Course material

1. Surveying and levelling in agricultural land area calculation and leveling
the field
agriculture exercise and need an explanation and answer to help me learn.
Requirements:
Surveying
What is Surveying?
Surveying is defines as the art of determining the relative positions of various points above,
on or below the surface of the earth by means of direct or indirect measurements and finally
representing them on a sheet of paper known as plan or map.
Leveling
Leveling is the art of determining the relative vertical distance of different points on the
surface of earth. Hence, in leveling, the measurements are taken only in the vertical plane.
Objectives of survey
The data obtained by surveying are used to prepare the plan and map showing the ground
features.
When the area surveyed is small and the scale to which its result plotted is large, then it is
known as plan.
When the area surveyed is large and the scale to which its result plotted is small, then it is
known as map.
To analyse and to calculate the field parameters for setting out operation of actual
engineering works.
Setting out any engineering works like buildings, roads, railway tracks, bridge and dams
involve in surveying.
Types of Surveying [Classification]:
Primary Classification or Primary Division :
Plane surveying and
Geodetic surveying
Plane Surveying :
The shape of the earth is spherical. Thus the surface is obviously curved. But in plane
surveying the curvature of earth is not taken into account. This is because plane surveying
is carried out over a small area, so the surface of the earth is considered as a plane. The
degree of accuracy required in this type of surveying is completely low. Plane surveying is

2. done on an area of less than 250 km2.
Geodetic surveying :
In geodetic surveying the curvature of the earth is taken into consideration. It is extended
over a large area greater than 250 km2. The line joining any two points considered as a
curved line. Very refined methods and instruments are used in this type of surveying. in this
method very high precision or accuracy is required.
Difference between Plane and Geodetic Surveying
Secondary classification:
Survey can be classified on different bases.
1. Based on instrument:
Chain Survey
Compass survey
Plane Table survey
Theodolite survey
Tacheometric Survey
Photographic survey
2. Based on methods:
Triangulation Survey
Traverse Survey
3. Based on Objects:
Geological survey
Mine survey
Archeological Survey
Military survey
4. Based on nature of field
A. Land Survey
B. Marine survey
C. Astronomical survey
Again Land Survey is classified into following Classes:
1. Topographical Survey
To determine natural features of a country such as valleys, rivers and artificial features such
as road, railways, etc.
2. Cadastral Survey:
To determine boundaries of field, estate
3. City survey:
To locate premises, streets, water supply and drainage systems
4. Engineering survey:
To collect detailed data for the design for of projects involving roads, railways, etc
Engineering surveys are sub divided into:
1. Reconnaissance Survey
2. Preliminary Survey
3. Location Survey
Uses of Surveying:

3. To prepare a topographical map this shows the hills, valley, rivers, villages, town, etc, of a
country.
To prepare a cadastral map showing the boundaries of fields houses, and other properties.
To prepare an engineering map to show details like roads, railways, canals, etc.
To prepare military map showing roads and railways, communication with different parts
of country.
To prepare contour map and to determine capacity of a reservoirs and to find the best
possible route for roads, railways etc.
To prepare a geological map showing areas including underground resources.
What is Chain surveying?
Chain surveying is the type of surveying in which only linear measurements are made in
the field. In this the area is divided into network of triangles since the triangle is the only
figure which can be plotted without any angular measurements.
Chain surveying is adopted in the following situations
When the ground is flat and with simple details.
When the area to be surveyed is small.
When large scale mapping is desired.
2.1 Purpose and Principle of Chain Survey
Chain surveying has the following purposes.
1) To collect necessary data for exact description of the land.
2) To calculate the area of the plot
3) To prepare the plan of the site
4) To demarcate the boundaries of the land
5) For division of land into smaller units.
Principle of chain surveying:
The triangle is the simplest figure that can be plotted from the lengths of its sides. Based on
this, the principle of the chain surveying is to divide the area into a network of well
conditioned triangles. The error will be least in plotting a triangle is when no angle of the
triangle is less than 300 and more than 120o. Such triangles are called well conditioned
triangles. Chain surveying is also called as chain triangulation.
