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lines cut the edge of the hill are projected on the horizontal



674 SURVEYING.

line L M. The irregular lines connecting the corresponding
points of projection are contours. In Fig. 294 they are
assumed to be 10 feet apart in vertical measurement.

1293. Conduct of a Topographical Survey.

The manner of conducting a topographical survey will de-
pend upon the extent and outline of the surface and the de-
gree of accuracy required. If the area be of comparatively
regular dimensions, such as town or park sites, the usual
practice is to lay out the area in squares. The lines of di-
vision are the bases for the location of all points within the
area whose elevations are determined by direct leveling.
If the area is long and narrow, as in a railroad survey, the
line of survey is the base for the location of all points and
for determining their elevations. Cross-sections of the sur-
face are taken at suitable intervals, and changes in the slope
of the surface are measured either by direct leveling or with
a clinometer or slope board.

\ 294. The Hand Level. The usual form, called the
" Locke level," from the name of the inventor, is shown in
Fig. 295. It consists of a brass tube A B, on the top of
which is a spirit level C. In the lower part of the tube is a




mirror which reflects the point at which the bubble should
be when the instrument is level. A small hole D at one end
and a cross-hair at the other give the level line. The ob-
server holds the level to one eye, bringing it to a level line
while he observes the object to which the level is directed
with the other. In taking cross-sections with a Locke level,
the following rule is recommended: The topographer has
two or more assistants, three is the better number, a rod-
man and two tapemen. The rodman is provided with a rod
at least 12 feet in length, of light weight, and of sufficient
width to admit of large, distinct figures being painted upon



SURVEYING.



675



it, and divided to tenths of feet. The rod is painted like the
Philadelphia rod; the face white, tenths of feet in black, and
feet in red. Tapemen should use a tape 100 feet in length,
of durable material. Chesterman with wire warp is best.
The topographer first measures the distance of his eye above
the ground, which is a constant quantity, to be subtracted from
all the rod readings. He then stands at a station and keeps
the rodman at right angles to the line of survey. The rod-
man, having reached the end of a slope, i. e., a point, where
the rate of slope changes, he holds his rod at the point and
the topographer takes the reading with the hand level.
From this reading the topographer subtracts the constant,
i. e., the height of his eye above the ground. The remain-
der is the difference between the elevation of the surface
where the topographer stands and the surface where the rod-
man stands. The tapemen having measured the distance
between the two points, the rate of slope is determined by
dividing the distance measured by the difference in eleva-
tion. This method of taking slopes or cross-sections is
illustrated in Fig. 296.

Let A be Station 156 of a preliminary survey. The topog-
rapher stands at A. The rodman goes to the point />',



30'




FIG. 296.



where the slope changes, holding his rod, which measures
16 feet in length, at that point. The topographer sights
with his hand level and reads 7.5 feet on the" rod. From this
reading he mentally subtracts 5.3 ft., the height of his eye



676 SURVEYING.

above the ground. The remainder, 2. 2 ft. , is the difference in
elevation between the points A and B. Meanwhile, the tape-
men find that the horizontal distance from A to B is 31 feet.
The rate of the slope A B is the horizontal distance between
the points^ and B, 31 ft., divided by 2.2, their difference in
elevation. The quotient is 14.1 and the slope is recorded

2 2

^-. The topographer then moves to the point />', and the
ol

rodman goes to C, which is so much lower than B that
with the rod held on the ground the line of sight will pass
over the top of the rod. Here the rodman gives a "long "
or " high " rod. Planting himself firmly at C, he raises the
rod until the line of sight, from the topographer's eye, cuts
the top of the rod, when the topographer calls " all right."
He then notes where the bottom of the rod comes, and
allows it to slide to the ground. Then adding to the length
of the rod 16 ft., the distance from the ground to the point
where the bottom of the rod came when the reading was
taken, he calls out their sum to the topographer. In this
example the rod is 16 feet and the addition 7 feet, making a
high rod of 23 feet, which is common enough. The hori-
zontal distance 33 feet, as measured by the tapeman, is also
called out. The topographer makes the subtraction 5.3
from 23.0, and the difference 17.7 is written as the numer-
ator of a fraction whose denominator is the horizontal dis-
tance 33. The slope being a descending one, the fraction

17 7

will be ~, a slope of 1 to 1.9. In Fig. 296, the slopes

oo

A B and B C are right slopes, i. e. , on the right side of
the line of survey.

