William David Pence.

A manual of field and office methods for the use of students in surveying online

. (page 13 of 20)
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148



TOPOGRAPHIC SURVEYING.



fundamental stadia formula. (9) Take the arithmetical
mean of the ten determina^iions as the true value. (10) Com-
pute the proibable 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.
E\>llow the prescribed form.



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PROBLEM E2. STADIA REDUCTION TABLE.

(a) J^gwipmcnt— (Nb instrumental equipment required.)

(b) Problem.— Compute a stadia redluction table giving the
horizontal distances fitnn a point in front of the objective
equal to the principal focal distance for the stadia imtervals
from 0.01 feet to 10 feet, for the transit used in Problem El.

(c) Jfc^Twds.— (1) Prepare form for calculation. (2) Com-
pute th« 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 th*e 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.)



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PROBLEMS. 149



PROBLEM E3. AZIMUTH TRAVERSE WITH TRANSIT
AND STADIA.

(a) J^guipmcfi*.— Complete tranelt, otadia rod, steel pocket
tape.

(b) ProBZem.— 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 back azimuth of the
preceding 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 height
of first station and read the vertical angle to the nearest min-
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, (this 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 antt 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 betore 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. (14) Compute the permissible error of closure
of the traverse by means of Baker's formula (see chapter
on errors of surveying), using "a" equals one minute times
square root of number of sides, and "b" equals IrSOO.* If
consistent, distribute the errors in proportion to the several
latitudes and departures, respectively. (15) Compute the
area by means of latitudes and departures, and reduce to
acres.



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150 TOPOGRAPHIC SURVEYING.

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) Prohlcm. — Make a survey of an assigned field by radi-
ation with the plane table.

(c) Methods, — (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 toward& the point. (4) Measure
the distance to th^ point with the stadia. (5) Lay ofC 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.

PROBLEM E5. SURVEY OP 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 fleld 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 OP FIELD WITH PliANE
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 fleld with the
plane table by intersection.

(c) Methods. — (1) Select and measure a base line having
both ends visible from all the stations in the fleld. (2) Set



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PROBLEMS.



151



the plane table over one end of the base line, sight at
the oither end of the base line and at each one of the .
fftaticms of the field. (3) Sett 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 ir the
field. (4) Complete map and compute area as in E4.



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PROBLEM E7. THREE POINT PROBLEM WITH PLANE
TABLE.

(a) Equipment, — ^Plane table, 2 fiag 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.— iX) Use Beseeirs solution. (2) Check by
using the mechanical solution.

PROBLEM E8. ANGLES OP TRIANGLE WITH SEX-
TANT.



(a) Equipment.— ^cjiidJii. 2 flag poles.



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152 TOPOGRAPHIC SURVEYING.

(b) Problem.— MesLSure the angles of an assigned triangle
with the sextant.

(c) Methods. — (To determine index error, sight at a dis-
tant object and bring the direct and reflected images into
coincidence. The reading of the vernier will give the index
error, which, with proper sign, must be applied to all angles
measured.) (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 venier, and cor-
rect the angle for index error. (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 prescribed 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) ProftZem.— Determine the coefficients of expansion,
stretch, and sag of an assigned tape. Make three deter-
minations of each, and take the arithmetical mean as the
true value.

(Standard Tapes. — In laying off a standard or measuring
a base line where a high degree of precision is required it
is important thajt all measurements be referred to the same
standard. 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 cei*tifled 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



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PROBLEMS. 15:^

langth of th-e tape on a plane surface at two different tern
peratures 'but with a constant pull determined by a spring
balance. Then substitute the lengths, 1 and J*, and tem-
peratures, t and T, in the formula

1 — L = e(t— T)l

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 arithmetical 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 pulls p, and P,
in the formula

1— L = s(p— P)l

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.— Remoye the handles fiHjm the tapa
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.



■-■^-iff)'



Repeat the measurements using a pull of 20 and 30 pounds,
respectively. Add the corrections for sag to each m>6a8ure-
ment and compare the results. The temperature should re-
main constant during the tests. To remove the possibility
r>f an error due to temperature, observe the temperature a^



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154 TOPOGRAPHIC SURVEYING.

the time of each, ofbdervaition and correct the observed
length for expansion before substituting in the formula.

Report the methods, diata, computations and results on a
suitable form.

PROBLEM ElO. ME>ASUREMENT OF BASE LINE.

