Page 1
? Theodolite survey ? Traverse surveying and omitted
measurements
CHAPTER HIGHLIGHTS
THeodoLite Survey
Introduction
Horizontal angles can be measured by compass. But to get
precise readings and to measure horizontal and vertical angles
another instrument called theodolite is used. It can be used for
laying off horizontal angles, locating points on line, prolong-
ing survey lines, establishing grades, determining diff erence
in elevation, setting out curves, etc.
Theodolites
1. Transit theodolite or transit: In transit theodolite
the line of sight can be reversed by revolving the
telescope through 180° in the vertical plane and is
commonly used.
2. Non-transit theodolite: These are either plain
theodolites or Y-theodolites in which the telescope
cannot be transited.
Parts of Transit Theodolite
1. Telescope: It is mounted on a spindle known as
horizontal axis or trunnion axis and internal focusing
type is widely used.
2. V ertical circle: It is a circular graduated arc attached
to the trunnion axis of the telescope and operated by
means of vertical circle clamp and its corresponding
slow motion or tangent screw. The circle is graduated
from 0°–360° in clockwise or it is divided into four
quadrants.
3. Index frame (T-frame or vernier frame): It is
T -shaped frame consisting of a vertical leg known as
clipping arm and a horizontal bar known as vernier
arm or index arm whose two extremities are fi tted
with verniers to read vertical circle. Clip screw is
used for slight adjustment. Altitude bubble is placed
on the top of the index frame.
4. The standards (or A-frame): Two resembling letter
‘A ’ are mounted on the upper plates. The trunnion axis,
T-frames and the arm of vertical circle clamp are
attached to the A-frame.
5. Levelling head: It consists of two parallel triangular
plates known as plates. Its functions are:
(a) To support main part of instrument.
(b) To attach the theodolite to the tripod.
(c) To provide a means for leveling the theodolite.
6. Lower plate (or scale plate): Lower plate carries
a lower clamp screw and a corresponding tangent
screw to rotate the plate and fi x at any position. Size
of theodolite is represented by the size of scale plate.
7. Upper plate (or vernier plate): This is connected to
inner axis and carries two verniers and also an upper
clamp screw and a corresponding tangent screw.
• On clamping upper and unclamping the lower clamp,
instrument rotates on its outer axis without any relative
motion between the plates.
• Lower clamp is clamped and upper unclamped, instru-
ment rotates on inner axis with relative motion between
vernier and scale.
Theodolite, Traverse Survey
and Omitted Measurements
Part III_Unit 12_Chapter 03.indd 1 5/31/2017 5:01:10 PM
Page 2
? Theodolite survey ? Traverse surveying and omitted
measurements
CHAPTER HIGHLIGHTS
THeodoLite Survey
Introduction
Horizontal angles can be measured by compass. But to get
precise readings and to measure horizontal and vertical angles
another instrument called theodolite is used. It can be used for
laying off horizontal angles, locating points on line, prolong-
ing survey lines, establishing grades, determining diff erence
in elevation, setting out curves, etc.
Theodolites
1. Transit theodolite or transit: In transit theodolite
the line of sight can be reversed by revolving the
telescope through 180° in the vertical plane and is
commonly used.
2. Non-transit theodolite: These are either plain
theodolites or Y-theodolites in which the telescope
cannot be transited.
Parts of Transit Theodolite
1. Telescope: It is mounted on a spindle known as
horizontal axis or trunnion axis and internal focusing
type is widely used.
2. V ertical circle: It is a circular graduated arc attached
to the trunnion axis of the telescope and operated by
means of vertical circle clamp and its corresponding
slow motion or tangent screw. The circle is graduated
from 0°–360° in clockwise or it is divided into four
quadrants.
3. Index frame (T-frame or vernier frame): It is
T -shaped frame consisting of a vertical leg known as
clipping arm and a horizontal bar known as vernier
arm or index arm whose two extremities are fi tted
with verniers to read vertical circle. Clip screw is
used for slight adjustment. Altitude bubble is placed
on the top of the index frame.
4. The standards (or A-frame): Two resembling letter
‘A ’ are mounted on the upper plates. The trunnion axis,
T-frames and the arm of vertical circle clamp are
attached to the A-frame.