In taking the left slopes, the rodman and topographer
change positions, the topographer going ahead and the rod-
man following. The topographer standing at D reads a rod
of 16 feet held at A. Subtracting the constant 5.3, the
remainder 10.7 is the difference between the elevations of A
and D and is an ascending slope. The horizontal distance

from A to D is 30 feet and the slope is recorded '-) ^-.

oO



SURVEYING.



677



1295. Slope Angles. Slopes are often measured
with an instrument called a clinometer, which measures
the angle which the line of slope makes with the horizontal,
and is shown in Fig. 297. Tables are compiled giving the




FIG. 297.

angle of slope and the horizontal distance for one foot of rise,
as follows:

1 is 57.3 feet horizontal per 1 foot rise.

2 is 28.6 feet horizontal per 1 foot rise.

3 is 19.1 feet horizontal per 1 foot rise, etc.

1 296. Platting Topography in the Field. While
some engineers favor the platting of contour maps in the
field, the majority do not. To plat the map in the field, the
topographer carries a case, the cover of which serves for a
drawing board. The line of survey is divided into sections
which are platted on different sheets, each sheet containing
some of the immediately preceding section, so that by over-
lapping and pinning them together, a complete map of the*
line is obtained. The topographer carries in his case the
sections covering his day's work, with the numbers and
elevations of each station marked on the map. He pins a
section to the cover of the case with thumb-tacks; his
assistants measure the angle of the slope with a clinometer,



SURVEYING.



together with the horizontal distance; and from the table
of slopes which he carries, the topographer determines the
location of the contours and sketches them on the map. A
better practice is to measure and record the slopes, keeping
as close to the transit party as possible, and provide an
extra man to work up the notes in the office under the
direction of the topographer.

1297. Eye Measurements. Though practice will
greatly aid the eye in estimating distances, yet it is not
to be relied upon when anything like exactness is required.
In taking slopes, the length of the last one only may be esti-
mated by the eye. More distant objects which lie without
the possible range of location may be sketched in with the
aid of the eye alone.

1298. Form of Topographer's Notes. A good
form for a topographer's notes is shown in the accompany-
ing diagram :



Station.


Lt.


Line.


Rt. Line.





8.4
"" ~45


10.0


11.4 8.8 ( ,


1


for 60'


1L5

40


11.0 7.0 ,


2


for 60'


10.3
40


11.5 6.8


100'


3


Same as 2 ^

G


Same as 2


4


for 50'


11.8
"40


10.5 7 ' 5 f or


100'


5


for 50'


12.0
"35


11.3 6.8..
'IT '40 for


100'


6


for 60'


104
40


10.5 7.5
50 43


100'



SURVEYING.



679



\




FIG. 298.



680 SURVEYING.

They are a record of the cross-sections or slopes of a pre-
liminary railroad survey, the line of which extends along
the side of a steep hill. The slopes are taken with a Locke
level and rod, giving the actual differences in elevation be-
tween the points of change of slope. The alignment of the
survey is shown in Fig. 298, and the contours are platted
from the foregoing notes. The contours are 5 feet apart,
i. e., the vertical rise between them is 5 feet.

The elevations of the stations the topographer has
obtained from the leveler. The stations are marked on
the plat, either by a dot, or, what is better, a dot enclosed
in a small circle. The number of the station is marked at
the right a little space ahead of the circle, the elevation on
the left of the line and opposite to the number of the station.
The cross-section lines are sometimes drawn on the map,
very fine and at right angles to the center line, but usually
the lines are omitted, the draftsman giving the true
direction with his offset scale when locating the contours.
In Fig. 298, the elevation of Station is 104.6 feet. To
reach the next contour above, viz., 105 ', a rise of .4 foot
must be made, and to reach the next lower contour a fall of
4.6 feet is necessary. From the notes, we find on the left
o'f the line a rise of 10 feet in a horizontal distance of 30 feet
or a rise of 1 foot in 3 feet, and for a rise of . 4 foot we must
go to the left of the line .4x3 1.2 feet to contour 105.
To reach contour 110, which is 5 feet higher, we must go
5x3 = 15 feet farther to the left. This distance added to
1.2, the distance to contour 105, gives 16.2 feet, the second
offset.^ We find by adding 10 feet (the rise in going 30 feet
to the left of the line) to 104. 6 feet, the elevation of Station
0, we have 114.6 feet, which is .the elevation of the end of
the first slope. An additional rise of .4 foot must be made
in order to reach contour 115. The second slope is a rise
of 8.4 feet in a distance of 45 feet, or a rate of 1 foot in
5.3 feet. Multiplying 5.b feet by .4, we have 2.1 feet, which
is to be added to 30 feet, to reach contour 115, and gives a
distance of 32.1 feet. Contour 120 will be 5.3 feet x 5 =
26. 5 feet beyond contour 115, or 58. 7 feet from the center line.



