1) When pointing to any station, the ver-
nier must always be set to read the index-reading for that
station; and (2) when pointing on tangent at any station,
the vernier must be set to read the index-reading for that
station. As a rule, the best program in curve location is:
Having P. I. located, (1) measure I and assume D; (2) cal-
culate T and E; (3) establish P. T. by chaining off T on
front tangent; (4) establish M. C. by laying off E on bisect-
ing line; (5) locate P. C. by interpolating hub at calculated
station number on back tangent; (6) move transit to P. C.
and fore sight on P. I.; (7) calculate curve notes (if not al-
ready done); (8) check sight on P. T. and M. C. and if satis-
factory, (9) run in curve, checking for distance and angle on
M. C. and P. T., moving transit ahead if desirable or neces-
sary; (10) set up at P. T. and resume front tangent. One
minute is the limit of allowable error in any curve. Mis-
takes in calculations or in measurements of angles will be
counted serious errors. On final location the curves will be
spiraled. After the line is located, reference out P. C., P. T.,
and other important hub points by two intersecting lines
and take careful notes of the same (see method (g), Fig. 5,
Chapter II.)
The transit notes should be reliable, complete, neat and
distinct. Each entry should have but one reasonable mean-
ing and that the correct one. Record station numbers from
the 'bottom upwards, usually with ten stations per page.
Repeat the last station at the top of the next page. Allow
two lines per station so as to provide for sketching at 200
feet to the inch. On the middle line of the right hand page
TRANSIT PARTY.
171
/*<?<?'
0*4 d+
10AO LOCATION SI RVEY.)
172 RAILROAD SURVEYING.
mark each station with a dot and number every fifth station
which should also be enclosed in a circle. The transit notes
should include sketches of prominent land and street lines,
stream crossings and other prominent topographic details,
with pluses shown in the sketch. The notes should include
date, weather, organization of party, etc. An appropriate
title page giving name of survey, date of commencement
and completion, etc., should be prepared. The notes will be
kept in the prescribed form. The field notes are to be re-
turned at the close of the day's work. All estimated data
should be noted as such.
Completeness and neatness of notes and records, facility
and accuracy in handling the instrument, and promptness
in advancing the progress of the survey will count in the
estimate of the work of the transitman.
Head Chainman. (Flag pole.) The progress of the
chaining depends chiefly on the activity of the head chain-
man. After setting a stake he should move off briskly (pre-
ferably at a trot) and be prepared for the "halt" signal as
he approaches the next station. When the full chain length
is pulled out, the head chaimman turns, holding the flag pole
in one hand and the chain handle in the other, and sets the
pole in line by signal from the rear chainman 01 transit-
man. Much time can be saved in this process if the head
chainman habitually walks about on line and if he sights back
over the two stakes last set. If on curve location, he should
line himself in on the prolongation of the preceding station
chord, and then offset by pacing or with flag pole a distance
in feet equal to 1% times the degree of the curve; the
calculation is made mentally and the pole can usually be set
within a few inches of the correct position by the time a
speedy transitman has the deflection angle set off. Having
the line established, the pole is shifted to the correct dis-
tance, and the stake is driven plumb in the hole made by
the flag pole spike. If the survey is a rapid preliminary line,
the head chainman hastens ahead the instant the stake is
started at the proper point, although in a more careful pre-
liminary the chainmen check the distance to the driven
steke. On location surveys it is customary for the chain-
men to wait until the stake is driven and mark the exact
distance on the top of the stake with the axe blade, and the
exact line by signal from the transitman. In this process,
TRANSIT PARTY. 173
the head chainman should keep in mind the convenience of
the transitman, and in case the line is being run to a front
flag, the chainman should be careful to clear the line fre-
quently to allow check sights ahead. In breaking chain on
steep slopes the full length of chain should usually be pulled
out ahead and the chain thumbed at the breaking points so
as to avoid blunders; a plumb bob or flag pole should be
used in the process. In passing over fences it often saves
time to drive a 10-d nail, with "butterfly" attached, in the
top plank to serve as a check back sight from the next tran-
sit point. The chainmen should carefully avoid obstruct-
ing the transitman's view, to which end they should walk
on the outside when locating curves.
Rear Chainman. (100-foot chain or tape, chaining pins
(if allowed), figuring pad or note book.) As the rear chain-
man approaches the stake just set, he calls out "halt" and
holds the end of the chain approximately over the stake.
quickly lines in the flag pole in the hand of the head chain-
man (or the pole is lined in by the transitman). the precise
distance is given, and the chainmen move on briskly. As a
rule, pluses should be read by the rear chainman, the front
end being held at the point to be determined. Frac-
tions will usually be taken to the nearest 01 foot, although
01 foot may at times be properly noted. It is the duty of
the rear chainman to keep a record of pluses and tooo-
graphic details when the transitman is not at hand. This
record may be kept on a figuring pad and the memoranda
handed at the first opportunity to the transitman, who
transfers the data to his book and carefully preserves the
slips for future reference. It is usually better, however, to
keep the auxiliary notes in a memorandum book instead of
on the loose slips. The chainmen should carefully avoid
disturbing the transit legs.
The responsibility for correct numbering of the station
stakes rests chiefly on the rear chainman. It is his duty
to remember the number of the previous station so as to
catch blunders on the part of the stakeman. As he reaches
the stake just driven, he mentally verifies its number and
repeats it distinctly for the guidance of the fetakeman in
marking the stake to be driven: the stakeman responds by
calling the new number, and each repeats his number as a
check before final approval. The rear chainman then
174 RAILROAD SURVEYING.
charges his mind with the numbers and checks the newly
set stake on reaching it. In case of doubt he returns to the
preceding stake and notes its number.
Stakeman. (Sack of flat and hub stakes, marking
crayon, handaxe.) The stakeman with his supply of flat and
hub stakes in a sack, should keep up with the head chain-
man and be standing, with stake and marking keel in hand,
ready to number the new station stake on hearing the rear
chainman call out the preceding station number; the num-
bering is repeated, as already explained, before the stake is
driven. Chaining pins are not used, but their equivalent in
checking tallies may be had by numbering the stakes ahead
and tieing them up in sets of ten. By numbering stakes at
slack moments the stakeman gains time to assist the axe-
man in clearing the line, etc. However, special care should
be taken to avoid omissions and duplicates. The stakeman
should finish numbering the stake and hand it to the axe-
man by the time the head chainman has fixed the exact
station point. The stakes should be numbered in a bold and
legible manner, the keel being pressed into the wood for
permanency. The number should read from the top of the
stake downward. Stakes on an offsetted line should be so
marked, as 4'L or 2'R, beneath the station number. When
survey lines are lettered, the serial letter should precede the
station number. Guard stakes for P. I., P. C., P. T.. refer-
ence points (R. P.), etc., should be clearly marked. The
stakeman should assist the axeman in clearing the line and
should drive stakes when the axeman is delayed. He should
carefully avoid obstructing the transitman's view. The
s<takeman is under the direction of the head chainman.
Axeman. (Axe, tacks., (and if so instructed) an extra
sack of stakes with marking keel.) It is the duty of the axe-
man to drive stakes, remove underbrush from the line,
clear an ample space about the transit station, etc. He is
expressly warned, however, in student field practice, not to
hack or cut trees or damage other property in any way, and 1
in general, not to trespass' on the rights of owners of
premises entered in the progress of the survey.
The flat station stakes are driven firmly crosswise to the
linje with the numbered face to the rear. Hubs are driven
about flush and usually receive a tack; they are properly
witnessed by a flat guard stake driven 10 inches or so to the
TRANSIT PARTY. 175
left, the marked face slanting towards the hub, as shown
in Fig. 9, Chapter II. The axeman receives the marked
stake from the stakeman and drives it plumb at the point
marked by the spike of the flag pole. On location or care-
ful preliminary surveys when the stakes are being lined in
by transit, the axeman should stand on one side when driv-
ing and keep a lookout for signals from the transitman. In
shifting the stake as signaled he should use combined driv-
ing and drawing blows with the axe. When the precise
point comes much to one side of the top of the hub, another
hub should be driven alongside and the first one driven out
of sight before the tack is set. The axeman should move
ahead briskly and avoid delay to the chaining. The stake-
man should, when necessary, drive the stake with the spare
handaxe. When the field force is scant, one man may serve
in "both capacities. The axeman is under the direct charge
of the head chainman.
Front Flagman. (Flag pole, small supply of hubs and
guard stakes in stake sack, handaxe, a few 10-d nails.) It
is the duty of the front flagman to establish hub points
ahead of the chaining party under the direction of the chief
and transitman. In selecting transit stations he should
keep in mind visibility and length of both fore sight and
back sight, and to this end, points should be taken on ridge
lines and where underbrush, etc.. is least in the way. The
practice of planting the flag pole behind the hub may be
warranted occasionally, as for example, when the field
party is shorthanded, but never when the regular flagman
is not specially detailed for other duties. The front flagman
should keep close watch on the transitman and should
habitually stand with the spike of the flag pole on the tack
head and plumb the pole by standing squarely behind it
and supporting it between the tips of the fingers of the two
hands. Should the front flagman be flagging for an inter-
polated point depending on a foresight which his pole would
conceal, he should clear the line for a check sight by lean-
ing the pole to 'one side. When crossing fences he should,
when convenient, establish check sights on the top plank
by driving a spike and attaching a "butterfly."
Rear Flagman. (Flag pole, hatchet, slips of paper.) T^he
rear flagman gives back sight on the preceding transit sta-
tion. The details of his duties are much the same as those
176 RAILROAD SURVEYING.
of the front flagman. It is an excellent plan for him to cut
a straight sappling or limb and plant it exactly behind the
hub when signaled ahead. This picket pole is made more
visible by splitting the top and inserting a slip of paper, to
make a "butterfly." A series of such pickets on a long
tangent line often affords a fine check on the work when
an elevated transit point is reached.
LEVEL PARTY. It is the purpose of the level party to
secure data concerning the elevations of the points along
the line so that an accurate profile may be made and the
grade line established. The leveling party should be on the
alert to detect errors in the work of the transit party, such
as omitted or duplicated stations, etc. The party consists of
two members: (1) leveler, (2) rodman. In very brushy
country an axeman may be added, but this is usually un-
necessary if the line cleared by the transit party is followed.