5. Levelling head: It consists of two parallel triangular
plates known as plates. Its functions are:
(a) To support main part of instrument.
(b) To attach the theodolite to the tripod.
(c) To provide a means for leveling the theodolite.
6. Lower plate (or scale plate): Lower plate carries
a lower clamp screw and a corresponding tangent
screw to rotate the plate and fi x at any position. Size
of theodolite is represented by the size of scale plate.
7. Upper plate (or vernier plate): This is connected to
inner axis and carries two verniers and also an upper
clamp screw and a corresponding tangent screw.
• On clamping upper and unclamping the lower clamp,
instrument rotates on its outer axis without any relative
motion between the plates.
• Lower clamp is clamped and upper unclamped, instru-
ment rotates on inner axis with relative motion between
vernier and scale.
Theodolite, Traverse Survey
and Omitted Measurements
Part III_Unit 12_Chapter 03.indd 1 5/31/2017 5:01:10 PM
• For using any tangent screw, its corresponding clamp
screw must be tightened.
8. Plate levels: These are carried by the upper plates
which are perpendicular to each other with one of
them parallel to turnion axis. These help the telescope
to settle in exact vertical position.
9. Tripod: It is a stand on which theodolite is mounted
10. Plumb bob: It is tool a having a cone shaped weight
attached to a long thread. The weight is hanged using
thread from centre of tripod stand and centering of
the odilite is done.
11. Compass: Simpler theodolites may contain circular
compass box in the centre of upper plate. It is useful
when we select north as the reference meridian.
Definitions and Terms
1. Vertical axis: This is the axis about which the
instrument can be rotated in a horizontal plane.
Lower and upper plates rotate about this axis. It is
also known as azimuth axis.
2. Horizontal axis or trunnion axis: is the axis about
which the telescope and the vertical circle rotate in
the vertical plane.
3. Line of sight or line of collimation: is the line
passing through the intersection of the horizontal
and vertical cross-hairs and the optical centre of the
object glass and its continuation.
4. Axis of level tube or bubble line: It is a straight line
tangential to the longitudinal curve of the level tube at
its centre. It is horizontal when the bubble is central.
5. Transiting: also known as plunging or reversing. It is
the process of turning the telescope in vertical plane
through 180° about the trunnion axis.
6. Swinging the telescope: The process of turning the
telescope in horizontal plane. If rotated clockwise,
it is called right swing. If rotated in anticlockwise
direction, it is called left swing.
7. Face left observation: If the face of vertical circle
is to the left of the observer, the observation angle is
called as face left observation.
8. Face right observation: If the face of vertical circle
is to the right of the observer.
9. Telescope normal or direct: Telescope is said to be
normal when the face of the vertical circle is to the
left side and the bubble is up.
10. Telescope inverted or reversed: When face of
vertical circle is to the right and the bubble down.
11. Changing face: It is an operation of bringing the face
of the telescope from left to right and vice versa.
Adjustments in Theodolite
Temporary Adjustments of Theodolite
• Setting: The instrument to be set over the station, center-
ing by a plumb bob and approximate levelling with the
help of tripod legs.
• Levelling: Done using leveling screws or foot screws to
make the vertical axis truly vertical.
• Elimination of parallax: Parallax is a condition aris-
ing when the image formed by the objective is not in the
plane of the cross hairs.
It is done in two steps:
1. Focusing the eye-piece: For distinct vision of the
cross hairs.
2. Focusing the objective: Focusing screw is turned till
the image appears clear and sharp and is in the plane
of cross hairs.
Permanent Adjustments of Theodolite
1. Adjustment of plate level: To make the axis of plate
bubble perpendicular to the vertical axis when the
bubble is central.
2. Adjustment of line of sight: Line of sight should
coincide with optical axis of the telescope.
3. Adjustment of horizontal axis: Horizontal axis
should be perpendicular to the vertical axis. Spire test
is done.
4. Adjustment of altitude level and vertical index
frame: Clip and tangent screws are used for adjusting
vertical frame and levelling of altitude.
Operations done with Theodolite
Measurement of Horizontal Angle
Repetition Method Used to measure horizontal angle to a
finer degree of accuracy than that obtained with the least
count of vernier.
Errors eliminated:
1. Errors due to eccentricity of verniers and centres are
eliminated by taking both vernier readings.