SURVEYING. 681

In the same way the contours to the right of the line are
located. Tenths of feet are dropped in the computed dis-
tances, as they are too small for platting, and the nearest
foot is taken.

Having located the contours by offsets for several con-
secutive stations,, points of equal elevation are joined free-
hand, forming the contour line, care being taken that lines
of different elevation are kept distinct from each other and
conforming to the curves and undulations of the original
surface.

1 299. Working Up Notes. A good rule is to work
up the notes for a considerable section before platting, thus
avoiding the delay from continual change of work. The
following form of working up notes is a good one, notes for
each station being separated from those for other stations
by a few strokes of a pencil. The example given is for
Sta. 0, in Fig. 298.

Sta. 0. Elev. 104.6.

Rt. 14 feet to contour 100. Lt. 1 foot to contour 105.

Rt. 29 feet to contour 95. Lt. 16 feet to contour 110.

Rt. 53 feet to contour 90. Lt. 32 feet to contour 115.

Rt. 81 feet to contour 85. Lt. 59 feet to contour 120.
Rt. 110 feet to contour 80.
Rt. 137 feet to contour 75.

Contour lines are usually drawn first with pencil and
afterwards inked in black. Short gaps are left in the lines
at suitable intervals, in which their elevations are written.
These should be of sufficient frequency to show at a glance
the elevation of any contour.

Situations are continually recurring where the side slopes
give but an inadequate idea of the topography. This is
particularly true when the line of survey follows a stream
with numerous tributaries and where highway crossings are
frequent. In such cases the topographer will supplement
the side slopes with free-hand sketches, which are invaluable
helps in making topographical maps.




682 SURVEYING.

INDIRECT LEVELING.

1300. Indirect leveling is the process of determining
elevations by either lines or angles or both. A common
example in indirect leveling is given in Fig. 299.

Let DB be a flag-staff whose height is required. Set up
a transit at A. Level carefully both the vernier plate and

the telescope. The
vertical arc will, if in
adjustment, read at
zero. Sight to C, the
point where the hori-

zontal line f sight
strikes the flag-staff.

4,2' ** Measure the distance

' FIG - 2 9 - AC= 180 feet, CD-

4.2 feet, and the diameter of the staff at C= 1.5 feet.

Measure the vertical angle C A B = 26 10'. From rule 5,

f f?

Art. 754, we have tan A = . r . ^. One-half

A C -f dia. staff

diameter staff at C= .75 foot. Substituting known values,

f* /?

we have tan 26 10' = , whence C B 180.75 X tan

lot). 4 5

26 10'= 180.75 X. 49134 =88. 809 feet; 88.809 + 4.2 = 93.009
feet = D B, the height of the flag-staff.

1301. Stadia Measurements. The theory of the
stadia is familiar to most engineers, yet comparatively few
of them make any practical application of it, even when it
would be greatly to their advantage.

In stadia work an ordinary leveling rod is generally used,
and answers every purpose. It should be made of hard
wood, such as mahogany, which is least affected by changes
of temperature, and should be from 10 to 12 feet long,
2 inches wide, and about \\ inches thick. It is divided into
feet, and each foot subdivided into tenths. The spaces
corresponding to these latter divisions are painted alter-
nately red and white, the number of tenths each space
represents being painted in prominent black figures on the



SURVEYING. 683

lines of division. The space directly below each footmark
should be inlaid with a mirror to reflect the light and enable
the surveyor to read the rod at long distances with greater
precision. The rod should also be provided with a sliding
target. The best instrument to employ in this class of
work is a transit reading to 30". Besides the horizontal and
vertical cross-wires which appear in the field of view of the
ordinary transit telescope, the stadia transit is provided
with two additional horizontal wires placed parallel with
the horizontal wire in the plain transit, and at
an equal distance above and below it, as shown

