Theodolite traversing

THEODOLITE TRAVERSING
Mahatma Gandhi Institute Of
Technical Education
& Research Centre, Navsari (396450)
SURVEYING
4TH SEMESTER
CIVIL ENGINEERING
PREPARED BY:
Asst. Prof. GAURANG PRAJAPATI
CIVIL DEPARTMENT

INTRODUCTION
• Theodolite is used to measure the horizontal and vertical angles.
• When the objects are at a considerable distance or situated at a considerable
elevation or depression ,it becomes necessary to measure horizontal and vertical
angles more precisely. So these measurements are taken by a instrument known
as a theodolite.
• Theodolite is more precise than chain survey, magnetic compass or plane table.
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APPLICATION OF THEODOLITE
• Measuring horizontal and vertical angles.
• Locating points on a line.
• Prolonging survey lines.
• Finding difference of level.
• Setting out grades
• Ranging curves
• Tacheometric Survey
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[A] Based on movement of telescope on horizontal axis in a vertical plane
1. Transit Theodolite
2. Non Transit Theodolite
[B] Based on an arrangement to measure the angles
1. Vernier Theodolite
2. Micro meter Theodolite
3. Electronic Digital Theodolite
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CLASSIFICATION OF THEODOLITES
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1. Transit Theodolite
• In case of a transit theodolite, the line of sight can be reversed by revolving the
telescope through 180 degree in the vertical plane.
• Internal focusing telescope is used in this theodolite.
• These theodolites are mainly used for surveying.
2. Non Transit Theodolite
• In case of a transit theodolite, the telescope can not be revolved round the
horizontal axis in a vertical plane completely.
• It can be rotated in a vertical plane for some limited angle.
• These theodolites have now become obsolete.
[A] Based on movement of telescope on horizontal axis in
a vertical plane
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1. Vernier Theodolite
• The theodolite in which Vernier is fitted to measure the angles, is called Vernier Theodolite.
• It can measure an angle up to 20”.
2. Micrometer Theodolite
• The theodolite in which Micrometer is fitted to measure the angles, ,is called Micrometer Theodolite.
• It can measure an angle up to 1”.
• It gives more accuracy.
3. Elecronic Digital Theodolite
• In Elecronic Digital Theodolite, the reading of angle is obtained in digital form.
• When E.D.M. (Electronic Distance Measuring) instrument is attached to the Elecronic Digital Theodolite,
it becomes TOTAL STATION.
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[B] Based on an arrangement to measure the angles
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• The diameter of the graduated circle on the lower plate indicates the size of
theodolite.
• For ordinary surveying works, theodolites of 8-12 cm size are used.
• For Triangulation survey and other accurate survey works, theodolites of larger size
are used.
• For Indian Triangulation survey, a theodolite of 91.4 cm (36”) diameter was used.
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SIZE OF THEODOLITE
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• PARTS OF THEODOLITE
• Telescope
• Vertical circle
• Index frame
• The standards
• The upper plate
• The lower plate
• The levelling head
• The shifting head
• Plate level
• Tripod
• Plumb bob
• Magnetic compass
TRANSIT VERNIER THEODOLITE
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PARTS OF THEODOLITE AND THEIR FUNCTIONS
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 Telescope
A telescope is a focusing instrument which has object piece at one end and eye piece
at the other end. It rotates about horizontal axis in vertical plane. The graduations are
up to an accuracy of 20’.
 Vertical Circle
Vertical circle is fitted to telescope and moves simultaneously with telescope. It has
graduation in each quadrant numbered from 0 to 90degrees.
 The Standards
The standards are the frames which supports telescope and allow it to rotate about
vertical axis. Generally, these are in letter A-shape. So, standards are also called as A-
frame.
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 Levelling Head
• The levelling head contains two parallel triangular plates called as tribrach plates.
• The upper one is known as upper tribrach plate and is used to level the upper plate
and telescope with the help of levelling screws provided at its three ends.
• The lower one is called as lower tribrach plate and is attached to the tripod stand.
It has a circular hole through which a plumb bob may be suspended.
 Function of Levelling head
• To support the main part of the instrument.
• To attach the theodolite to the tripod.
• To provide a mean for levelling the theodolite.
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 Two spindles or axis
• The inner spindle or axis is solid and conical.
• The outer spindle or axis is hollow and ground conical in the interior.
• The inner spindle is also called the upper axis since it carries the Vernier or upper
plate.
• The outer spindle carries the scale or lower plate.
• Both the axes have a common axis which form the vertical axis of the instrument.
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 Lower Plate (Scale plate)
• This is also called as scale plate because it contains a scale on which 0 to 360
readings are graduated.
• It is attached to the outer spindle and consists lower clamping screw.
• If lower clamp screw is loosened and upper clamp screw is tightened, both plates
can rotate together.
• Similarly, if lower clamping screw is tightened and upper clamp is loosened then,
only upper plate is movable and lower plate is fixed with tribrach plate.