2. Errors due to in adjustment of line of collimation and
the trunnion axis are eliminated by taking both face
readings.
3. Error due to inaccurate graduations are eliminated by
taking the readings at different parts of the circle.
4. Errors due to inaccurate bisection of the object,
eccentric centering, etc., may be to some extent
counter-balanced in different observations.
5. Errors due to slip, displacement of station signals and
want of verticality of the vertical axis, etc., are not
eliminated since they are all cumulative.
Direction Method or Reiteration Method This is also
known as method of series and is suitable for the measure-
ment of the angles of a group having a common vertex point
and finally the horizon is closed such that sum of angles
equal to 360°.
1. Measurement of vertical angles.
2. Measuring magnetic bearing of a line.
Part III_Unit 12_Chapter 03.indd 2 5/31/2017 5:01:11 PM
Page 3
? Theodolite survey ? Traverse surveying and omitted
measurements
CHAPTER HIGHLIGHTS
THeodoLite Survey
Introduction
Horizontal angles can be measured by compass. But to get
precise readings and to measure horizontal and vertical angles
another instrument called theodolite is used. It can be used for
laying off horizontal angles, locating points on line, prolong-
ing survey lines, establishing grades, determining diff erence
in elevation, setting out curves, etc.
Theodolites
1. Transit theodolite or transit: In transit theodolite
the line of sight can be reversed by revolving the
telescope through 180° in the vertical plane and is
commonly used.
2. Non-transit theodolite: These are either plain
theodolites or Y-theodolites in which the telescope
cannot be transited.
Parts of Transit Theodolite
1. Telescope: It is mounted on a spindle known as
horizontal axis or trunnion axis and internal focusing
type is widely used.
2. V ertical circle: It is a circular graduated arc attached
to the trunnion axis of the telescope and operated by
means of vertical circle clamp and its corresponding
slow motion or tangent screw. The circle is graduated
from 0°–360° in clockwise or it is divided into four
quadrants.
3. Index frame (T-frame or vernier frame): It is
T -shaped frame consisting of a vertical leg known as
clipping arm and a horizontal bar known as vernier
arm or index arm whose two extremities are fi tted
with verniers to read vertical circle. Clip screw is
used for slight adjustment. Altitude bubble is placed
on the top of the index frame.
4. The standards (or A-frame): Two resembling letter
‘A ’ are mounted on the upper plates. The trunnion axis,
T-frames and the arm of vertical circle clamp are
attached to the A-frame.
5. Levelling head: It consists of two parallel triangular
plates known as plates. Its functions are:
(a) To support main part of instrument.
(b) To attach the theodolite to the tripod.
(c) To provide a means for leveling the theodolite.
6. Lower plate (or scale plate): Lower plate carries
a lower clamp screw and a corresponding tangent
screw to rotate the plate and fi x at any position. Size
of theodolite is represented by the size of scale plate.
7. Upper plate (or vernier plate): This is connected to
inner axis and carries two verniers and also an upper
clamp screw and a corresponding tangent screw.
• On clamping upper and unclamping the lower clamp,
instrument rotates on its outer axis without any relative
motion between the plates.
• Lower clamp is clamped and upper unclamped, instru-
ment rotates on inner axis with relative motion between
vernier and scale.
Theodolite, Traverse Survey
and Omitted Measurements
Part III_Unit 12_Chapter 03.indd 1 5/31/2017 5:01:10 PM
• For using any tangent screw, its corresponding clamp
screw must be tightened.
8. Plate levels: These are carried by the upper plates
which are perpendicular to each other with one of
them parallel to turnion axis. These help the telescope
to settle in exact vertical position.
9. Tripod: It is a stand on which theodolite is mounted
10. Plumb bob: It is tool a having a cone shaped weight
attached to a long thread. The weight is hanged using
thread from centre of tripod stand and centering of
the odilite is done.
11. Compass: Simpler theodolites may contain circular
compass box in the centre of upper plate. It is useful
when we select north as the reference meridian.
Definitions and Terms
1. Vertical axis: This is the axis about which the
instrument can be rotated in a horizontal plane.
Lower and upper plates rotate about this axis. It is
also known as azimuth axis.