in Fig. 300. These two extra wires are so

placed that, if the stadia rod is held at a point
100 feet distant from the telescope, they will
enclose 1 foot of the length of the rod. For FlG - 30 -
example, if the lower wire coincides with the 4-ft. division,
and the upper wire with the 5-ft. division of the rod, the
distance from the center of the instrument to the rod will
be 100 ft. + the constant for the particular transit used.
The starting point for stadia measurements is often indis-
criminately assumed to be either the center of the instru-
ment, the center of the cross-wires, or from a plumb line
dropped from the object glass; but, owing to the deflection
of the sight due to the action of the lenses, the precise
starting point for stadia measurements is a point as far in
front of the object glass as its focal length; for example, if
the focal length of the object glass is 6 inches, the starting
point is 6 inches in advance of a plumb line dropped from
the object glass. The distance from this point to the centei
of the instrument is "constant" for the same instrument,
and must be added to the recorded stadia distance at every
sight. In making a stadia survey, the transit should first
be tested. Having found as level a plane as possible, test
and adjust the level so that the vertical arc will read zero
when the telescope is in a perfectly horizontal position;
measure off very carefully from the center of the instru-
ment, the short distance equal to the constant of the instru-
ment, say 1.25 feet; from this point accurately measure a



684 SURVEYING.

distance of 400 feet, driving a stake at each 100 feet. It is
advisable to measure this test line with two or more steel
tapes, and then take the average. As it will be necessary
to test the cross-wires every few days, it is important that
the test line should be conveniently located and very accu-
rately measured. The line now measures 401. 25 feet, as
follows: First section, measuring from the center of the
instrument, 101.25 feet, then three sections of 100 feet each,
as shown in Fig. 301.




400'

FIG. 301.

Direct the rodman to hold the rod on the point 201.25 feet
from the instrument, and adjust the stadia wires so that
they will include 2 feet on the rod. First adjust the upper
to the center wire so as to include 1 foot, then adjust the
lower to the center to include one foot. When this has
been done, let the rod be held at the point 301.25 feet distant.
The wires should now inclose 3 feet, 1.5 feet being included
between the upper and center wires and 1.5 feet between
the center and lower wires. Now test the point at the ex-
tremity of the line; the wires should at this distance include
4 feet. Instruct the rodman to hold the rod on the first
point, 101.25 feet from the instrument, and if the stadia
wires now include one foot, the instrument is in adjust-
ment; if not, the operations must be repeated until the
instrument reads correctly at every point. The ratio of the
constant does not increase with the distance, but remains
the same whether the distance of the sight be 50 or 2,500
feet.

At the beginning of a survey, the target on the rod is set
at a height equal to that of the instrument, i. e., the dis-
tance from the ground-line to the axis of the telescope.
This is done with the view of having the line of sight par-
allel with an imaginary line between the foot of the instru-



SURVEYING. 685

ment and the foot of the rod, which gives the exact vertical
angle or degree of slope between the instrument and rod
and a perfectly level plane. The rod is now held on a point
where a sight is desired, and the transitman turns the tele-
scope until the center wire and the center line of the target
coincide; see Fig. 302. He then clamps the telescope, and
reads the angle of elevation or depression, as the case may
be, on the vertical arc, which is say 10 26' ; and, if the rod
is held on a point at a greater elevation than that of the
telescope, this angle will be one of elevation, and he will
record it thus, + 10 26'; but if the rod is held on a point
lower than the instrument, the telescope will be correspond-
ingly depressed, and the angle is recorded thus, 10 26'.
The distance on the rod intercepted by the stadia wires is




read and recorded. Assuming that the lower wire coincides
with the 3.5 ft. division line, and the upper one cuts the rod
at 7.46 feet, the intercepted distance is 7.46 3.5 3.96
feet, and is thus recorded. The needle is next read, or, if it
be an angular survey, the direction is platted and recorded.
Having thus obtained the vertical angle, intercepted dis-
tance, and bearing, this sight is finished and the surveyor is
ready to move to the next station.

Before any platting can be done, the distances must be
calculated and reduced to the horizontal. This may be ac-
complished by means of the table of Horizontal Distances
and Differences of Elevation for Stadia Measurements. In
using the tables, proceed as follows: Look .for the vertical
angle, in this instance 10 26', and under the head Hor. Dist.
find the number 96.72. Then, this number multiplied by



686 SURVEYING.

the distance intercepted by the stadia wires, viz., 3.96,
equals 96.72 X 3.96 = 383.01; now, at the foot of the page,
under 10 and opposite c 1.25 (the constant of the instru-
ment), find the corrected distance 1.23, which, added to
383.01, gives 384.24 feet, the corrected horizontal distance,
which is recorded in the column provided for that purpose
in the note book.