Equipments Used in Chain Surveying and their Functions
The following equipments are used in chain surveying
1) Chain
2) Tape
3) Ranging rod
4) Cross staff
5) Arrows
6) Pegs
7) Plumb bob etc.
1. Chain: This is an instrument used for measuring distance. There are four types of chains.
a) Metric chain: In metric system the chains of 20m and 30m are commonly used. The chain
is made with galvanized steel wire of 4mm diameter. Each meter is divided into 5 links of
20mm length. It is provided with brass handles on either ends. The tallies are fixed at every

4. 5m length and small brass rings are provided at every meter length. The chain is shown in
the fig.
b. Günter’s Chain:
It is 66 fit long and is divided into 100 links. Each link is 0.66 ft long. It is very convenient for
measuring distance in miles and furlongs. Also for measuring area and when the units of
area is an acre
10 square Gunter’s chains = 1 Acre
10 Gunter chains = 1 Furlong
80 Gunter chains = 1 mile
c. Revenue Chain:
It is commonly used for measuring fields in cadastral survey. It is 33 ft long and divided into
16 links. Each link is 2.0625 ft long.
d. Engineer’s chain:
It is 100 ft long and it is divided into 100 links. Each link is 1 ft in a length. Used in all
Engineering surveys.
2) Tape: The tapes are divided according to the materials used as following
(i)) Metallic tapes (ii) Steel tapes (iii) Invar tapes
(i) Metallic tapes: This tape is made with water proof linen with brass, copper wires to
avoid stretching. The tapes available in lengths 2, 5, 10, 20 and 30 m.
Steel Tape Invar Tape
(ii) Steel tapes: This is most accurate tape for taking measurements. If carelessly handled it
gets broken
(iii) Invar tapes: If the measurements are to be made with highest precision this tape is
used. These are 6mm wide and available in lengths of 30, 50 and 100 m.
3. Ranging rods: The ranging rods are used for ranging lines and to mark stations which are
at greater distance. They are made of well seasoned straight grained timber of teak, blue
pine, sisso or deodar. They are circular or octagonal in cross section of 3 cm nominal
diameter and pointed metal shoe of 15 cm long is provided at the lower end to facilitate
fixing in the ground. They are made of two sizes namely one of 2 m and the other of 3 m and
are divided into equal parts each 0.2 m long. In order to make them visible at a distance,
they are painted alternately black and white, or red and white or red, white, and black
successively. When they are at a considerable distance, red and white and yellow flags
about 25 cm square be fastened at the top to improve the visibility.
4. Arrows: Accompanying each chain are 10 arrows. They are also called marking or
chaining pins, and are used to mark the end of each chain during the process of chaining.
They are made of good quality metallic wires of 4 mm in diameter and of a minimum tensile
strength of 700N/ mm2. The wire is black enameled. The arrows are made 400 mm in
length, are pointed at one end for inserting into the ground and bent into a ring at the other
end for facility of carrying. They should have a piece of white or red tape tied to the ring so
that they can be made easily visible at a distance. To mark the end of each chain length, the
arrow is inserted in the ground, but when the ground is hard, a scratch may be made with
the pointed end (Fig.4).

5. 5. Pegs: Wooden pegs are used to mark the positions of stations. They are made of hard
timber and are tapered at one end (Fig.6). They are usually, 2.5 cm square and 15 cm long,
but in soft ground, pegs 40 to 60 cm long and 4 to 5 cm square suitable.
7. Cross staff: Cross-staff is used for (i) finding the foot of the perpendicular from a given
point to a line, and (ii) setting out a right angle at a given point on a line. There are two
types of cross-staff, namely, (1) the open and (2) the French, the first one being in common
use.
(i) Open cross staff: The simplest form of cross staff is the open cross staff. It consists of
two parts (1) the head and (2) the leg. The head consists of four metal arms with vertical
slits. The arms are rigidly fixed in such a manner so that the center of one pair of arms
forming a straight line makes right angle with the other pair of arms. In one line, one of the
slits is narrower than the other. One horse hair is fixed at the center of the wider slit. The
object is sighted from the narrow slit in line with the hair. The cross staff is mounted on 25
mm diameter, about 1.5 metre long pole for fixing on the ground.