(a) Equipment, — Standard tape, transit or level, stakes
(number and size to be speoified by instructor), axe, spring
balance, 2 thermometers, laith stakes, 8-h1 nails, steel rule,
pieces sheet zinc 2 by 2 inches.

(b) Problem. — ^Measure an assigned base line with a stan-
dard tape.

(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 tape length apart The
top 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 ait 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 noil through
each lart;h stake o/t 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 determiu'atlons 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 OP TRIANGULATION
SYSTEM.

(a) Equipment — Seven-place table of logarithms.

Digitized by VjiOOQlC



PROBLEMS. 155

(b) Problem. — Adjust and calculate an assigned triangula-
tion system and plot the skeleton.

(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-
culart)e 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 th-o skeleton of the triangulation system to the pre-
scribed scide by means of the coordinates of the points.
Check by lengths of sides. Use steel straight edge.

PROBLEM E12. SKETCHING TOPOGRAPHY.

(a) ^gwipmenf.— -Small drawing board or plane table, plat
of assigned field, 4H pencil.

(b) ProftZem.— Sketch in the road«, walks, buildings and
five^oot contours on the plat of the assigned field by eye
having given the elevations of the ruling points.

(c) Methods^il) 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
distance should be frequently checked by pacing). (3)
E3stimate 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 B13. FILLING IN DETAILS WITH TRANSIT
AND STADIA.

(a) ^^tiipmewt.— Complete transit, 2 stadia rods, pocket
tape.

(b) ProBZcm.— Locate the topographic details of an as-
signed area with the transit and stadia.



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156



TOPOGRAPHIC SURVEYING.







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(c) Methods.— {!) Set transit up over assigned triangu-
lation or other point. (2) Orient instrument, i. e. set plates
to given azimuth and sight at given back sight. (3) Measure
height of axis above station hub with tape or by graduations
on tripod leg, and set target to cx)rrespond. (4) Take shot
on given back sight and reduce results as a check before pro-
ceeding. (The program for each shot is: (a) set middle
hair roughly on target, then set one stadia hair on nearest
foot-mark and read intercept; (b) set middle hair precisely
on target and signal rodman "all right"; (c) read vertical
angle; (d) read azimuth.) (5) Take side shots to represen-
tative points, keeping in mind the scale of the proposed
map. Select points according to a systematic plan, follow-
ing along ridges, gullies, etc. Contour points should be taken
with reference to change of slope. (6) Reduce and plot the
notes, and interpolate the contours, as in the accompanying
diagram. (This topography sheet should be carefully pre-
served for use in Problem E15.) (7) After completing the
survey at the assigned station, move the instrument ahead
to a new stadia station, taking both fore and back eights.
(8) Lose no opportunity to take check sights at other trian-
gulation stations, traverse points, etc.



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PROBLEMS. 157



PROBLEM E14. FILLING IN DETAILS WITH PLANE
TABLE AND STADIA.

(a) Equipment.— Camvl^e plane table (preferably with
prismatic eyep-ieoe), 2 stadia rods, engineers* divided scale,
drawing paper, 6H pencil, pocket tape.

(b) Problem. — Locate tbe 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 points
by number and write the elevation of each point under the
number in the form of a fraction. L-ocate 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.



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158 TOPOGRAPHIC SURVEYING.

PROBLEM E15. TOPOGRAPHIC SURVEY.

(a) Equipment. — Oomplete 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).

(b) ProUem. — ^Ma-ke 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 weil 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 ElO. (4) Measure the
angles by. repetition as described in Problem D13. (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 to 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 approve4 by the instructor trace it on tracing linen.
The title, meridian, scale, lettering and border should re-
ceive careful attention.




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CHAPTER Vn.
LAND SURVEYING.



Kinds of Snrreys. — Surveys of land are of two kinds:
(a) originfd surveys; (b) reeurveys.

Original Surveys. — An original survey is made for the
purpose of establishing monuments, comers, lii^es, bound-
aries, dividing land, etc. The survey of a townsite and the
government survey of a section are examples of original
surveys.

Resnrveys. — ^A reeurvey is made for the purpose of iden-
tifying and locating corners, monuments, lines and bound-
aries that have been previously established. The reeurvey of
a city block, or a survey to relocate a speotion 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 act only as an
expert witneesi. 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 ^ieed 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.



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160 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, dlistance, quantity.

(9) A lohg established fence line is better evidence ol
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 diecisions on that particular point should be con-


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Online LibraryWilliam David PenceA manual of field and office methods for the use of students in surveying → online text (page 13 of 20)