The difference of level is found thus : Under the head
Diff. Elev., find 17.81, the number corresponding to the
vertical angle 10 26'. This number multiplied by the in-
tercepted distance equals 17.81 X 3.96 = 70.53; at the foot
of the column find .23, which, added to 70.53, gives 70.76
feet as the difference of elevation, and is recorded as such
in its proper place. Proceed in the same manner to find
the horizontal distances and differences of level of all the
other points observed. The relative elevations of the vari-
ous points observed, above or below any adopted datum line
or plane of reference, can be readily determined by means
of the signs -f- and prefixed to each vertical angle recorded.
Thus, assuming the survey to start from a B. M. 497.32 feet
above the adopted plane of reference, and the first angle re-
corded to be, as before stated, -j- 10 26', corresponding to a
difference of level of -|- 70.76 feet, the point observed will be
497. 32 + 70. 76 = 568. 08 feet above the datum plane. Where,
however, boundary lines only are being run, it is unneces-
sary to compute the levels, but the vertical angles must be
recorded in all cases, in order to correct the distances.

The calculations may be made, without the use of tables,
in the following manner:

To obtain the horizontal distance, the following formula
is employed :

D = c cos n + a k cos 3 , (94.)

in which D = the corrected distance ; c = the constant ; a k =
the stadia distance, and n = the vertical angle.

Assume, as before, a vertical angle of -(- 10 26' and air
intercepted distance of 3.96 feet. As each foot of the rod
intercepted by the stadia wires corresponds to a distance of



SURVEYING.



687



100 feet, an interception of 3.96 feet corresponds to a dis-
tance of 396 feet, called herein the stadia distance, i. e., the
distance from the rod to the point outside the telescope
where the stadia measurement begins.
Applying the formula, we have,

D - 1.25 cos 10 26' + 396 cos' 10 26' =
125 X .98347 + 396 X .98347' = 384.24 ft.

To obtain the difference of level E, apply the following
formula:

, sin 2 n

E = cs\nn + ak - . (95.)

Applying this formula to the preceding example, we have
E = 1.25 X .18109 + 396 X .17810 = 70.75, since 2 n =



10 26' X 2 = 20 52' and



sin 20 52' .35619



= - -=.17810.



SURVEY OF BEAVER CREEK.

































5 "^


1

2


tation


5


5


Bearing.


Vert.
Angle.


<ti <y

5 ^


11


co


cO




u








J





1


396


384


N 1 15 W


+ 10 26'


+ 70.71


1142.21


1


^


201




Due E


+ 20 11'






1


/'


404




S 80 10 W


- 11 14'






1


C


187




S 76 20 W


- 14 22'






1


D


563




S 68 32 W


+ 3 12'






1


2


384




N 20 15 W


- 16'







The tables of Horizontal Distances and Differences of
Elevation for Stadia Measurements are computed for
observations taken on a vertical rod held perfectly plumb.

Fig. 303 shows the method of keeping sketch and notes in
topographical work.



688



SURVEYING.



13O2. An efficient topographical survey is one

which fully serves every purpose for which it is made. Its
value depends more upon the accuracy of that which is
represented rather than the minuteness or quantity of
detail. The topographer should be able to readily and in-
telligently decide between what is important and what is
not important, and invest his time and labor accord-




FlG. 303.

ingly, taking nothing for granted and never indulging in
guesswork.

13O3. The Aneroid Barometer. Fig. 304 shows
an aneroid barometer, a substitute for the mercurial barom-
eter, which latter is not readily portable. It consists of a
box of thin corrugated copper, exhausted of air. An in-
crease in the weight of the atmosphere compresses the box,
and a reduction in weight admits of the box being expanded
by a spring inside. This spring is connected, by a system of
levers, with a dial which indicates the pressure of the
atmosphere. The face is graduated to correspond with the
heights of the mercurial barometer. A thermometer is also



SURVEYING.



689



attached to the face and shows the temperature when the
readings are taken.




FIG. 304.

13O4. How to Determine Difference in Eleva-
tions With the Aneroid Barometer. The formula
given is that used by the Engineer Corps of the United
States Army. The aneroid barometers used are adjusted
to agree with the mercurial barometer at a temperature of
32 Fahrenheit at the sea level in latitude 45. Observa-



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