Leveler. (Level, adjusting pin, level note book.) The
leveler should follow the most approved methods described
under the head of differential and profile leveling in Chap-
ter IV. The nearest 0.01 foot should be observed on turn-
ing points and bench mark rod readings and elevations and
on occasional important profile points. The fore sight rod
readings on ground profile points are to be taken only tb
t;h nearest 0.1 foot and- the nearest 0.1 foot in the height of
instrument is to be used in calculating the elevation. (Be-
ginners sometimes calculate elevations to 0.01 foot when the
rod readings are taken only to the nearest 0.1 foot.) The
leveler should be rapid with his level as well as with fig-
Tires. He should calculate elevations as fast as the rod read-
ings are taken and should systematically check up the
turning point and instrument heights as the work proceeds.
As results are verified the same should be indicated by check
marks. Each page of notes should be checked by summing
up turning point back and fore sight rod readings, and com-
paring their difference with the difference between the first
and last elevations or instrument heights, as the case may
be, on the page. Follow the prescribed form. As far as
possible, bench marks should be checked by including them
in the circuit as turning points. Balance back and fore
sight distances on turning points. Permanent bench marks
should be established at least every 1500 feet, and located
in places at once convenient and free from disturbance
LEVEL PARTY.
177
during construction. Later levels should check within 0.05
foot into the square root of the length of circuit in
miles. When a discrepancy is found, a line of check levels
must be run to fix responsibility for the error. In cross-
ing streams, secure high water elevations, with dates, es-
pecially of extraordinary Hoods, also low water level. In
crossing highways obtain elevations each side for some
distance with a view to avoid grade crossings. In going up
or down steep slopes, gain all the vertical distance possible
each setting, and follow a zig-zag course. The bottom of
deep gullies may be determined by hand level. Assist the
rodman in plumbing the rod, and on turning points and
benches have the rod gently swung in a vertical plane to and
from the instrument and take the minimum reading. The
self-reading rod is to be preferred. Many levelers use the
Philadelphia rod without target. If the target is used on
turning points, the leveler should check the rod reading
when practicable.
Completeness, correctness and neatness of notes and rec-
ords, and facility and accuracy in 'handling the level will
be given chief weight in fixing the merit of the leveler's
178 RAILROAD SURVEYING.
work. The level notes are to be returned at the end of the
day's work.
Rodman. (Leveling rod, peg book, hatchet, turning
point pegs, spikes, keel.) The rodman holds the rod at
station stakes and at such plus points as may be required
to make a representative profile. It is his duty to identify
each station point and be on the lookout for duplicated or
omitted stations. To this end he should habitually pace in
each station, especially in grass or underbrush, and call out
or signal the station number to the leveler. Should a blunder
in station numbering appear, he should positively confirm
the fact by retracing several stations, and then carry the
corrected stationing ahead. The rod should be held truly
plumb, which is best done by standing squarely behind the
rod and supporting it with the tips of the fingers of both
hands. On turning points, the rod should be waved gently
in a vertical plane to and from the instrument. The rod-
man should pay special attention to placing the target
right for long rode and examine it to note if it has slipoed
before reading the rod. Errors of 1 foot. 0.1 foot. etc..
should be carefully guarded against. Turning noints should
be selected with special reference to their solidity, and care
should be taken not to disturb them. Station pegs and
hubs are often used for turning points: when so xised, the
precise fore sight to 0.01 foot should follow the usual ground
rod reading to the nearest 0.1 foot. The rodman should
use good judgment in selecting bench marks, locating them
out of reach of probable disturbance during construction
and describing them so as to be easily found. He should
be active and do his best to keep close up with the transit
party. The rodman should keep a peg book for recording
turning points and instrument heights, and check his com-
putations independently and compare results with the
leveler.
TOPOGRAPHY PARTY. It is the purple of the
topography party to secure full data for manning contours,
property lines, buildings, roads, streams, and other import-
ant topographic details. The width of territory to be em-
braced in the survey depends on local conditions: in places
it may be as much as one-fourth or one-half mile from the
line, although it is usually better to run alternate lines when
the distance to be included becomes so great. The topog-
TOPOGRAPHY PARTY. 179
raphy party often consists of only two men, but a party
of four is much more efficient. Sometimes no regular topog-
raphy party is provided, but after running a few miles of
line ahead, the transit and level parties are formed into
several parties to bring the topography up to the end of the
preliminary line. For student practice the topography
party will consist of four members: (1) topographer, (2)
assistant topographer, (3) topography rodman, (4) tapeman.
Topographer. (Topography board, topography sheet (or
several sheets), hard pencil, compasses, eraser, etc.) The
topography sheet should be prepared before going to the
field, showing the alinement and other data needed from the
transit notes., and elevations of all stations and pluses from
the level notes. Cross-section paper is to be preferred.
The center line may be plotted to one side of the center line
of the sheet, when the topography is to be takf-n farther in
one direction than the other. In order to secure full details,
the scale of the field plat may well be double (or even more)
that of the finished map. The topography sheet should show
local conditions, such as gravel banks, rock ledges, etc.,
suitable for ballast or other constructive use; out-croopings
of rock or other material which may affect the classification
of the graduation; character of substrata at sites of bridge
or other masonry work; springs, wells, streams, etc., suit-
able for water supply; approximate flood levels and other
data relating to waterways or surface drainage; location of
streams, especially with reference to desirable crossings,
freedom from probable change of channel, etc.; location of
highways including elevations some distance either way
with special reference to avoiding grade crossings; other
railroad lines, with the same point in view; character and
condition of crops and other farm improvements, names of
ov.-ners, etc.. in short, any and all information that is at all
likely to be of service in mapping the route, projecting the
location, during construction, etc. In locating a group of
buildings some distance from the line, fix the principal one
by tie lines, by intersection or polar coordinates, and the
others by measurement and sketch from it. Locate build-
ings near the line by rectangular offsets, or by intersections
of the principal outlines with the survey line. Contours are
located by means of the hand level used by the assistant
topographer. The contour interval should be five feet or-
180 RAILROAD SURVEYING.
dinarily, but may be increased to ten or more feet on very
steep slopes. The contour data should be selected with
special reference to ridge and gully lines (see problem and
plat on contour leveling, Chapter IV.) Ordinarily hand
level lines may be run out at right angles; angling lines
along gulches and ridges may be located by estimation,
pocket compass or tie lines. The plat is made by the topog-
rapher from data collected by the other members of the
party. A common fault with the beginner in such work is
the omission from the plat of important numerical data,
such as station numbers of land-line crossings, etc., owing
to an undue attention to the minute details of the drafting
work. A good topography record with contour notes' on
the left hand page and field sketch showing all numerical
data on the right, is shown in the accompany form.
Assistant Topographer. (Hand level, pocket compass,
topography note book.) It is the duty of the assistant
topographer to collect data for the use of the topographer
in making the plat. He uses the hand level, notes> station
numbers, distances, bearings, etc., and makes such record
of the same as may be required to fit local conditions. In
COP touring, a special rod with adjustable base (see Fig. 19,
Chapter IV.), if available, may be used; otherwis-e, an or-
dinary flag pole with alternate feet red and white is em-
ployed. Beginning with the known profile elevation, as ex-
tracted from the leveler's record, even five-foot contours are
located, as a rule, nominally every 200 to 500 feet at right
angles to the line, except as ruling ridges or gullies may
suggest other directions. His record should be ample and
legible, and include data and information which may not
properly be placed on the plat. All estimated elevations,
distances or dimensions should be noted as such. The assist-
ant topographer works under the direction of the topog-
rapher, but is expected to take the initiative in the collec-
tion of data so as to permit his superior to devote proper
attention to the field plat.
Topography Rodman. (Topography rod with adjust-
able base (see (f), Fig. 19, Chapter IV.) or flag pole, hatchet.)
It is the duty of the rodman to hold the topography rod as
directed by the assistant topographer. He should be active
and continually on the alert for information or data which
the record book or sheet should contain. The rodman holds
OFFICE WORK.
181
the zero end of the tape in measuring the distances. He
should acquire skill in pacing on rough as well as smooth
ground, and when sufficiently exact especially on ground
remote from the surveyed line, he should gain time by pac-
ing in the distances to contour lines.
Tapeman. (Metallic (or band) tape, set of chaining pins,
flag pole.) It is the duty of the tape-man to determine dis-
tances with the help of the rodman. He should be vigilant
in checking up tallies, reading fractions, leveling the tape,
breaking chain, plumbing down ends, etc., and should never
be the cause of needless delay in the work. When required,
he should measure angles, take tie lines, etc., with the tape.
OFFICE WORK. The office work of each student in-
cludes; (1) reconnaissance map, profile and report; (2) map
showing preliminary lines with topography and projected
location lines; (3) preliminary profile with grade lines, ap-
proximate estimate of quantities, etc.; (4) final location map
(traced from preliminary map) ; (5) location profile; (6)
copies of field notes; (7) cross-section notes and estimate
of graduation quantities; (8) estimate of cost of construc-
tion; (9) monthly estimates, progress profile, haul, pris-
182 RAILROAD SURVEYING.
moidal and curvature corrections, vouchers, etc., final
estimate.
Reconnaissance Report. The reconnaissance map
showing the area examined will be based upon such maps
of the route as may be available. It should show the sev-
eral ruling points and general routes selected for actual
survey. The profile should be based upon barometric or
hand level observations and distances scaled from the map
or determined roughly by pacing or otherwise on the
ground. The report should refer to the map and profile
and state the general scheme, the several ruling considera-
tions or conditions, the details of the examination, a rough
comparison of the several alternative routes, and a final
summary and conclusion with definite recommendations.
The report should be made in accordance with best usage as
to form, composition, etc.
(Considering the limited point of view of the beginner,
the reconnaissance reports may not be required until the
actual surveys are well along. In such case, however, the
student is not to draw data from sources other than those
above outlined.)
Preliminary Map. Themappingshould be the best prod-
uct of the student's skill as a draftsman, and should con-
form closely to the department standards, which are based
upon best current usage of leading American railroads. Un-
less otherwise instructed, the preliminary map will be made
on eggshell or paragon paper. There are three ways to plot
the skeleton of the preliminary survey: (1) by laying off
each successive deflection angle and distance from the pre-
ceding line; (2) by laying off the successive calculated
courses and distances from a precisely drawn meridian or
other reference line; and (3) by rectangular coordinates.