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 Upper Plate (Vernier plate)
• The top surface of upper plate gives support to the standards.
• It also consists an upper clamping screw with respect to tangents screw which
helps to fixing it to the lower plate.
• When the upper clamping screw is tightened both upper and lower plates are
attached and moved together with some relative motion because of upper tangent
screw.
• The upper plate also consists two verniers with magnifiers which are arranged
diagonally. It is attached tow inner spindle.

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 Upper and lower clamp screw
• The upper plate carries an upper clamp screw and a corresponding tangent screw.
• The upper plate can be fixed to the lower plate by tightening the upper clamp
screw.
• The upper plate can be slightly rotated for adjustment with the help of the upper
tangent screw.
• The lower plate carries a lower clamp screw and a lower tangent screw.
• When the lower clamp screw is tightened, the lower plate is fixed to the upper
plate and it can be rotated slightly for adjustment with the help of the lower
tangent screw.

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 Level tubes or plate levels
• The upper plate carries two level tubes, also known as plate levels, at right angles to
each other.
• One of the level tube is kept parallel to the trunnion axis.
• The spirit level is can be centred with the help of the foot screw.
 Plumb Bob
• Plumb bob is tool having a cone shaped weight attached to a long thread.
• A plumb bob is suspended from the hook fitted to the bottom of the vertical axis.
• It is used to centre the instrument exactly over a station point.

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 Compass
• The theodolite may contain circular compass or through compass or tubular compass
box in the centre of upper plate.
• It is used to take bearings.
• It is fitted to the A – frame.
 Shifting head
• An arrangement is of Shifting head is made for quick and accurate centring of the
theodolite.
• By this arrangement, the theodolite can be shifted in the horizontal plane with respect
to the tripod head, to bring the plumb bob exactly over the station peg.

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 Clip Screw
• It is fitted at the lower end of clipping arm for slightly rotating the index arm for adjustment.
• When the telescope is moved in the vertical plane, the vertical circle moves relative to the
verniers and thus readings are taken.
• For adjustment purpose, however, the index arm can be rotated slightly with the help of a clip
screw.
 Altitude level tube
• Some theodolites are provided with altitude level tube fitted over the telescope.
• It is used to test the horizontality of the trunnion axis.
• The bubble of the altitude level tube can be centred by clip screw.

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FUNCTION OF CLAMP SCREW AND TANGENT SCREW IN
THEODOLITE
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• Clamp screw
• When the upper clamping screw is tightened but the lower clamp screw is loose,
the instrument rotates on its outer axis, without any relative movement between
the two plates. It is called lower motion. In this case, there is no change in vertical
reading.
• When the lower clamping screw is tightened but the upper clamp screw is loose,
the instrument rotates on its inner axis, with any relative movement between the
Vernier and the scale.. It is called upper motion. In this case, there is change in
vertical reading.
• When both upper clamp screw and lower clamp screw are tightened, the
instrument cannot rotate at all.

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FUNCTION OF CLAMP SCREW AND TANGENT SCREW IN
THEODOLITE
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• Tangent screw
• The upper plate carries an upper tangent screw and the lower plate carries an lower
tangent screw.
• For small movements of plates (Fine adjustment), corresponding tangent screw are
used.
• Before using any tangent screw, the corresponding clamp screw must be tightened.
• Thus,
 After clamping the upper clamp, fine adjustment of upper plate for bisecting the target
(Ranging rod) can be made by rotating the upper tangent screw.
 After clamping the lower clamp, fine adjustment of lower plate for bisecting the target
(Ranging rod) can be made by rotating the lower tangent screw.

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DEFINITIONS AND TECHNICAL TERMS
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• VERTICAL AXIS
It is the axis about which the telescope can be rotated in a horizontal plane.
It is also known as the azimuth axis.
This is the axis about which the lower and upper plate rotate.
• HORIZONTAL AXIS (TRUNNION AXIS)
It is the axis about which the telescope and the vertical circle can be rotated in a
vertical plane.
• LINE OF SIGHT OR LINE OF COLLIMATION
It is the imaginary line passing through the intersection of the cross hairs of the
diaphragm and the optical centre of the objective.
• AXIS OF THE TELESCOPE
It is the line joining the optical centre of the object glass to the centre of the eye-piece.