For laying out a right angle at a point on the chain line, the cross staff is held vertically on
the supporting pole at the given point. Ranging rod is fixed on the chain line on either side
of the cross staff and sighted through the slit and horse hair. The cross staff is turned till the
ranging rod is visible. At this time, one sight through the other pair of slits and another
person fixes a ranging rod in this line of sight. Foot of the cross staff joined with the ranging
rod gives perpendicular line with the chain line.
(ii) French cross staff: This cross staff is an octagonal brass tube with slits on its eight faces.
With this cross staff we can set the object at an angle of 450 also.
Fig: Cross staff
Fig: Ranging rod Fig: Arrows Fig: Pegs
8. Plumb bob: A plumb bob consists of a metal weight made of brass with a pointed end
(Fig.5). It is suspended by a string and is used to locate points directly below or above
another point. It is also used for accurately centering of compass or level or theodolite over
a station mark, and for testing the verticality of ranging poles.
9. Optical Square: This is an instrument used for setting out right angles to the chain lines
and to find out the foot of the perpendicular on the chain line from an object. It works on the
principle of reflection.
Errors in Chaining
Errors will be introduced in chaining due to the following reasons.
a). Instrumental errors: these are due to defective conditions of instrument.
E.g. a chain may be either too long or too short.
b). Natural errors: These are due to variations in the natural phenomena
E.g. changes in length due to temperature.
Fig: Plamb bob Fig: Optical Square
Correction Due to Incorrect Length of the Chain or Tape
If a chain has been damaged and it may be too short or too long of the true length of the
chian, and all the measurements taken will be too long or too short, conversely a contracted

6. or stretched chain will give incorrect measurements of the true lengths.
The correct lengths of a measured distance is found from
Correct Length = Measured Length x
Or Correct Length = Measured Length x L’/L
where
L’ = Incorrect length of chain or tape
L = Correct length of chain or tape
If an area has been calculated then,
Correct area = Calculated area x
If an volume has been calculated then,
Correct volume = Calculated volume x
Ranging: During measurement of the length of a line, it is necessary that the chain should
be laid out on the ground in a straight line between the end stations. If the chain is long or
end station is not clearly visible, it is necessary to place intermediate ranging rods to
maintain the direction. The operation of establishing intermediate points on a straight line
between the terminal points is known as ranging. Ranging should be done prior to chaining.
Ranging is usually done by eye or by using instruments like line ranger and theodolite.
Ranging is of two kinds, namely, direct and indirect ranging.
i) Direct ranging: When the end points are visible from one another, intermediate ranging
rods are placed in line by direct observation, the process is known as direct ranging.
Procedure: Let us assume that, “a” and “d” are end points of a survey line visible from one
another (Fig). We have to locate a points “b” and “c” so that both those points lie in the
straight line joining “ad”. Ranging rods are fixed vertically both at “a” and “d”. Now one
person stands near point “b” with a ranging rod and another person stands behind the
ranging rod at “a” and looks towards “d”. Then the person standing at starting point will
direct the person holding rod at “b” point to fix a rod in such a position that all the three
points namely, “a”, “b” and “d” lie in a straight line. Similar way, he directs to fix rod at “c”
also. Likewise, the process of fixing rods at intermediate points is continued. After fixing all
intermediate rods, all the rods should be in a straight line joining “ad.
Fig Direct ranging
3.6.2 Indirect ranging: When the end stations of a line are not intervisible due to high
ground or intervening hill and also when the ends of a line are not distinctly visible from
one another due to distance being too great, then indirect ranging can be adopted. Various
obstructions, such as ponds, hills, buildings, rivers are continuously come across in chaining
process. It is however essential that chaining should be continued in a straight line, special
methods are therefore employed in measuring distances across the obstructions. The
various cases may be classified as:
i) Chaining is free, vision is obstructed, eg. raising ground (or) a hill intervening.
ii) Chaining obstructed but vision free, eg. pond, river, plantations, and tank.
iii) Both chain and vision are obstructed, eg. buildings
i) Chaining is free vision is obstructed: In this case, the ends of a line are not inter visible.