The first method should not be used, since cumulative errors
are probable. The second is rapid and free from serious
objection; if preferred, a modified base line may be assumed
and the calculated bearings transferred to the same; the
angles may be laid off by means of scale and table of nat-
ural trigonometric functions from a precisely drawn base
line and then transferred, as required, by parallel ruler or
triangle; this method is used most in practice. The third
method is the most exact, and will be used by the student
unless the second is specified. It involves the calculation of
OFFICE WORK.
183
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184 RAILROAD SURVEYING.
a plotting sheet, as shown in the accompanying form. The
axis is usually a meridian line, but any line may be taken
and the courses changed to suit. In making the plotting
table, the data, calculated bearings, distances, etc., should
be carefully checked through to the last point in the skele-
ton before the plotting is begun. Only one axis should be
plotted, preferably the one having greater totals, so as to
give short perpendiculars. Starting from the origin, 1000-
foot points are pricked in along the axis to the specified
scale, and marked 0, 10, 20, etc.; the totals are interpolated
on the axis and lettered; exact perpendiculars about the
right length are erected; the second point is established by
scaling the perpendicular and the line is checked back on
the preceding point; if correct, the stations are pricked in
and every fifth station and deflection points are enclosed in
a small circle and neatly numbered; the next course is so
located and checked back by length of hypothenuse, the sta-
tions fixed and numbered, and so on to the end of the line;
the courses should be taken in their order and none passed
without checking satisfactorily. After the skeleton is com-
pleted, the topographic details are penciled in, and the map
finished and inked. The title, border, meridian (both true
and magnetic), etc., should be first-class in quality and in
keeping with the rest of the map. Crude or careless letter-
ing or other details of the map will cause its rejection. The
title of the map, profile, etc., should be given in brief on the
outside of the sheet or roll at each end.
Preliminary Profile. Use Plate A profile paper in mak-
ing the profiles. The level notes should first be carefully
verified and then one person should read off while another
plots the data. A hard pencil, 6H or 7H, sharpened to a
long needle point should be used. The stations are first
numbered along the bottom from left to right (or the re-
verse, as prescribed); leaving six inches or so at the left for
a title, and beginning at a prominent line with station 0,
every tenth station is so numbered. The notes are examined
for lowest and highest elevation and a prominent line is
assumed as an even 50 or 100-foot value relative to the
datum. The horizontal scale is 400 feet and the vertical
scale 20 feet to the inch. Points should be plotted no heav-
ier than necessary, since the surface of profile paper will
not permit much erasing. The surface line should be traced
OFFICE WORK, 185
in close up to the plotted points, owing to the danger of
overlooking abrupt breaks such as streams, ditches, etc.
Pluses should be fixed by estimation. The surface line when
completed should be inked with a ruling pen used freehand;
the weight of the line should be about the average of the
ruled lines on the profile paper. (A special profiling or con-
touring pen is much used for this purpose.) The profile
should show the grade line, grade intersection, elevations
and rates of grade in red; water levels, and data relative
to same in blue; surface line, station numerals, etc., in
black; the alinement, important land lines, streams, etc.,
should be shown at the bottom of the profile in black. The
grade line should be laid nominally with a view to balance
the cut and fill quantities, but this should be varied to
suit local conditions, such as drainage, the elimina-
tion of grade crossings, classification of materials, etc. The
maximum gradients, the rate of compensation for curva-
ture, etc., will be made to suit the specified conditions. The
compensation for curvature will be allowed for on the pre-
liminary profile by dropping the grade line on maximum
gradients at each deflection point. Grade intersection ele-
vations and rates of grade will be given to the nearest 0.01
foot.
Approximate Estimates. Rapid estimates of earth-
work quantities may be made direct from the profile either
by reference to a table of level sections, or preferably by
means of an earthwork scale, shown in the accompanying
diagram. This scale is graduated in hundreds of cubic
yards for the particular roadbed base and side slopes. The
data for making the scales are given in the table. The
quantities may be jotted down for addition or lumped men-
tally, or an adding strip may be inserted in slits near one
edge of the scale. In using this scale it is customary to
make no deduction for minor waterways. Estimates made
in this way from the profile of a careful preliminary survey,
often do not vary more than five per cent from the final
construction quantities.
Location Map. The location map may be traced from
the preliminary map and should include the topography and
such details as usually appear on the final record map of the
located line. Contour lines may be traced in cadmium yel-
low to insure satisfactory blue printing.
Location Profile. The location profile should be exe-
186
RAILROAD SURVEYING.
14-FT. ROADBED.
SLOPES 1 To I.
Hundred of Cu.Yds.
per Station.
20-Fr. ROADBED.
SLOPES 1 To I.
96
Fig. 39.
cuted according to the standard specimen, and should in-
clude estimates of earthwork as determined from the ac-
tual cross-section notes, and quantities of other construc-
tion materials. Curvature compensation will be shown on
the location profile by reduced maximum gradients. Verti-
cal curves will be calculated at a rate of change not to ex-
ceed 0.05 foot per station, except at summits where it may
be 0.10 foot or more per station. It should be prepared as
OFFICE WORK.
187
CENTER CUT OR FILL. IN FEET
FOR GIVEN QUANTITIES PER STATION.
(DATA FOR EARTHWORK SCALE.)
CUBIC
YARDS
Per
IOO
SIDE SLOPE, I TO 1.
SlDESLOPE.ll TO I.
CUBIC
YARDS
Per
100
Feet
WIDTH OF ROADBED
in Feet.
WIDTH OF ROADBED
in Feet.
Feet
14
16
18
20
22
14
16
18
20
22
too
zoo
3OO
40O
500
600
00
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194
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188 RAILROAD SURVEYING.
the final record profile. Approximate profiles of projected
lines, determined from the contour map, with rough esti-
mates of quantities will also be prepared, as specified.
Office Copies of Notes. The complete level and transit
notes, and topography notes as assigned, must be copied
in the individual books by each student. These copies will
be in pencil (or ink if so specified) and will be executed in
a faithful and draftsmanlike manner according to the de-
partment standards of lettering, etc.
Estimates of Quantities. The cross-section notes will
be copied and the quantities of excavation and embankment
calculated, as assigned. The cross-sectional areas will be
calculated arithmetically and checked, especially on rough
ground, by means of planimeter. The quantities will be
calculated by average end areas, by tables, and by diagrams,
so as to afford ample practice for the student in all the cur-
rent methods. The estimate will also include all the other
materials of construction.
Estimate of Cost. Each student will make a detailed
summary of the quantities, fix prices, and estimate the
probable total cost of the work, or of the assigned section.
The prescribed form will be followed. The prices should
be based on local conditions as far as possible.
Construction Estimates. Monthly estimates, estimates
of haul, borrow pit estimates, classification, prismpidal and
curvature corrections, progress profile, vouchers, force ac-
count, etc., and final estimate will be prepared by each
student in accordance with prescribed forms and standards.
Right of Way Records. Each student will be assigned
a share of work in the preparation of right of way deeds
and record maps. The following forms (from the ''Engi-
neering Rules and Instructions," Northern Pacific R. R.)
will be used as models in preparing right of way descrip-
tions.
(Through government subdivisions): "A strip, piece or
parcel of land one hundred feet in width, situated in the
northwest quarter of the northwest quarter of section ten,
in township two north, range one west (S. 10, T. 2 N., R.
1 W.), Madison county, Montana, and having for its bound-
aries two lines that are parallel with and equidistant from
the center line of the railroad of the Railway Com-
pany, as the same is now located (and constructed.) For a
CROSS-SECTIONING.
189
(ESTIMATE OF COST OF
RAILROAD c
OMSTR
JCTION.)
ITEM.
M<, ur<!
Price
Quantity
An,*.*.
/. Carth Excavation.
Cu. You,
Z. forth Embankment Sorrowed.
CV. Yds.
3 Earth Embankment Ovrrnat/f*ot.
CuYd-Stas.
4. Loose ftoctl Excavaf/ort.
Cu. Ya/s.
Sotiet ffocft Excavation.
Cu Yo/e.
Clearing.
Acres.
Grubbing.
Sta.
BRIO NO, CULVERTS. ETC.
Timber in Bridges.
M.Ft B.H.
Iron in Bridge*.
Lbs.
Pi/ing Driven.
Lin. Ft.
Timber in Culvert*.
M.F* B.M.
Iron in Cu/vrrts.
Lit.
Vitrified />/>.
iia.ff.
Caffle Suordf.
Cach.
L umber in ffoad Cros f,ings.
M.Ft. 8 M.
Sfifm in Crosses.
Lbs.
TRA .
Ties.
EorcA.
Rail.fWf.prrvd.)
LongTont.
An 9 lfB<trs.(m pn- pair)
Lbs.
Tracn-Bo/n. (Stir.)
Htas^.pr.Kg)
S/oities.fSiie.)
H fg s(Wf. f r.H 3 .
3~itch Stands and Fixtures.
Sett.
frogs.
Each.
$*fifch Timbers.
Sets.
TKM:* Laying and Surfact'ng.
Miles.
MIS LLANEOU&.
Fenc/no.
fleets.
Tf/ear<*ph Line,
flUes.
Builctinas.
Each.
"'9** of Way.
AerfS.
f*r Cent.
more particular description, reference may be had to the
plat drawn upon and made a part of this deed."
(Lots in platted tracts): "Lot seven (7), block six (6), in
Smith's addition to Helena, Lewis and Clark county,
Montana, according to the recorded plat thereof."
CROSS-SECTIONING PARTY. It is the duty of the
cross-sectioning party to set slope stakes for the proposed
roadbed and to secure data for the calculation of earth-
work quantities. The data should first be transcribed from
the location level notes and profile into the cross-section
book, including station numbers, surface and grade eleva-
tions, rates of grade, bench mark record, etc. In order to
avoid confusion in relation to directions right and left, the
station numbers should run up the .page, and plenty of
space left for pluses in the notes, especially on rough
190
RAILROAD SURVEYING.
FOR ^
FOR
ROSS-
SCCTIOM
MO
TCS.)
X
Surf Rod
Grodettofl
w
U
c
R
Perr, CT rS.
130
7*2.5
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79
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II
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0>-
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rl^f o J
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.? <j
"73$
(Grade point, L,C 0/tfiJ
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+3*
H- end s fringe^ Br. J^o-iS
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720.S
7V.C
7.7
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&
,
iza
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73e.SH
S .1
CA<./J
Bridge Ho. fS$lZB +34
rK*
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fSO
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3. end stringer, Bridge /8-
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TYPICAL CASES
CROSS-SECTIONING
191
130
129
HEAD OF DUMP.