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• FACE LEFT:
When the vertical circle is to the left side of the observer, then the position of the theodolite is called
face left.
• FACE RIGHT:
When the vertical circle is to the right side of the observer, then the position of the theodolite is called
face right.
• TRANSITING:
It is the process of turning the telescope in vertical plane through 180o about the trunnion axis.
It is also known as plunging or reversing.
In case of transiting, the position of object glass and eye-piece are interchanged and the line of sight is
reversed.
• SWINGING THE TELESCOPE:
It means turning the telescope about its vertical axis in the horizontal plane.
If the telescope is rotated in clockwise direction, it is known as right swing.
If the telescope is rotated in anticlockwise direction, it is known as left swing.

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• TELESCOPE NORMAL
A telescope is said to be normal, when the vertical circle is to the left of the observer.
• TELESCOPE INVERTED
A telescope is said to be inverted, when the vertical circle is to the right of the
observer.
• CHANGING FACE:
It is an operation of bringing the face of the telescope from left to right and vice-versa.
• AXIS OF THE LEVEL TUBE
The axis of the level tube or the bubble line is the straight line tangential to the
longitudinal curve of the level tube at its centre.
The axis of the level tube is horizontal when the bubble is at centre.

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TEMPORARY ADJUSTMENT OF A THEODOLITE
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• Temporary adjustments are the adjustments which are required to be made at
each setting of the instrument before taking observations.
• These adjustments are also known as station adjustments.
• There are three temporary adjustments of a theodolite.
1. Setting up the theodolite over a station.
2. Levelling up.
3. Elimination of parallax.

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1. SETTING UP AND CENTRING
 Procedure:
• Place the tripod over the station. The legs of the tripod should be spread so that they make an angle of
60o with horizontal.
• Take out the instrument from the box. Lift the instrument from the base and screw it firmly on the
tripod head.
• Adjust the height of the tripod so that the telescope is at a convenient height.
• Suspend a plumb bob from the hook beneath the inner spindle.
• Approximate centring is done by means of the tripod legs. The tripod legs are moved radially or
circumferentially for centring. Sometimes he instrument and the tripod have to be moved bodily for
centring to bring the plumb bob over the station mark.
• In modern theodolites, the shifting head is provided for easy and accurate setting up of the instrument.
• The approximate levelling is done either with reference to a small circular bubble tube provided on
tribrach or is done by eye adjustment.

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2. LEVELING UP:
• The purpose of the levelling is to make the vertical axis shall be truly vertical.
• Accurate levelling of the theodolite is done with the help of levelling screws or foot
screw with reference to the plate levels.
 Procedure:
• Turn the upper plate until the longitudinal axis of the plate level is roughly parallel to a
line joining any two of the levelling screws (A & B).

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• Hold these two levelling screws between the thumb and first finger of each hand uniformly so that the thumb
moves either towards each other or away from each other until the bubble comes to the centre.
• Turn the upper plate through 90º i.e. until the axes of the level passes over the position of the third levelling
screw ‘C’.
• Turn this levelling screw until the bubble comes to the centre.
• Rotate the upper plate through 90º to its original position fig (a) and repeat step (2) till the bubble comes to the
centre.
• Turn back again through 90º and repeat step 4.
• Repeat the steps 2 and 4 till the bubble is central in both the positions.
• Now rotate the instrument through 180º. The bubble should be remaining in the centre of its run, provided it is
in correct adjustment. The vertical axis will then be truly vertical.

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3. ELIMINATION OF PARALLAX:
• Parallax is a condition arising when the image formed by the objective is not in the plane of the cross hairs.
• Unless parallax is eliminated, accurate sighting is not possible. Parallax can be eliminated in two steps.
 Focusing of eye-piece.
• The eye piece is focused to make the cross hairs distinct and clear.
 Procedure
• Point the telescope to the sky or hold a piece of white paper in front of telescope.
• Move the eye-piece in and out until a distinct sharp black image of the cross-hairs is seen.
• This confirms proper focusing.
 Focusing of object glass.
• The objective is focussed to bring the image of the object in the plane of cross hairs.
 Procedure
• First, direct the telescope towards the object for observation.
• Next, turn the focusing screw until the image of the object appears clear and sharp as the observer looks through properly focused eye-
piece.
• When focusing has been done properly, there will be no parallax i.e., there will be no apparent movement of the image relative to the cross
hairs when the observer moves his eye from one side to the other or from top to bottom.