There are two cases to be considered.
Case-1: Both ends may be visible from intermediate points on the line.

7. Case-2: Both ends may not be visible from any intermediate point.
Procedure for case-1: Let A and B are the two stations across a hill. Ranging rods are placed
at one of them is not visible from other. The following may be followed for ranging.
1) As shown in Fig, select two intermediate points C and D such that ranging rods at B and D
are visible from C and ranging rods at A and C are visible from D. Also A, C, D, B should be
nearly as possible in a straight line.
2) The person at C looks towards B and directs the man at D to fix his ranging rod in a
manner such that C, D, B are in one straight line.
3) Now the person at D looks towards the ranging rod at A and directs the man at C to fix his
ranging rod at a place such that A, C and D are in one straight line.
4) Steps 2 and 3 above are repeated till the person at C finds C, D,. B to form a straight line
and simultaneously, the person at D finds A, C, D also to form a straight line, then all the four
points A, C, D, and B are lie in straight line.
Fig: Indirect method of ranging
Procedure for case 2: This case occurs, when it desired to run a line across a wooded field,
the trees and under-bush preventing the fixing of intermediate stations. In such a case, the
method of random line is the most suitable.
As shown in Fig. , let AB be the line whose length is required. From A, run a line (AB1),
called a random line in any convenient direction, but as nearly towards B as can be judged
and continue until the point B is visible from B1. Chain the line to B1, where BB1 is
perpendicular to AB1 and measure BB1, then AB = .
Fig Random method of ranging
Chaining obstructed, but vision free: This problem is to find out the distance between two
convenient points on the chain line on either side of the obstruction.
There are two cases
Case-1: In which, it is possible to chain round the obstruction.
Ex: A thorny hedge, a pond, a bend in the river.
Case-2: In which, it is not possible to chain round the obstruction.
Ex: River
Procedure for Case-1: Let us consider that the chain line AB is obstructed by a pond (Fig.)
then, the following procedure can be adopted to chain across pond.
Fig. : Chaining across pond
1. Select two convenient points A and B on the chain line on either side of the pond.
2. Erect perpendicular AC at A on AB.
3. Erect perpendicular BD at B on AB, such that BD = AC.
4. Join C and D. Measure CD. Obviously, AB = CD.
5. Knowing the chainage upto A, the chainage upto B can be determined.
Chainage upto B = Chainage upto A + length CD
Procedure for Case-2 Let us consider that the chain line AB is obstructed by a river (Fig.)
then, the following procedure can be adopted to chain across river.
Fig. : Chaining across river

8. 1. Select two points A and B on the chain line on either side of the obstacle.
2. Erect a perpendicular AD on AB at A.
3. Bisect AD at C.
4. Erect a perpendicular DE at D on AD such that point E is in line with C and B.
5. Measure DE
6. Obviously, DE = AB
iii) Both chaining and vision both obstructed: In this case the problem consists in
prolonging the line beyond the obstruction and determining the distance across it. A
building is a typical example of this class of obstruction.
Procedure: Choose two points A and B on the chain line PR (Fig.). At A and B, erect
perpendiculars AE and BF of equal lengths. Check the diagonals BE and AF, which should be
equal and also EF, should be equal to AB. Prolong the line EF past the obstruction and select
two points G and H on it. At G and H, set out perpendiculars GC and HD are equal in length to
AE. The points C and D are obviously on the chain line PR and BC=FG. Great care must be
taken in setting out perpendiculars and to see that their lengths are exactly equal.
Fig: Both chaining and vision are obstructed
Chain triangulation and Cross-staff survey
4.1 Measurement of areas One of the main purpose of surveying is to measure the area of an
agricultural farm, area of plots to be used for construction purposes, command area of tube
wells, canals etc. Two general methods for measuring areas are: i) Triangulation, and ii)
Traversing. In traversing, the length of connected lines as well as their directions are
measured by chain and compass respectively.