+54
CROSS-SECTION AT STATION 125.
ECvfT
IE5
192 RAILROAD SURVEYING.
ground. As shown in the form, the left hand page sho-ilcl
be used for data and the other for the cross-section notes.
The organization and equipment of the cross-sectioning
party when using the engineers' level is: (1) recorder
(notebook), (2) leveler (engineer's level), (3) rodman (self-
reading leveling rod, 50-foot tape), (4) axeman (axe, sack of
flat stakes, marking keel). The usual routine is: (1) De-
termine height of instrument by back sight on identified
bench or turning point. (When a bench mark is remote
and an original turning point can not be found, it may
suffice in an emergency to check on the ground at several
stations to the nearest 0.1 foot and use the mean height of
instrument. Such places should be verified later.) (2)
Having the height of instrument, check the original eleva-
tion of the station about to be cross-sectioned, reading the
rod and checking off the elevation if it does not differ more
than 0.1 foot or so; in case of a new plus, take a rod read-
ing and record the elevation. (3) Determine the "grade
rod" for the station by subtracting the height of instrument
from the grade elevation; then note that cut or fill at any
point of the cross-section is equal to surface rod minus
grade rod; (counting rods as minus when downward from
the plane of the level and those upward as plus, this rule
gives results always plus for cut and minus for fill, which
agrees with the conception that cross-section notes are
rectangular coordinates of the sectional area referred to
the center of the finished roadbed as an origin.) (4) If the
ground is level transversely, that is. does not vary more
than 0.1 foot or so within the limits of the proposed grad-
ing, then the distance from the center out to each side
slope stake is half width of roadbed plus center cut or fill
times rate of side slope; (thus for 20- foot roadbed, side
slopes 1 to 1, and a cut of 18.6 feet, the distance out to slope
stake on a level section would be 28.6 feet, or with a =lon>3
of 1% to 1, the distance out would be 10 plus l 1 ^ times 18.6.
or 37.9 feet. Calculations of this sort should be dope men-
tally in an instant.) (5) On three-level ground estimate
the rise or fall of the surface from the center to about
where the side slope stake should come, and add the same
to, or subtract it from the center cut or fill, as U.e case
may be; compute the distance out to the point where the
side slope line would pierce the ground surface and test
CROSS-SECTIONING. 193
the same with tape, rod and level by the foregoing rule for
cut or fill; continue to construct points on the side slope
line until the common point is found. (6) The axeman
marks "S. S." (slope stake) on one side of the stake with
the cut or fill to the nearest 0.1 foot (as C 6.8 or F 10.2) and
the station number on the other side; the stake is driven
slanting towards or away from the center line according
as it is cut or fill. (7) On five-level ground or, in general,
on ground involving any number of points or angles in the
section, the cut or fill is taken at each break. (8) Should
there appear to be danger of land slips, the cross-sectioning
should be carried well beyond the limits of the slops sta\e
points. (9) The cross-section notes are recorded as in the
accompanying form, expressing the coordinates of each
point in the form of a fraction, and distinguishing the slope
stake points by enclosure in a circle. (10) Having com-
pleted the cross-sectioning at the station, the same program
is followed at the next point, first checking the elevation
obtained in the original location levels; the jjrad^ rod
should be determined as before by subtracting the height
of instrument from the grade elevation, and Chen checked
by applying to the preceding grade rod the rise or fall of
grade from the preceding point. (11) Cross-sections should
be taken as a general rule at every station and at ?ueh
intermediate points as will insure a reliable measurement
of the earthwork quantities. It is not necessarily the low-
est and highest points that are required, but those points
which, when joined by straight lines, will give the contents
as nearly as possible equal to the true volume; if the "aver-
age end areas" method is to be used in calculating the Quan-
tities, sections should be taken every 50 feet when the dif-
ference of center height is as much as 5 feet; as a rule,
slope stakes need not be set at cross-sections taken between
stations. (12) "Grade point" stakes (marked 0.0), should
be set where the center line and each edge of the roadbed
pierce the ground; and also in side-till sections in both cut
and fill, where the roadbed plane cuts the ground line; if
the width of roadbed is different in cut and fill, the greater
half-width is commonly used in locating the side grade
point; in the simplest case a contour line is perpendicular
to the center line and the three grade points are at the
same cross-section, forming two wedges; in the more usual
194 RAILROAD SURVEYING.
case the contour line is diagonal, and the three grade
points are not in the same section, so that two pyramids are
formed; if the station numbers of the two side grade points
differ by only a few feet, it is usual to simplify the record
by taking the notes as for a wedge at the station uumber of
the center grade point, although the side grade point stakes
are set in their true positions; as a rule, a complete cross-
section is taken at each grade point. (13) In cross-section-
ing for the end of an embankment at a wooden trestle the
end slope is made the same as the side slope, and the end
and side planes are joined by conical quadrants; the dis-
tance between "heads of dump" (H. D.) is usually 10 feet (5
feet at each end) less than the total length of stringers; a
complete cross-section is taken at the "head of dump," and
the "toe of dump" (T. D.) on each edge of the end slope is
located and recorded; on level ground the volume of the
wedge-like solid so formed is found by dividing it into a
triangular prism and two right conical quadrants; on
ground sloping transversely the end of dump is made up
of a middle prismoid and two conical quadrants, each of the
latter being generated by a variable triangle revolved about
a vertical axis through a corner of the top roadbed plane
at "head of dump."
The calculations in the foregoing method of cross-section-
ing may be simplified by preparing a table of distances out
for the standard roadbed widths and slopes, or by using a
special tape having the zero graduation at a distance from
the end equal to the half-width of roadbed, and the re-
maining graduations modified to suit the side slope ratio.
The calculations may be further simplified by using a spe-
cial rod havig an endless sliding tape graduation. The stu-
dent will be given practice with these labor saving devices
after he has first acquired familiarity with the principles
of cross-sectioning without these aids.
Cross-sectioning with rods alone is done in much the
same manner as that described above. Two rods aro used.
The usual length of the rods is ten feet, and each is gradu-
ated to tenths and has a bubble vial in one or both ends.
The slope stake point is determined by leveling out from
the ground at the center stake with reference to the center
cut or fill, each rod being held alternately level and plumb.
Other points in the cross-section, as well as grade points,
CROSS-SECTIONING. 195
etc., are determined in the same manner. The notes are
kept as in the other method. On very rough ground, the
rod method is usually the more rapid. Some engineers
cross-section on rough ground by taking the elevation of
each point and plotting the notes on cross-section paper,
then using the planimeter to determine the areas. Borrow
pits are often cross-sectioned by taking elevations at the
intersections of two series of parallel lines forming
squares.
Land-Line Party. It is the duty of the right of way
party to secure data for the preparation of right of way
deeds. The party should consist of at least four: (1) re-
corder, (2) transitman. (3) head chainman, (4) rear chain-
man, (the chainmen also to serve as axemen and flagmen
as required.) Their equipment is the usnal one of a transit
party for such work. The party should secure ties with
all section and other land lines whenever crossed. The
notes should show station numbers and angles: of intersec-
tion and distance along land line to the nearest identified
land corner and also to important fences. As a rule, make
the intersection by running through from one corner to the
other. Where the line passes through a town, tie the cen-
ter line to the plats, block lines, monuments, etc. Secure
any records and make tracings of any plats, etc., at the
recorder's office, that may be of service in preparing deeds.
Bridge and Masonry Party. The bridge and masonry
survey party will determine drainage areas for culverts and
other waterways, prospect for foundations, and stake oat
trestles, masonry work, etc. The usual organization will
be four men: (1) recorder (in charge), (2) transitman or
leveler, (3) chainman, rodman, flagman, etc., (4) chainman,
axeman, flagman, etc.. as the work assigned may demand.
Resurvey Party. The resurvey party will be assigned to
such duties as the resurvey of yards, the collection of data
for crossing frogs, running centers on old track, including
spiraling, etc. It will usually be a party of four.
Seminary Work. The purpose of the seminary work is
(1) to give the student a knowledge of the literature of rail-
way engineering, and (2) to afford training in the collection
and preservation of engineering information and data, and
in the preparation of abstracts and reports of a technical
nature. The reading will be done in accordance with a
196 RAILROAD SURVEYING.
systematic outline and the notes will be submitted in pre-
scribed form.
PROBLEMS IN RAILROAD SURVEYING.
PROBLEM Gl. ADJUSTMENTS OF LEVEL AND
TRANSIT.
(a) Equipment. Engineers' level and transit, adjusting
pin.
(b) Problem. Test the essential adjustments of the as-
signed instruments and correct any discrepancies found.
(c) Methods. This problem is designed to freshen the
student's knowledge of the adjustments of the instruments,
as well as to place the equipment in condition for accurate
work. The adjustments will be made under the personal
dirtxrtion of the instructor. The student should attempt to
be speedy as well as accurate in testing and making the ad-
justments.
PROBLEM G2. USE OF FIELD EQUIPMENT.
(a) Equipment. Complete equipment for railroad transit
and level party, as specified in foregoing pages.
<b) Problem. Practice the detailed duties of each position
in the transit and level party.
(c) Method*. This problem is designed as a "breaking in"
exercise preparatory to engaging in the regular field work
of railroad location. With the manual in hand the duties
of each position will be studied and practiced in turn.
For example, each student will go through the following
exercise with the transit as briskly as possible: (1) set
transit over tack in hub, (2) level up, (3) set plate to zero,
(4) reverse telescope and sight on back flag, (5) release
needle, (6) plunge telescope, (7) read and record needle on
back line prolonged, (8) sight at front flag pole, (9) read
and record deflection angle right or left, (10) read and
record needle on front line, (11) lift needle, (12) plunge
telescope and check on back flag, (13) calculate needle angle
and compare with plate reading, and if checked, shoulder
transit; now repeat entire process at the same hub, more
briskly than at first, if practicable, avoiding reference to
PROBLEMS.
197
preceding record until the full series of steps is completed.
Let the student prepare a similar numbered program for
each of the other positions and practice the same systemati-
cally. This series of exercises may profitably occupy two
or more assignments, since the speed and quality of the
actual surveys to follow are certain to be much enhanced.