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FUNDEMENTAL AXES OF THEODOLITE
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 The fundamental axis of theodolite are:
• Vertical axis
• Trunnion axis
• Line of collimation
• Altitude level axis
• Axis of plate level
 A theodolite is said to be in proper condition if the following conditions are
satisfied:
• The axis of the plate is perpendicular to the vertical axis
• The trunnion axis is perpendicular to the vertical axis
• The line of collimation is perpendicular to the trunnion axis
• The axis of the altitude level is parallel to the line of collimation

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MEASUREMENT OF HORIZONTAL ANGLE
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Following are the Methods t measure the horizontal angle:
1. General Method
2. Repetition Method
3. Reiteration Method

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1. General Method
• Set up the theodolite at station point O and level it accurately.
• Set the vernier A to the zero or 3600 of the horizontal circle. Tighten the upper clamp.
• Loosen the lower clamp. Turn the instrument and direct the telescope towards A to
bisect it accurately with the use of tangent screw. After bisecting accurately check the
reading which must still read zero. Read the vernier B and record both the readings.
• Loosen the upper clamp and turn the telescope clockwise until line of sight bisects
point B on the right hand side. Then tighten the upper clamp and bisect it accurately
by turning its tangent screw.
BA
O

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• Read both verniers. The reading of the vernier a which was initially set at zero gives
the value of the angle AOB directly and that of the other vernier B by deducting
1800 .The mean of the two vernier readings gives the value of the required angle
AOB.
• Change the face of the instrument and repeat the whole process. The mean of the
two vernier readings gives the second value of the angle AOB which should be
approximately or exactly equal to the previous value.
• The mean of the two values of the angle AOB ,one with face left and the other with
face right ,gives the required angle free from all instrumental errors.

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2. Repetition Method
• The method of repetition is used to measure a horizontal angle to a finer degree of
accuracy.
• By this method, an angle is measured two or more times by allowing the vernier to
remain clamped each time at the end of each measurement instead of setting it back at
zero when sighting at the previous station.
• Thus an angle reading is mechanically added several times depending upon the number
of repetitions.
• The average horizontal angle is then obtained by dividing the final reading by the
number of repetitions.
• For very accurate work the method of repetition is used.

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 PROCEDURE:
• Select a station point O.
• Set the theodolite at O and do the temporary adjustments. The
telescope is adjusted for right face right swing.
• Set the vernier A to zero using upper clamp. Loosen the lower clamp,
direct the telescope to the station point A and bisect A exactly by
using the lower clamp and lower tangent screw.
• Note the vernier readings (A and B).
• Loosen the upper clamp and turn the telescope clockwise until the
point B is exactly bisected.
• The mean of the two vernier readings gives the value of <AOB.
A
O
B

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• Loosen the lower clamp and turn the telescope to station point A and bisected A by
using the lower clamp and lower tangent screw.
• Loosen the upper clamp and turn the telescope clockwise until the point B is exactly
bisected. Now the vernier reading is twice the value of the angle.
• Repeat the process for the required number of times (usually 3).
• The correct value of the angle AOB is obtained by dividing the final reading by the
number of repetition.
• Adjust the telescope for left face left swing.
•
 Repeat the whole process by turning the telescope in anticlockwise
direction.
 Take the average of face left and faces right observation to give the
horizontal angle AOB.

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• 3. Reiteration Method
• Reiteration is a method of measuring horizontal angles with high precision.
• It is less tedious and is generally preferred when there are several angles to be
measured at a station.
• Several angles are measured successively and finally the horizon is closed.
• Closing the horizon is the process of measuring the angles around a point to obtain
a check on their sum which should be equal to 360o.

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 PROCEDURE:
• Select a station point O.
• Set the Theodolite at O and do the
temporary adjustments. The telescope is
adjusted for right face right swing.
• Set the vernier A to zero using upper clamp.
Loosen the lower clamp, direct the
telescope to the station point A and bisect A
exactly by using the lower clamp and lower
tangent screw.
• Loosen the upper clamp and turn the
telescope clockwise until the point B is
exactly bisected.
A B
C
D

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• The mean of the two vernier readings gives the value of <AOB.
• Bisect all the points successively and note the readings of both venires at each
bisection.
• Finally close the horizon by sighting the station point A. The A vernier should be
3600. If not, note the closing error.
• Adjust the telescope for left face left swing.
• Repeat the whole process by turning the telescope in anticlockwise direction.
• Distribute the closing error proportionately the several observed angles.
• Take the average of face left and face right observations to give the corresponding
horizontal angles.