4.1.1 Triangulation survey Triangulation is the basis of trigonometrical or geometric
surveys. As such triangulation refers to a system of surveying in which one line is measured
with a chain and all the three angles are measured correctly by compass or theodolite. In
case, only the sides of the triangles are directly measured in the field and no angular
measurement is taken, it is called triangulation (or) chain surveying. The whole area is
suitably divided into number of triangles and computes the area of individual triangles and
added to get total area. In dividing the total area into triangles, care should be taken to see
that the triangles are almost equilateral as far as possible to minimum the errors. Although,
the chain triangulation is very simple, but it is suitable only for small plane areas without
much obstruction.
Survey stations A survey station is a point of reference at the beginning and end of a chain
line. Stations are of two types, they are:
i) Main stations
ii) Subsidiary on tie stations.
Main stations are the ends of the lines which connect the boundaries of the survey, and the
lines joining the main stations are called the main survey or chain lines.
Subsidiary or tie stations are the points selected on main survey lines to run auxiliary lines
to locate the interior details such as fences, hedges, buildings etc. when they are distant
from the main lines. The symbol “O” is used to denote stations. Capital and small letters are
used to represent main and tie stations respectively.
Fig: Base, check and tie lines in triangulation survey

9. Base Line: The longest chain line in chain surveying is called the base line. This is the most
important line and the whole framework of triangles is based on this line and therefore, the
baseline should be very accurately measured (Fig.13). It should be passing through the
centre of the area.
Subsidiary or tie lines: When numbers of features are to be located and they are far away
from the main chain lines, then subsidiary or tie lines are used to locate such details. In
fig.13., tie line FG is used to locate number of features. Tie line is obtained by joining two
fixed points on the main survey line. Tie lines can also be used as check lines to check the
accuracy of measurements and plotting.
Check lines: Check lines are also called as proof lines. The mistakes of the measurement and
plotting can be easily checked with the help of check lines. The check line is a line joining
the apex of a triangle to some fixed points on the opposite side, a line joining some fixed
points on any two sides of a triangle. Every triangle should be provided with a check line.
Plotting procedure of chain survey After the survey is completed, the recorded information
is taken to the office and they are plotted on a drawing sheet using a suitable scale.
While plotting a chain survey, the following steps are to be followed:
(i) Depending upon the area covered in the survey and its importance, a suitable scale is
chosen. Boundary lines are drawn leaving a suitable margin all around.
(ii) The base line which is the mainline in the survey should be suitably located in the map
to accommodate the whole plotting easily in the drawing sheet. The base line should be
most accurately plotted.
(iii) The intermediate stations are marked on the base line and the frame work of triangles
is completed.
(iv) Chainage lengths are measured along the chain lines for various offsets and points are
marked. From these points perpendiculars of suitable lengths are drawn to locate the
offsets.
(v) The accuracy of plotted frame work may be checked by means of check and tie lines.
(vi) The field book should be kept side by side in the same direction as the survey
proceeded in the field parallel to the chain line to be plotted.
(vii) For drawing different objects, conventional symbols should be used.
(viii) The title of the survey, name of the surveyor, date etc., should be written at the right
hand bottom corner. The scale is drawn below the map.
CALCULATION OF FIELD AREAS
Importance: The calculation of areas of the tracts of the land is required for documents. The
areas of the fields are also required for planning and management. For instance, the
catchment area of a river is required for the design of bridges, dams, reservoirs, etc. The
areas of roads are required for their cost estimates. The areas are also required for the
computation of earthwork.
Field area calculations
Case 1: Regular shaped fields
Case 2: irregular shaped fields
Case 1: Regular shaped fields - The regular shaped lands can be easily computed by the
formulae. Some of the regular shaped fields are square, rectangle, triangle (including right

10. angle triangle and other shaped triangles), circle, trapezoids etc,.