PROBLEM G3. PRELIMINARY FIELD CURVE PRAC-
TICE.
(a) Equipment. Transit party equipment, as prescribed in
instructions.
(Rf suits fa 0.0/
Problem 2.
IL__ B CzJiso-n'*. rt.,Tc,ndE.
^s\~>tL, GiveiWo-**'?' Ream'red j rat By 1-rigo.
>-.'>.< '* (.R(4'n') = l3376S I tb)By ToUt I'
\\A ^ '
Indicated WorK.
Length of Curve. L .
Tangent Distancg, T.
at T=f?tanZ
= 1337.65 XO.S8 066
=<7?7/)
External Distance. .
Calculatic
7) 1
2
I7) '4.0739 60.2
;*gg3Jj
/ 4. 0739
376S T,(eo'/6)= 33Z60
7;t(o'/8') = 33283
T, (6<f/7) = 332 7. /S}&833(3)
293833 776-77
76-77 3Z8SS O.k.
D,ff due to appro*.
basis of method (b).
> f 60''6'}= 89S
S36SfO > (60''8')=896S ____
,3 376 E,C60'i7'j=89S.9S)4.f833
6688 8S6S7 209.17
6688
6
_ fi_
Z09.,S
O.OZ
* Diff. due +o 3o
appro*, basis of mefhoal fb}.
198 RAILROAD SURVEYING.
(b) Problem. Run out the assigned practice curves in the
field, with the prescribed organization and conditions.
(c) Methods. The preliminary curve practice is designed
to give the student a practical knowledge of the principles
of railroad curves and the routine method's used in location
surveys. The several positions in the field party will be
filled in succession, and each student is expected to respond
heartily to the spirit of the practice, whatever his assigned
duties. Each member of the party should engage in the
calculations as far. as practicable. The report of the field
work should state the precision of linear and angular
checks. The field practice will be based in part on the
indoor curve problems.
PROBLEM G4. CURVE PROBLEMS.
(a) Equipment. Drafting instruments, paper, etc,
(b) Problem. Solve the assigned problems in railroad
curves and submit results in a neat and draftsmanlike form.
(c) Methods. (I) Draw a plain figure to the largest con-
venient scale. (2) State problem and present data in a
concise and systematic manner. (3) show the separate steps
clearly; first state formulas in general terms, then substi-
tute values and give results; as a rule, show actual calcu-
lations adjacent to the indicated work; habitually verify
results by an independent process; use common sense
checks and contracted methods of calculation; in general,
make full use of the opportunity to gain skill as a com-
puter. (As a rule, the nearest 0.1 foot only is required in,
field measurements on curve location, but it is excellent
practice, especially for the beginner, to preserve the nearest
0.01 foot in the calculations.)
CHAPTER IX.
ERRORS OF SURVEYING.
Errors. Errors of observations are of three kinds, viz.,
(1) mistakes; (2) systematic errors; (3) accidental errors.
Systematic errors includes all errors for which corrections
can be made, .as erroneous length of standard, errors of
adjustment, refraction, etc. Accidental errors are those
which still remain after mistakes and systematic errors
have been eliminated from the results.
It has been found from experience that accidental errors
are not distributed at random but follow mathematical
laws. These laws are fundamental in the Theory of Least
Squares and are: (1) small errors are more frequent than large
ones; (2) positive and negative errors are equally numerous;
(3) very large errors do not occur.
Arithmetical Mean. The most probable value of a
quantity obtained by direct measurements is the arith-
metical mean of all the determinations where the observa-
tions are of equal weight, or is the weighted mean where
the observations are of unequal weight.
Precision of Observations. In the adjustment of obser-
vations it is often necessary to combine results of different
degrees of precision or weight. It is also desirable to have
some means of comparing observations so that the com-
puter may know what degree of confidence to place in the
results. The quantity commonly used for comparing the
precision of observations is the probable error.
Probable Error. The probable error is such a quantity
that it is an even wager that the number of errors greater
is the same as the number of errors less than the probable
error. It is also the limit within which the probability is
one-half that the truth will fall. For example, if 4.63
0.12 is the mean of a number of observations, the true value
is as likely to be between 4.51 and 4.75 as it is to be some
value grea'ter or less.
Probable error is also useful in finding the relative weights
that should be given different sets of observations, as it has
been found that the weights of observations vary inversely
as the squares of their probable errors.
200 ERRORS OF SURVEYING.
Formulas:
Let E! = probable error of a single observation.
E m = probable error of the mean of all the observa-
tions.
n = the number of observations,
d = the difference between any observation and the
mean of all the observations.
S = symbol signifying sum of.
Then from the Theory of Least Squares
E! = 0.6745 ^?2 (1)
E ni -= 0.6745 J * d ' (2)
1 n(n-l)
= =. (3)
Vv.
The probable error of the weighted or general mean is
Sy^ (4)
where 2 p = summation of the weights.
The probable error of a quantity with a weight p is equal
to E divided by the square root of p.
The probable error of Z where Z = z x z 2 and R 1? r t ,
and r 2 are the probable errors of Z, z t and z 2 , respectively, is
R? = r\ + r 2 (5)
The probable error of Z, where Z = az is
R? = a 2 r 2 (6)
The probable error of Z, where Z = z l z 2 is
R 2 = z 2 r 2 + -L\ r? (7)
This would be the probable error of the area of a rectan-
gle where r l and r, are the probable errors of the sides z,
and z 2 , respectively.
Example. As an example of the application of these
formulas consider the two following series of measurements of
an angle given in Table I. The first set was taken with a
transit reading to 10 seconds, the second with a transit
reading to 30 seconds.
PROBABLE ERROR.
201
FIRST TRANSIT.
SF.COM) TRANSIT.
No. | Angle.
d
d 2
No.
Angle.
d
d'
O ' "
' "
1
34 55 35
2
4
1
34 56 15
39
1521
2
35
2
4
2
55 80
6
36
3
20
13
If.'.i :;
54 30
66
4356
4
05
28
784
4
55 15
21
441
5
56 15
42
1764
5 56 00
24
576
6
55 40
7
49
6
55 45
9
81
7
10
23
529
7
55 30
6
36
8
30
3
9
8
55 30
6
36
9
50
17
289
9
56 00
24
576
10
30
3
9
10
55 45
9
81
Mean 34 55' 33"
2cP = 3610
Mean 34 55' 36"
2cP=-774<>
Em = 0.
7740
,= 6" .3
The weights of these nnan values vary inversely as the
squares of the probable errors ; or in this case the weights
are as -^^ to g yj or as 12 to 5. The most probable value
of the angle measured with the two transits will be the
weighted mean
17
= 34 5-V 33M
The probable error of this result from (5) since
12 5
Z = 17 z i + 17 z > is
ERRORS OF SURVEYING.
12
Substituting r 2 2 = __1 r L 2 we have
o
R! = 4."3 J.. 1 - 2 = 3".6.
* 17
For other examples in the use of probable error see prob-
able error of measuring a base line, probable error of set-
ting a level target, probable error of setting a nag pole. '
Angla Measjrement. The measurement of an angle re-
quires two pointings and two readings. If r r and r s are the
probable errors of reading and pointing, respectively; the
probable error of the measurement of an angle will from i5|
be
R i = l r r 2 + r s 2
If r t is the probable error of a single reading
If the value of an angle is determined by n separate meas-
urements the probable error due to reading will be
If the value of an angle is determined b\ measuring the
angle n times by repetition the probable error due to reading
will be
It will thus be seen that the probable error due to reading
is very much reduced by measuring an angle by the method
of repetition. The errors of pointing, etc., however, make
it doubtful whether it is ever advantageous to make n exceed
5 or 6 with an engineers' transit.
Angle Adjustment. When the three angles of a triangle
have been measured with equal care they should be adjusted
TESTS OF PRECISION. 203
by applying one-third of the error as a correction to each
angle.
When the interior angles of a polygon having n sides
have been measured with equal care they should be adjusted
by applying one-nth of the error as a correction to each
angle.
When n 1 angles and their sum angle at a point have
been measured with equal care they should be adjusted by
applying one-nth part of the error as a correction to each
angle.
In a quadrilateral the true values of the angles fulfil the
following geometrical conditions: (1) the sum of the angles
of each triangle is equal to 180 plus the spherical excess
(the spherical excess in seconds of arc is equal approxi-
mately to the area in square miles divided by 78); (2) the
computed length of any side when obtained from any other
side through two independent sets of triangles is the same
in both cases.
When the angles of a quadrilateral have been measured,
errors are certain to be present and the corrections that
satisfy one of these conditions will not satisfy the other.
The most probable values of the corrections to the angles
are then determined by the Theory of Least Squares.
TESTS OF PRECISION.
Practical Tests In careful surveying where blunders
are eliminated and the systematic and accidental errors are
small and under control, it is found that the magnitude of
the errors increases in close accord with the foregoing
rational basis, that is, as the square root of the number of
observations. The following practical tests of precision are
based on this truth. (The diagrams have been prepared
with a view to supply extra copies for insertion in the field
note book where they may be consulted as the results are
obtained.)
Linear Errors. Cumulative or systematic errors usually
increase directly as the length of the line chained, while com-
pensating or accidental errors vary about as the square root
of the length. AVhile both kinds of errors affect all linear
measurements, the former chiefly control the results of crude
and the latter of accurate chaining. It is thus fairly con-
sistent to express the precision of chaining in crude work
204 ERRORS OF SURVEYING.
in terms of the simple ratio of the length; but as the chain-
ing becomes more and more exact, the variation of the dif-
ferences between duplicate measurements approximates
more and more closely to the law of square roots.
Coefficients of precision derived from the latter relation
may be based on either 100-foot units or foot units in the
distance chained, as preferred. The former basis is used in
the chaining diagram, while the latter is found in the last
paragraph of the explanatory matter on the second page
referring to the precision of traverse surveys.
The diagram of chaining errors shows chaining ratios by
right lines radiating from the origin, and the law of square
roots by means of parabolas. The coefficient of precision
for a given observed difference between duplicate chainings
is determined by inspection from the diagram, interpolating
between curves if an additional decimal place is desired in
the result. In actual practice a pair of careful chainmen
may determine the coefficient corresponding to a given
degree of care, and then use this value either in testing
their duplicate results, or in estimating the probable uncer-
tainty of the lengths chained.