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MEASUREMENT OF VERTICAL ANGLE
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• Vertical Angle
A vertical angle is an angle between the inclined line of sight and the horizontal.
It may be an angle of elevation or depression according as the object is above or
below the horizontal plane.
B
O
A
B
O
HORI. LINE
O
HORI.
LINE
β
HORI. LINE
VERTICAL ANGLE
A
Fig.a
Fig. b Fig. c
B
A
AOB= α+ β
AOB= α - β
β
β
α
α
α

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 ToMeasure the Vertical Angle of an object A at a station O
• Set up the theodolite at station point O and level it accurately with reference to the
altitude bubble.
• Set the zero of vertical vernier exactly to the zero of the vertical circle clamp and
tangent screw.
• Bring the bubble of the altitude level in the central position.
• The line of sight is thus made horizontal and vernier still reads zero.
• Loosen the vertical circle clamp screw and direct the telescope towards the object A
and sight it exactly by using the vertical circle tangent screw.
• Read both verniers on the vertical circle, The mean of the two vernier readings gives the
value of the required angle.
• Change the face of the instrument and repeat the process. The mean of the two vernier
readings gives the second value of the required angle.
• The average of the two values of the angles thus obtained, is the required value of the
angle free from instrumental errors.

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 For measuring Vertical Angle between two points A &B
• Sight A as before , and take the mean of the two vernier readings at the vertical
circle. Let it be α.
• Similarly, sight B and take the mean of the two vernier readings at the vertical
circle. Let it be β.
• The sum or difference of these readings will give the value of the vertical angle
between A and B according as one of the points is above and the other below the
horizontal plane. or both points are on the same side of the horizontal plane Fig b
& c.

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TO PROLONG A STRAIGHT LINE
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There are three different methods to prolonging the given straight line:
1. Fore Sight Method
2. Back Sight Method
3. Double reversing Method

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1. Fore Sight Method:
• Set up the theodolite at A and level it accurately .Bisect the point b correctly.
Establish a point C in the line beyond B approximately by looking over the top of
the telescope and accurately by sighting through the telescope.
• Shift the instrument to B ,take a fore sight on C and establish a point D in line
beyond C.
• Repeat the process until the last point Z is reached.

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2. Back Sight Method:
• Set up the instrument at B and level it accurately .
• Take a back sight on A.
• Tighten the upper and lower clamps, transit the telescope and establish a point C in
the line beyond B.
• Shift the theodolite to C ,back sight on B transit the telescope and establish a point D in
line beyond C. Repeat the process until the last point ( Z) is established.
• Now if the instrument is in adjustment, the points A,B,C,D and Z will be in one line,
which is straight but if it is not in adjustment i.e. line of collimation is not
perpendicular to the horizontal axis ,then C’, D’ and Z’ will not be in a straight line.

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3. Double reversing Method
When the line is to be prolonged with high precision or when the instrument is in
imperfect adjustment, the process of double sighting or double reversing, is used.
• Suppose the line AB is to be prolonged to a point Z.

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• Set up the theodolite at B and level it accurately.
• With the face of instrument left, back sight on A and clamp both the upper and lower
motions.
• Transit the telescope and set a point C1 ahead in line.
• Loosen the lower clamp ,revolve the telescope in the horizontal plane and back sight on
A .Bisect A exactly by using the lower clamp and its tangent screw. Now the face of
instrument is right.
• Transit the telescope and establish a point C2 in line.
• The exact position of the true point C must be mid-way between C1 and C2.
• Measure C1 C2 and establish a point C exactly mid-way, which lies on the true
prolongation of AB.
• Shift the instrument to C, double sight on B ,establish the point D1 and D2 and locate the
true point D as before.
• Continue the process until the last point Z is established.

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Theodolite Traversing
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• A traverse is a series of connected lines whose lengths and directions are measured
in the field.
• The system of surveying in which the angles are measured with the help of a
theodolite, is called Theodolite surveying
Different methods of Traversing:
1. Traversing by included angles
2.Traversing by deflection angles

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1. Traversing by included angles
• This method is more accurate than
the fast needle method. Traversing by the
method of included angles is the most
commonly used method.
• In this method, the magnetic bearing
of any one line is measured in the field.

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2.Traversing by deflection angles
This method is suitable for open traverse and is mostly employed in the survey of
rivers, coast line, roads, railways, canals, etc

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Theodolite traversing

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