Case 2: Irregular shaped fields
When the land shape is irregular, the area is divided into right –angled triangles and
trapeziums with the help of cross staff (fig.: Cross staff Survey – Mainly cross staff is used to
set offsets for the corner points of the irregular field in order to calculate the area of the
field which will be a resultant of all the triangles and trapeziums areas). The bases and
perpendicular lines are measured in this method (Cross staff survey). The chain and the
cross staff are the principal instruments used in the work. Two chains are usually provided,
one for measuring distances along the chain line and other for measuring the offsets. The
cross staff is used to set out the perpendicular directions for offsets. In this method of
survey, the base line runs through the centre and extends the whole length of the area
under survey so that offsets to the boundaries on either side of it are fairly equal. The
offsets are taken as they occur in the order of their chainages.
Note: The steps involved in cross staff survey are similar to the chain survey. But, when the
survey refers to be a cross staff survey, it is usually done for calculating the area of the
irregular shaped field.
To check the accuracy, the lengths of the boundary lines may also be measured. After the
field work is over, the survey is plotted to a suitable scale. The area of the field is the sum of
the areas of the right-angled triangles and trapeziums comprising the field.
Q.4: The sheet from the field book of cross staff surveyed area is presented below. The
readings refer to lengths in metres. Find the area of the field.
Solution: With the above readings, the cross staff surveyed area can be represented as
below:
Now, the whole area comprises of four triangles (serial nos. 1,3,4 and 7) and three
trapeziums (2,5 and 6.)
Now, the formulae of right angle triangles and trapeziums can be applied to find the total
area of the field.
Area of right angle triangle = A = 0.5 (Base x Height)
Area of trapezium = A =
Fig: The cross staff surveyed area
1. Area of triangle AbB = 0.5(39) x 54 = 1053 m2
2. Area of trapezium BbdC = 0.5 (39+50) x 36 = 1602 m2
3. Area of triangle CdD = 0.5(50) x 30 = 750 m2
4. Area of triangle DeE = 0.5(27) x 8 = 108 m2
5. Area of trapezium EecF = 0.5 (27+60) x 42 = 1827 m2
6. Area of trapezium FcaG = 0.5 (60+35) x 30 = 1425 m2
7. Area of triangle AaG = 0.5(35) x 40 = 700 m2
Therefore, total area = Sum of the areas of the above triangles and trapeziums = 7465 m2.
(Ans).
Levelling may be defined as an art of determining the relative heights or elevations of points
or an object on the surface of the earth.

11. Definitions of some important terms
1. M.S.L – Mean Sea Level : The water level in a sea representing a level surface if it is not
affected by tides.
2. Datum surface: It is level surface which is taken as a reference surface for the
determination of elevations of various points.
The most commonly used datum is the mean sea level (M.S.L.) and in India,
originally the datum adopted was the mean sea level at Karachi. At present, the mean sea
level at Madras (Chennai) is used.
3. Bench Mark: A bench mark is a fixed point of reference of known or assumed elevation
with respect to which other elevations are calculated.
There are four kinds of Bench marks
G.T.S (Great Trigonometrical Survey) bench mark
Permanent bench mark
Arbitrary bench mark
Temporary bench mark
a. G.T.S bench mark: These bench marks are established with very high precision at
intervals all over the country by Survey of India department.
b. Permanent bench mark: These are the fixed points of reference established between the
GTS bench marks by Government agencies such as PWD, railway, irrigation etc.
c. Arbitrary bench mark: These are the reference points whose elevations are arbitrarily
assumed. They are used in small levelling operations.
d. Temporary bench mark: These are the reference points established at the end of day‟s
work or when there is a break in the work. The work, when resumed, is continued with
reference to these bench marks.
4. Elevation: It is the vertical distance of the point above or below the datum surface.
5. Reduced Level (R.L.): The reduced level of a point is its height (elevation) relative to the
datum.
6. Line of collimation: It is the line joining the intersection of cross hairs to the optical centre
of the object glass and its continuation. It is the line of sight through the levelling
instrument.
7. Back Sight (B.S.) / Plus (+) Sight: It is the first reading taken after the level is set up. It is
taken on a bench mark or a change point. Staff reading taken on a point of known elevation.