For accurate chaining with the steel tape, duplicate
measurements reduced for temperature, etc., or made under
sensibly identical conditions, should not differ more than
0.05 foot into the square root of the distance in 100-foot
units. Careful work with the common chain (estimating
fractions to 0.01 foot) should not differ more than 0.1 foot
into the square root of the distance in 100-foot units.
A.ngular Errors. In measuring deflection angles by alti-
tude reversals, as in railroad traversing, there is, of course,
a cumulative discrepancy due to the collimation error;
but generally speaking, careful angular measurements with
good instiuments are subject only to compensating or ac-
cidental errors. Under the latter conditions the magnitude
of the error of closure in a series of angles, either in a
closed polygon or about a point, varies about as the square
root of the number of angles. This relation is indicated
graphically in the diagram of angular errors.
In measuring angles with a transit reading to the nearest
minute, the compensating uncertainty of a single reading
is probably somewhat under 0. 5 minute per angle, or about
one minute for the closure of a triangle. If a reading glass
TESTS OF PRECISION. 205
THE PRECISION OF CHAINING.
THE PRECISION OF ANGULAR MEASUREMENTS.
;s
5 10 IS
Number of Angles in Polygon or Series,*.
THE PRECISION OF TRAVERSE SURVEYS.
The error of closure of a traverse is usually expressed as the
ratio of the calculated linear error to the length of the perimeter of the
fie/at or polygon. The following table shows the limits prescribed by
various authorities
Prescribed Limits For Closure Of Traverses.
Authority.
Conditions.
L'im'its.
Cillespfe. (1855).
"Surveying" p. /49.
Compass Surveys
I.-3OO to I:IOOO
Alsop. f/8S7J.
Compass Surveys.
I: SOO
"Surveying" p. 199.
Transif Surveys.
1:1000 to /:isoo
Davies. (/87O).
"Surveying* p. 127.
farm Surveys.
/:soo to i:/ooo
Jordan. (1877).
German Gov't Surveys.
"Handbuch der
Baden Instructions.
i:4OO
Yermessungs-
ffun de" Vot. /, p. 96.
Str/SS Gov't Surveys.
1.333 to I-.IOOO
Ordinary Country.
1:400 to /:8OO
Mountainous Country.
i:Z67 to 1: 533
Hodgman. (/88S).
"Surveying" p. 119.
Compass Surveys.
/:joo to 1:1000
Johnson. f/886J.
Farm Surveys.
1:300
"Sur veying" p. SOI.
City Surveys.
I.-/OOO to l:5OOO
Ba/fer. * (/88S).
"Engineers ' <5ur veyi ng
ins ti-umen ts," p. 5-3.
(See Footnote).
(See Footnote).
Car hart. (/888).
"Surveying" p. I6/.
Ordinary Farm Surveys.
r.SOO
Leve/ Ground.
/:/ooo
Rough Ground.
1:200 to i:3oo
Average Transit" -Surveys.
1:1200
Wood.
(See Footnote).
(See Footnote).
(Roanoke, va., 1892).
(Baltimore, Md-, /894).
^Precise Traverses with\
\ Repeated Angles. J
t:/o ooo
/:/500o-t-.04f r t.
Raymond. C/896J.
"Surveying," p. 144.
Ordinary Farm Surveys.
i:foo
Good Farm Surveys.
1:2000
* Baker derives the formula .= p ~f d l + 72
is the permissible linear error of closure, P the length of the
perimeter, I'-d the ratio of the chaining error, and a the angular
error of closure in minutes. A thorough test of this formula under
a wide range of conditions proves it to be trustworthy.
However, the use of a chaining ratio, r.d, presumably of fixed
value for the same chainmen, does not accord with the results of
experience in careful worK; for it !s found that the differences
between duplicate chalnings vary about as the. square ryot of the
length of Jine.
On the following pigs a simplified formula js obtained by as-
suming the more consistent relation Just stated -for the chaining
errors. The results ars about th& same as those obtained with
Baker's formula^ and the form of the expression is identical
Hrith that used by Wood in the Bo/frmore Survey. ,
THE PRECISION OF TRAVERSE SURVEYS.
The reasonable or permissible error of closure of a traverse
survey may be determined by the formula dorived be/o*v f provided
the errors of ff'eld iworh are under control and their magnitude
is kno*n, at /ea-s* appro* 'fmafely.
Let P = length of perimeter.
L - calculated error of /atftud&s.
D calculated err-or of departures.
E a ~ actt/a/ or ca/cu/ared linear error of c/osure of traverse.
c coefficient of precis/on of cha/n/'/yg.
?= angular error of c/osure /n f-rj/ntjfes.
ft =* /inear error of c/o-sur^ a f c/ t ro angu/ar errors.
Ep= perrnissib/e.or reasonable //'near error of clo$ure> due to
errors of chaining and angle.
/n the triang/e of error the hypothenuse /$ ^^ f L z -rD z .
/n Diagram A be/ow va/ttes of a may be read c/o&e enough for
most coses. Diagram A rhay a/so serve a-s a crude graph/ oaf *rraY-
erse tab/e, and b/tmders in fhe fie/a" i/yorM may &e focated toy /'r.
/n carefa/ chaining by men of some training, the error* rar/e>$ abasi-
as the square root of the d/'stance. /f*c be the compensating error-
for the unit distance, then C= cVr>.
arrrcng the sia'es in proportion to their lengths. Assuming rhis to b&
the case, the resufting linear error /$ A-aP.arc/'^ .OOOSaP.
In cjooa 4 worK -the errors are &fr>a/f in amount and eauaf/y
liable to 6e p/us and minus. Hence, the pro&ab/e error of c/osxr-c-
due to the t*o causes, i.e. rhe- reasonab/e or perm/'-S&iMe //'near- e-r~
ror of c/osure /s E p = ^A*+C* =JtO0O3ctP)*+c*P -
7~h/s forma/a may be much 'Simplified' by comp/etfna, trt& sat/ar^
anct dropping the negative ferm under the rad/'cu/, whence with
sufficient exactness, there results the qeneraJ formu/ct
Ep=.0003af>+l7OOc* (I)
77?^ very exact sfandard, P-Z-/5 OOO+.O4-ft., used at Baltimore,
(see table, precea'ing page), may be obtn/'n&el from (t} by matting aj
somewhat /ess that
may be obtat/'n&el from (t} by maHing aj
?ufe, and c = .oo5rf., these vafaes bring
ay be taHen as fo//otvs:- For best w
ige work (c<,.O!Oft.),.Zft.; for fa
The ya/ue of c may be
the chaining term of (I)
worH (c<.OiS) r .4* ft.; ana" for poor worn (c^-020), .8ft. /n &are-
ful traverse surveys the angle ftrrm alone afFords a rigid test, so that
for the genera/ ru
A. Actual Error.
10' 15 Z0 Z5 50 35 40
B. Permissible Error.
See Formula CZ).
THE PRECISION OF LEVEL CIRCUITS. -
The precision of spirit leveling is expressed by the formula
Error of Closure = Constant 1 'Length of Circuit.
In the following summary of practice in representative Surveys of
The United Starts, is the maximum limit of error of closure of a
tevel circuit having a length of K kilometers or M miles.
MAXIMUM PERMISSIBLE ERROR OF CLOSURE.
Metric UniT& British Units.
NAME OF SURVEY. Coefficient TO Coefficient to nearest
nearest mm. O.OOIft. 001 ft.
Chicago Sanitary District. E = 3mmtfT = 0. 012 ft.^M = O.OIft.iM
Missouri River Commission. = 3mmVSK = 0.018 ft. Y^F]
Mississippi River Commission. (1891). E= 3mmffi< = 0.0/8 ft. W ^= 0.02 ft.iM
Mississippi River Com'n (Before 1891). E- 5mmrfrT = 0.021 ft.^W)
United States Coast Survey. E= SmmjIzR - 0.029 ft. ~/M - 0.<75 ft.^M
United States Lake Surrey. E=IOmmlfK = 0.042 ft. W =0.04ft.iM
Umted States Geological Survey. E= 0.050 ft. VM' =O.Q5ft.^M
A simple practical test of the dearee of precision attained in spirit
leveling is found in the last column Of the above table. This graduated
scale of precision is aiven below gi-aphically for distances to ten miles.
000
Length
234
of Level Circuit, Af, Miles.
THE PRECISION OF^ LEVEL CIRCUITS.
(For Good Average Practice.)
When the length of tht level circuit is /fnotvn in 100-ft stations,
or rthen merely the number of settings of the instrument and the approx-
imate average distance covered per setting are known, the following
modifications of the preceding test are valuable.
Let = maximum permissible error of closure of level circuit.
M = length of level circuit in miles.
L = , ,. 100-ft. stations.
L'= approximate average distance covered per setting
of the instrument in 100-ft. stations.
5 = number of instrumental seltings in the circuit.
For good average work with the engineers' level
O.OO7ftrfL
and
Substituting for 400 -ft average sights, L'=8, E = 0.0135ft. VJ
- 3 SO-- L'=7, E =0.0/82 ft. T/J
3 00-- ~ L'=6, E=O.OI63ft.TfS
250- " " L'=S, E= 0.0154 ft.VJ
For a very rapid approximate check under ordinary conditions, it may
be assumed that E O.OZft.YS^. A graphical representation of these
formulas is given below.
Length of Level Circuit, M, Miles.
S 10 15 20
E5
30
35
40
AS
0.35
'0.00
10 20 30 40 50 60 70 80 90 100
Length of Level Circuit, L. 100-Foot Stations; or Number of Level Settings, 5.
210 ERRORS OF SURVEYING.
be used and the vernier reads to the nearest half minute,
the uncertainty is still further reduced.
Again, in estimating the needle reading of a compass to
the nearest 5 minutes (one-sixth part of half-degree), the
uncertainty of reading alone is perhaps 8 minutes, although
this is increased by other conditions such as sluggishness
of needle, etc., probably causing an uncertainty of as much
as 5 minutes per angle, which latter limit would produce an
error of closure of a triangle of say 10 minutes, and of a
five-sided polygon of perhaps the same amount. ^See dia-
gram.)
Traversing Errors. The errors of traversing are made
uj) of the combined errors of linear and angular measure-
ments. If the error of closure as determined from the lati-
tudes and departures is large, the work should be scanned
closely to detect blunders such as the substitution of sine
for cosine, errors of 100 feet in chaining, misplacing deci-
mal point, etc. After establishing the consistency of the
residual errors, they should be distributed either -in propor-
tion to the lengths of the several courses, as in the more
common usage, or in the proportion of the respective lati-
tudes and departures, as would seem to be more consistent.