8. Fore Sight (F.S.) / Minus (-) Sight: It is the last staff reading taken denoting the shifting of
the level or closing the work of taking levels.
9. Intermediate Sight (I.S.): All sights (staff readings) taken between the back sight and the
fore sight are known as intermediate sights.
10. Change Point (C.P.) / Turning Point (T.P.): It is the point on which reading is taken just
before and after shifting the instrument.
11. Station: A station is a point whose elevation is to be determined. Thus station is a point
where the levelling staff is held and not the point where the level is set up.
12. Height of Instrument (H.I.): It is the reduced level of the line of sight when the levelling
instrument is correctly leveled.
Determination of reduced level: Whenever any leveling is to be carried out, the first reading

12. is taken on a point of known elevation. This is called back sight (B.S.) reading. Before
shifting the instrument one reading is taken on a firm object whose elevation is to be
determined. This is known as fore sight (F.S.) reading. Between the B.S and F.S numbers of
readings known as intermediate sights (I.S) are taken. All these readings are required to be
tabulated and converted to reduced levels (R.L) for practical use. There are two systems of
working out the reduced levels of points from the staff readings in the field: (i) the
collimation or the height of instrument (H.I.) and (2) the rise and fall system.
The collimation system: At first, the R.L. of the plane of collimation i.e., height of instrument
(H.I) is calculated for every setting of the instrument and then R.L. of different stations re
calculated with reference to the height of the instrument. In the first setting, the H.I. is
calculated by adding the B.S. reading with the R.L. of the bench mark. By subtracting all the
readings of all the intermediate sights and that of the first change point from the H.I. , then
their reduced levels are calculated. The new H.I is calculated by adding the B.S. reading with
the R.L. of the first change point. The process is repeated till the entire area is covered.
Arithmetical check: The difference between the sum of back sights and the sum of fore
sights should be equal to the difference of first and last R.L.
Rise and fall system: The level readings taken on different stations are compared with the
readings taken from the intermediate proceeding stations. The difference in the readings
indicates rise or fall depending upon whether the staff reading is smaller or greater than
that of the preceding reading. The rise is added and fall is subtracted from the R.L. of a
station to obtain the R.L. of the next station.
Arithmetical check: The difference between the sum of back sights and the sum of fore
sights is equal to the difference between the sum of the rise and fall and should be equal to
the difference of first and last R.L.
If the R.L. of A is known, the R.L. of B may be found by the following relation:
R.L of B = R.L. of A + -
The R.L‟s of the intermediate points may be found by the following relation:
R.L. of a point = R.L of B.M + -
The difference of level between A and B is equal to the algebraic sum of these differences or
equals the difference between the sum of back sights and the sum of the foresights (. - ). If
the difference is positive, it indicates that the point B is higher than the point A, while if the
negative, the point B is lower than the point A.
Height of Instrument Method
The arithmetic calculations made in the computations of the height of instrument (H.I.) and
the reduced levels (R.L.) can be checked by applying the following simple arithmetic check.
∑ B.S. - ∑ F.S. = Last R.L. – First R.L.
In above table
2.730 – 4.395 = 98.335 – 100.000
Or 1.665 = 1.665 (Proved).
Rise and fall method
The R.L. of the various stations are computed by adding the rise to the R.L. of the preceding
station or by subtracting the fall from the R.L. of the preceding station.
The computations are checked by applying the following arithmetic check.

13. ∑ B.S. - ∑ F.S. = ∑ Rise - ∑ Fall = Last R.L. – First R.L.
In the above table,
2.730 – 4.395 = 0.0 – 1.665 = 96.1 – 100.0
Or 1.665 = 1.665 = 1.665 (Proved).
Q.1: The following are the readings recorded from dumpy level continuously at an interval
of every 20 metres from one station to another station. The first reading is recorded at first
station (A) and last reading is recorded at last station (Z) respectively.
4.200, 4.000, 3.700, 3.500, 3.600, 3.300, 3.100, 3.200 and 3.000 metres.
The instrument has been shifted after 4th and 7th readings.