If the several courses have not been surveyed with like
precision, weights should be assigned in distributing the
errors. Absurd refinements should be avoided in making
the distribution of errors.
Leveling Errors. Perhaps in no phase of surveying
measurements is it more clearly established that accidental
errors follow the law of square roots than in careful leveling.
The precision diagrams are based on best current usage.
CHAPTER X.
METHODS OF COMPUTING.
Introduction. To no one is the ability to make calcula-
tions accurately and rapidly of more value than to the engi-
neer. Many fail to appreciate the value of rapid methods
of calculation, and have no conception of the amount of
time that can be saved by the skillful use of arithmetic,
logarithms, reckoning tables and computing machines.
In the Held the engineer has to depend upon the ordinary
methods of arithmetic, or a table of logarithms for his
results. The use of these aids should therefore receive special
attention, for the engineer cannot afford to lose the time of
his assistants while he makes unnecessary or extended com-
putations.
In the office tables of squares, reckoning tables, slide rules
and computing machines can be used in many cases with
profit.
Consistent Accuracy. It is safe to say that at least one-
third of the time expended in making computations is
wasted in trying to attain a higher degree of precision than
the nature of the work requires.
In making arithmetical computations where decimals are
involved it is a common practice to carry the result out to
its farthest limit and then drop a few figures at random.
In using logarithms time and labor are lost by using
tables that are more extensive than the data will warrant.
The relative amount of work in using four, rive, six and
seven-place tables is about as 1, 2, 3 and 4. Besides the
extra labor involved, the computer has a result that is liable
to give him an erroneous idea of the accuracy of his work.
In making computations, in general, calculate the result
to one more place than it is desired to retain.
If several numbers are multiplied or divided, a given
percentage of error in any" one of them will produce the
same per cent of error in the result.
In taking the mean of a series of quantities it is consist-
ent to retain one mpre_ptace than is retained in the quan-
tities themselves.
212 METHODS OF COMPUTING.
In direct multiplication or division retain four places of
significant figures in every factor for an accuracy of about
one per cent.; retain five places of significant figures in
every factor for an accuracy of about one-tenth of one per
cent.
I ,OG ARITHMIC CALCULATIONS.
Logarithm Tables. Logarithm tables contain the decimal
part of the logarithm called the mantissa, the integral part
called the characteristic is supplied by the computer.
Four-place tables give the mantissa to four decimal
places of numbers from 1 to 999, and by interpolation give
the mantissa of numbers from 1 to 9,999. Four-place log-
arithms should be used where four significant figures are suf-
ficient, and should not be used where an accuracy greater
than one-half of one per cent is required.
Five-place tables give the mantissa to five decimal places
of numbers from 1 to 9,999, and by interpolation give the
mantissa of numbers from 1 to 99,999. Five-place loga-
rithms should be used where five significant figures are
sufficient, and should not be used where an accuracy greater
than one-twentieth of one per cent, is required. Five-place
tables are sufficiently accurate for most engineering work.
Six-place tables give the mantissa to six decimal places
of numbers from 1 to 9,999, and by interpolation give the
mantissa of numbers from 1 to 99,999, the same as the five-
place tables. Six-place tables are of no practical value as
the labor of using a six instead of a five-place table is
about as 2 to 3, and as the interpolation for the next signif -
cant figure is made with larger differences: it is less reli-
able than with the five-place table.
Seven-place tables give the mantissa to seven decimal
places of numbers from 1 to 99,999, and by interpolation
of numbers from 1 to 999,999. Seven-place tables are
rarely needed in engineering work, except in triangulation
work where the angles are measured by repetition.
ARITHMETICAL CALCULATIONS.
Requirements. To become a rapid computer the follow-
ing requirements are essential:
(1) A good memory for retaining certain standard num-
bers for reference.
ARITHMETICAL CHECKS. 213
(2) The power of performing the ordinary simple arith-
metical operations of multiplication, division, etc., on num-
bers with facility, quickness and accuracy.
. (3) The power of registration, /. e., of keeping a string
of numbers in the mind and working accurately upon them.
(4) The power of devising instantly the best method of
performing a complicated problem as regards facility,
quickness and certainty.
It is obvious that all do not have the ability to become
rapid computers, but even these can become fairly skillful
by constant practice and perseverance. The ordinary pro-
cesses of arithmetic should be performed with numbers in
all possible positions. No more figures should be put down
than necessary, and all operations should be performed
mentally whenever possible. In the mental part the results
should alone be stated, much time being lost by repeating
each separate figure.
Checks. In order to check his work the computer should
keep the following well known properties of numbers well
fixed in his mind:
(1) The sum or difference of two even or of two odd
numbers is even .
(2) The sum or difference of an even and odd number is
odd.
(3) The product of two even numbers is even.
(4) The product of two odd numbers is odd.
(5) The product of an even number and an odd number
is even.
(6) Checking results by the familiar operation of cast-
ing out the 9's depends upon the following properties of
numbers:
(a) A number divided by 9 leaves the same remainder
as the sum of the digits divided by 9. For example:
4384^9=487+1
(4+3+8+4)^-9=2+1
(b) The excess of 9's in the product equals the excess of
9's in the product of the excesses of the factors.
473,295 Excess = 3
4,235 Excess = 5
2,004,404,325 Excess
[5
214 METHODS OF COMPUTING.
(r) The excess of 9's in the dividend equals the excess
of 9's in the product of the excesses in the divisor and quo-
tient plus the excess in the remainder:
56/244:} Excess in divisor = 2
4:{+:{5 Excess in quotient = 7
Excess in remainder=8
Excess in (2X74- 8) =4 /
Excess in dividend = 4 \ ]
(7) Results should be checked by taking aliquot parts
wherever possible, and by performing the operations in
inverse order or performing inverse operations, Computa-
tions performed by means of logarithms should be checked
by making the computations roughly by means of arithme-
tic. The probability of error should be recognized and pre-
caution taken to verify results.
ADDITION. Since the eye is accustomed to pass from left
to right time can be saved, where the columns are not too
long, by adding in the same way. The device of increasing
or diminishing the numbers to make them multiples of ten
and then subtracting or adding to the result is very con-
venient, especially where several columns are added at one
time.
A'.r. /. 96
47 143
212 69
32
87 331
49
380
The mental work in detail is as follows:
100+47=147; 1474=143; 143+70=213; 2131 = 212:
212+30+90= 332 ; 332- 1 = 33 1 ; 331+50 38 1 ; 38 1 - 1 = 380
Expert accountants use the method of adding col-
umns in groups of 10, 20, 30, etc.. -small figures, indicat-
ing the number of the group, being placed along the column
at intervals depending upon the computer. This method is
well adapted to the addition of long columns where one is
liable to be called away from his work. The progress of
the work being then shown by the number of the group
plus the excess.
K.r. 7. 4,324X 625 = 4,324( 5X . 1QJ ) (4,324,OOOX 5)
MULTIPLICATION. 215.
MULTIPLICATION. In order to make the best use of
the methods given, the computer should have perfect com-
mand of the multiplication table as far as 20 at least.
Multiples of 10. To multiply by some number which is
a factor of 10 or some multiple of 10, for example: Multiply
A bv B, where B=
d
Annex n ciphers to A, multiply by C and divide by d.
2,702,500.
/v r . j?._ 7,924X25 792,400 s-4 198,100.
Squaring Small Numbers. Numbers may "be squared
mentally by the following rule: Add to or subtract from
one factor enough to make its units figure zero. Subtract
from or add to the other factor the same amount. Multiply
together this sum and difference, and to the product add
the square of the amount by which the factors were increased
or diminished.
Proof.- a 2 b 2 = (a+b) (a b)
a 2 (a+b)(a b)+b 2
(76) 2 (72x80i+4 2 5.776
(127) 3 (124X130)4-3 3 16,129
Kx. 3. (64) 2 (6X6|)+(i) : ' 39-! 1 ,, 1
K.c. 4. (6.1) 2 . (6X7) + (|) 2 42}
Ex. '>. (7.5) 2 (7X8)+(5) 2 56.25
It will be seen that the process is very simple where the
units place is 5.
(2) When the tens differ by unity and the sum of the units
equals 10. numbers may be multiplied by the following rule:
From the squares of the tens of the larger number subtract
the square of the units of the larger number. For the num-
bers may be represented by (a+b) and (a b), and the
product will be (a+b)(a b)' a 2 b 2 .
K,r, 6'. (93X87) = 90 3 3 2 = 8,100 9 = 8,091.
216 METHODS OF COMPUTING.
(3) The product of composite numbers is best obtained
mentally by resolving them into their factors and taking
the products of the factors.
26X 36 -9X13X 8 -=936
48X24 <24) 2 X2 .-1,152
(4) Having the square of any number the square of the
number next higher is obtained by the following rule: To
the known square add the number and the next higher and
the result will be the square of the next higher number.
Ex.9. (25) 2 625. (26) 2 - -625 +25+26 676
(5) A very close approximation to the square of a quan-
tity which is very near unity is obtained by adding algebra-
ically two times the difference between the quantity and
unity to the quantity.
Proof. (lib) 2 I2b-f-b 2 = l2b, (approximate).
Ex. 10. (1.05) 2 = 1+2 (1.05 !) = !+. 10=1. 10
Ex. 11. -(.94) 2 =1 2 (1 .94)=! .12=. 88
Ex. 12. (2.034) 2 =2 2 (1+2X.017)=4(1.034)=4. 136
Cross-Multiplication. This consists in aking the
product of each digit in the multiplicand by each digit
in the multiplier and taking the sums, products of the same
denomination being determined thus: unitsX units gives
units; tensX units and unitsXtens gives tens; unitsX
hundreds, tensXtens and hundredsX units give hundreds,
etc. All products are added mentally, only the final result
being put down.
Ex. 1. (2,347) 2 =5,508,409 the final result being all that
it is necessary to write down. The mental work is as
follows, the figures in heavy type being figures in the pro-
duct: 7X7=49; 4 + 2(7X4)=60; 6+2(7X3)+4 2 =64;
6+2 (2X7)+2(3X4)=58; 5+2 (2X4)+3 2 =30; 3+2(3X2)
= 15; l + 2 2 =5.