Find out the slope of the line ‘AZ”.
Solution: Considering above given data and accounting shifting of dumpy level, the readings
can be tabulated as follows:
Height of Instrument Method
The computations are checked by applying the following arithmetic check.
∑ B.S. - ∑ F.S. = ∑ Rise - ∑ Fall = Last R.L. – First R.L.
In the above table,
11.000 – 9.600 = = 100.000 – 101.400
1.4 = 1.4 (Proved).
Now, Slope of AZ = (h/L)*100 = (1.4 / 120)*100 = 1.167% (Ans.)
Contouring: A contour or contour line is defined as a line of intersection of level surface
with the surface of the ground. Thus, every point on a contour line has the same elevation.
Therefore, contour line may also be defined as a line joining the points of equal elevation.
The shore line of a reservoir with still water represents a contour line of fixed reduced level.
As the water level changes, the new shore line represents another contour of a different R.L.
The contour lines of an area are presented in a map known as a contour map or topographic
map. In addition to contour lines, a topographic map includes the features like streams,
rivers, reservoirs, valleys, hills, bridges, culverts, roads, fences etc.
Contour interval: The constant vertical distance between two consecutive contour lines is
called the contour interval. The contour interval is kept constant; otherwise the map will be
misleading. The horizontal distance between any two consecutive contour lines is known as
the “horizontal equivalent/ interval”. The horizontal equivalent, for a given contour interval
depends on the nature of the ground. The contour interval depends upon the following
factors:
(i) Purpose and extent of survey.
(ii) Nature of the ground, and
(iii) Scale of the map.
The following contour intervals are generally used:
(i) For flat agricultural land, calculation of earthwork, land leveling etc. 0.15 to 0.50 m,
(ii) For construction of reservoirs and town planning 0.5 to 2m,
(iii) For location surveys 2 to 3 m, and
(iv)For small scale topographic map of hilly area 3m to 25m.
Characteristics of contour lines
1. All points on a contour line have the same elevation (Fig1. ).

14. Fig. 1: Contour map showing various topographic features.
2) Widely spaced contour lines indicate a flat ground and closely spaced contour lines
indicate steep ground.
3) Uniformly spaced contour lines indicate a uniform slope whereas, straight, parallel and
equally spaced lines indicate a plane surface.
4) A series of closed contours with the higher values inside indicate a summit or hill.
Fig. 2: Contour lines indicating hill
5) A series of closed contours with the higher values outside indicate a depression.
Fig.3: Contour lines indicating depression
6) If the contour lines form V – shaped curves and the lower values of contour are inside the
loop, it indicates a valley line.
Fig. 4: Contour lines indicating Valley line
7) If the contour lines form U – shaped curves and the higher values of contour are inside
the loop, then it indicates a ridge line.
Fig. 5: Contour lines indicating Ridge line
8) Contour lines cannot cross one another or merge on the map except in case of an over
hanging cliff.
Fig. 6: Hanging cliff
9) If several contour lines coincide, then the horizontal equivalent is zero, then it indicates a
vertical cliff.
Fig. 7: Vertical cliff
10. Contour lines cannot end anywhere, but close on themselves, either within or outside
the limits of the map.
Advantages / Uses of contour maps or contour lines:
1. Contour map indicates the characteristics of the ground whether it is flat, regular slopy
land or undulating ground etc.
2. Contour map is very useful for taking up land levelling works
3. With the help of contour map, suitable site for reservoirs, canal, drainage channels, roads,
railways etc. can be selected.
4. Total drainage area and capacity of reservoirs can be determined with the help of contour
map
5. Cost estimates of land development projects can be made (Computation of earth work is
possible from contour map).
6. Contour maps are essential for taking up any soil and water conservation works like
bunding, terracing, farm pond, construction of spillways, check dams and other gully control
structures.
7. Watershed boundaries can be clearly delineated.
8. Irrigation water distribution systems and land drainage systems can be conveniently
planned on contour maps.
9. Inter-visibility of any two points can be known from the contour map
10. A route with a given slope can be traced on a contour map.