Ex. 2. The product of any two numbers may be found
in the same manner.
CROSS-MULTIPLICATION. 217
The mental work is as follows: 8X2=6; 3X3+8X2=
25; 2+3X4 + 8X3+5X2=48; 4+3x9+8x4+5X3+2X2
=82; 8+8X9+5X4+2X3=106; 10+5X9+2X4=63; 6+
2X9=24.
Ex. 3. The process of cross-multiplication may be sim-
plified as follows: Required to multiply 4,328 by 736;
write the multiplier on a slip of paper in inverse order and
place it below the multiplicand with the left hand figure
below the units place of the multiplicand thus:
Multiply together the figures in the same vertical column,
6X8=48; set down the 8 and carry the 4; then move the slip
one space to the left, thus,
4,328
inn
8
Multiplying together the figures in the same vertical columns
and taking the sum, 4+6X2+3X8=40; set down the and
carry the 4; then move the slip one space to the left,
multiplying together the figures in the same vertical col-
umns, adding, etc., we will finally have the work standing
thus :
liemo\ ing the slip we have
4,328
736
3,185,408
218 METHODS OF COMPUTING.
The multiplier may be written on the bottom of a sheet
in inverse order and placed above the multiplicand instead
as above described. The work, however, is very much
simplified by simply writing the multiplier in inverse order
without using the slip:
The mental work being as follows: 6 - S - 4s: 4+6x2
+8x8=40; 4+6X3+2X 3+7X8=84; 8+6X4-:; > 7
2=55; 5 + 3X4+7x3=38:3+7x4=31. It \\ ill he set-n
that this device removes most of the mental strain, there
being no cross-products.
CONTRACTED MULTIPLICATION. In multiplying
decimals, when the product is required to a few places of
decimals, the work may be shortened as follows: Required
a product correct to the nth decimal place. Write the multi-
plier with its figures in inverse order, its unit place under
the nth decimal place of the multiplicand. Multiply the
multiplicand by the figures in the multiplier, beginning
with the ri ht hand figure: rejecting those fiuur s in the
multiplicand which are to the right of the figure used as a
multiplier, increasing each product by as many units as
would have been carried from the rejected part of th^
multiplicand, taking the nearest unit in each case place the
right hand figure of each partial product in the same col-
umn, and add as in common multiplication.
In most cases it is best to carry one more place than re-
quired. The following examples illustrate the process:
Ex. 1. The radius of a circle is 420.17 ft. What is its
semicircumference to nearest 0.01 ft.? (V = 3.14159265 I
In the work below the partial products in the contracted
multiplication are seen to correspond to the partials of the
common method, tiken in reverse order, the part to the
right of the vertical line being rejected. The contracted
multiplication is carried one more place than required. A
dot is placed above each figure when it is rejected from the
multiplicand.
CONTRACTED MULTIPLICATION. 219
420.17
3./4/S93
ffo
I2605/
/320.003 /3Z0.003
Z605I
8/53
08S
17
'3081
Ex. a. The observed length of a line is 2231.63 ft.
with a tape having a length of 100.018 ft. Required the
reduced length of the line to the nearest 0.01 ft.
Noting that each foot of the tape = 1.00018 ft.
Z23/.63 2Z3/.63
&l OOO.I /.OOP / 8
223/6-3 /7\8S304
22 ^2\3/63
/8 223/63\000
2232.03 B232.03\/6934
EJ-. .?._Same observed length with a tape 99. ( )82 ft.
long. Required the reduced length.
Each foot of the tape = 0.99982 (= 10.00018) ft.
223/.6S
0.99 98 a
20084
I'l.f. 4 To compare contracted multiplication with
logarithmic work, calculate 861.3 ft. X sin 17 19' to the
nearest 0. 1 ft.
220 METHODS OF COMPUTING.
= 2.408864
2S6-4
CONTRACTED DIVISION. If the quotient is desired cor-
rect to the nth decimal place, the followitg method may be
used: Find one-half of the desired figures in t^he quotient
in the usual way and do not bring down a figure for the
last remainder. Drop a figure from the right of the divisor
and find another figure in the quotient. Then without
bringing down any more figures continue to discard figures
from the divisor until the required places are obtained.
Ex. 1- Divide 443.9425 by 24.311 to nearest hun-
dredth. There will be four figures in the quotient, so we
will find the first two in the ordinary way. A dot is placed
over each figure in the divisor when it is rejected.
34.32) 44 3. 9 42S (t8.2S
Divisor Near Unity. When the divisor is near unity a
very close approximation is given by the method shown in
the following problems:
Ex. i. 1 Q 39 - 4 =5 (l.003254)=5x. 996746=4. 98373
correct to within one unit in the fifth place.
Ex. 2. -^ = 7 ( 1+ ( 1- .9982)) 7X 1.0018- 7.0126
correct to the last place.
SQUARE ROOT. 221
CONTRACTED SQUARE ROOT. A result correct to a re-
quired number of decimal places may be found by a process
similar to the method employed for contracted division.
Ex. /.Required the square root of 12,598.87325 correct
to thousandths. We see by inspection that the root will
contain six h'gures. Find in the ordinaiy way the first
three figures. Form a new trial divisor in'the usual way,
and bring down only one figure for the dividend in place of
two. Find the remaining figures by contracted division.
The last figure brought down is not increased whatever it
may be followed by, since the contracted process tends to
make the result a little too large. This method may be ap-
plied to the extraction of cube roots, where it saves much
work in finding long tiial divisors.
Square Root of Small Numbers The approximate square
roots of small Lumbers may be found by means of the
following rule: Divide the given number by the number
whose square is nearest the given number. The arith-
metical mean of the quotient and divisor will be the ap-
proximate square root of the number. The nearer the num-
ber is to a perfect squa r e the less the error. For example,
Ex. 1. ^35=: ( a /+6) -4- 2 = 5.92.
Ea^ 2.^ V~%~= (f + 3) -s- 2 = 2.83.
E.T. 3. V"79= (+' 9) + 2 .8.89.
Ex. 4. Vl28 (H-H)-*-2-- 11.31.
222 METHODS OF COMPUTING.
Square Root by Subtraction. While it possesses no points
of merit in this connection, it would not be proper to pass
the subject of square root without presenting the novel meth-
od of extracting square roots used with the Thomas Com-
puting machine. The method depends upon the relation
existing between odd numbers and squares in the system of
numbers having a radix ten. If we sum up the odd num-
bers, beginning at 1, we will observe the following relation:
1--1 3 ; 1+3--4---2 2 ; l + 3+5=9-=3 a ; 1 + 3+5+7-15 4'-',
etc. It will be seen that the square root of the sum in each
case is the number of the group.
The method of extracting square roots is as follows: Point
off in periods of two figures each: subtract from the left
hand period the odd numbers in order, beginning at unity,
until a remainder is obtained less than the next odd num-
ber. Write for the first figure in the root the number which
represents the number of subtractions made. Double the
root already found and annex unity. Subtract as before,
using for subtrahends the successive odd numbers, the root
figure being the number of subtractions made.
Ex. 1. Extract the square root of 53,824.
3 2 subtract ons
MISCELLANEOUS FORMULAS'. The engineer should
have ready knowledge concerning approximate formulas and
values. This knowledge can be obtained by the expenditure
of very little energy and time if rightly applied. For ready
COMPUTING INSTRUMENTS.
223
~t
224 METHODS OF COMPUTING.
computation and reference he should reduce as much of
his knowledge as possible to mathematical language and
express known relations by means of formulas. The fol-
lowing will illustrate this point.
Cost of Sewer Pipe. The Western Price List of sewer
pipe is comprised in the formula, C-=0.4 d 2 +14. Where
C-=cost in cents per foot and d diameter of pipe in inches
For 75 per cent off, the formula is C 1 0.1 d a +3.5, a form-
ula very easily remembered.
RECKONING TABLES. Tables for use in computing are
so numerous and well known that it would be useless to trj'
to refer to them by name. Two valuable tables for obtain -
ing products of numbers which are well known in Ger-
many, but comparatively unknown in this country are,
"Crelle's Rechentafeln," which gives the products of num-
bers of three significant figures by three significant figures to
999 by 999; and "Zimmerman's Rechentafeln," which gives
the products of numbers of two places of signigcant figures
by numbers of three significant figures to 100 by 999.
COMPUTING MACHINES. In Fig. 40, (a) is a Kuttner
reckoning machine; (b"> a Thomas computing machine; (c) a
Fuller slide rule; (d) a Thacher slide rule; (e) an ordinary
slide rule; (f) a Colby Stadia slide rule; (g) a Colby sewer
slide rule; (h) a Grant calculating machine; (i) a full circle
protractor; (j) a Crozet protractor; (k) a protractor tee
square; (1) a polar planimeter; (m) a "jack knife" planim-
eter; (n) a pantagraph; (o) a section liner; (p) a spher-
ical planimeter.
In using the "jack knife" planimeter, the point is placed
at the center of gravity, and the knife edge is placed on a
line passing through the center of gravity of the figure.
The point is then made to traverse the perimeter of the fig-
ure to be measured; passing out to the perimeter and re-
turning to the center of gravity of the figure on the same
line. The distance from the final position of the knife edge
to the line through the center of gravity, multiplied by the
length of the arm of the planimeter will give the area of
the figure. The arm of the protractor is usually made ten
inches long and the distance measured in inches.
The other machines are described in the instructions ac-
companying them when purchased.
CHAPTER XI.
FREEHAND LETTERING.
Practice Plates. A magnified scale is used in the first six
plates to give familiarity with form of letter and numeral,
and also to produce freedom of hand motion. The six
plates should first be made with a soft pencil sharpened to
a needle point, and afterwards with pen and India ink. In
Plate 7 the height of letter is that prescribed in Chapter I.
This standard size is not only well adapted to field notes
and general drafting, but is economical of execution, as
shown by the diagram.
ECONOMY DIAGRAM
ENGINEERING NEWS STYLE OF
FREEHAND LETTERING.
3 4 5 6 7 89 10
Height of Letter SOths Inch, as per Samples.
FREEHAND LETTERING.
PLATES.
227
228
FREEHAND LETTERING.
^
i
PLATES.
229
230 FREEHAND LETTERING.
PLATES.
231
232
FREEHAND LETTERING.
I
(
I
uv
J