2. Horizontal axis or trunnion axis: is the axis about
which the telescope and the vertical circle rotate in
the vertical plane.
3. Line of sight or line of collimation: is the line
passing through the intersection of the horizontal
and vertical cross-hairs and the optical centre of the
object glass and its continuation.
4. Axis of level tube or bubble line: It is a straight line
tangential to the longitudinal curve of the level tube at
its centre. It is horizontal when the bubble is central.
5. Transiting: also known as plunging or reversing. It is
the process of turning the telescope in vertical plane
through 180° about the trunnion axis.
6. Swinging the telescope: The process of turning the
telescope in horizontal plane. If rotated clockwise,
it is called right swing. If rotated in anticlockwise
direction, it is called left swing.
7. Face left observation: If the face of vertical circle
is to the left of the observer, the observation angle is
called as face left observation.
8. Face right observation: If the face of vertical circle
is to the right of the observer.
9. Telescope normal or direct: Telescope is said to be
normal when the face of the vertical circle is to the
left side and the bubble is up.
10. Telescope inverted or reversed: When face of
vertical circle is to the right and the bubble down.
11. Changing face: It is an operation of bringing the face
of the telescope from left to right and vice versa.
Adjustments in Theodolite
Temporary Adjustments of Theodolite
• Setting: The instrument to be set over the station, center-
ing by a plumb bob and approximate levelling with the
help of tripod legs.
• Levelling: Done using leveling screws or foot screws to
make the vertical axis truly vertical.
• Elimination of parallax: Parallax is a condition aris-
ing when the image formed by the objective is not in the
plane of the cross hairs.
It is done in two steps:
1. Focusing the eye-piece: For distinct vision of the
cross hairs.
2. Focusing the objective: Focusing screw is turned till
the image appears clear and sharp and is in the plane
of cross hairs.
Permanent Adjustments of Theodolite
1. Adjustment of plate level: To make the axis of plate
bubble perpendicular to the vertical axis when the
bubble is central.
2. Adjustment of line of sight: Line of sight should
coincide with optical axis of the telescope.
3. Adjustment of horizontal axis: Horizontal axis
should be perpendicular to the vertical axis. Spire test
is done.
4. Adjustment of altitude level and vertical index
frame: Clip and tangent screws are used for adjusting
vertical frame and levelling of altitude.
Operations done with Theodolite
Measurement of Horizontal Angle
Repetition Method Used to measure horizontal angle to a
finer degree of accuracy than that obtained with the least
count of vernier.
Errors eliminated:
1. Errors due to eccentricity of verniers and centres are
eliminated by taking both vernier readings.
2. Errors due to in adjustment of line of collimation and
the trunnion axis are eliminated by taking both face
readings.
3. Error due to inaccurate graduations are eliminated by
taking the readings at different parts of the circle.
4. Errors due to inaccurate bisection of the object,
eccentric centering, etc., may be to some extent
counter-balanced in different observations.
5. Errors due to slip, displacement of station signals and
want of verticality of the vertical axis, etc., are not
eliminated since they are all cumulative.
Direction Method or Reiteration Method This is also
known as method of series and is suitable for the measure-
ment of the angles of a group having a common vertex point
and finally the horizon is closed such that sum of angles
equal to 360°.
1. Measurement of vertical angles.
2. Measuring magnetic bearing of a line.
Part III_Unit 12_Chapter 03.indd 2 5/31/2017 5:01:11 PM
3. Measuring direct angles and deflection angles.
4. To prolong a straight line.
5. To locate point of intersection of two straight lines.
6. To lay off a horizontal angle.
7. To lay off an angle by repetition.
Fundamental Lines and Their
Desired Relations
1. Vertical axis
2. Horizontal axis (trunnion or transit axis)
3. Line of collimation (line of sight)
4. Axis of plate level
5. Axis of altitude level
When the theodolite is in proper adjustment:
• The axis of the plate level must lie in a plane perpendicu-
lar to the vertical axis.
• The line of collimation must be perpendicular to the hori-
zontal axis at its intersection with the vertical axis.
• Horizontal axis must be perpendicular to vertical axis.
• Axis of altitude level (telescope level) must be parallel to
line of collimation.
• Vertical circle vernier must read zero when the line of
collimation is horizontal.
Sources of Error in Theodolite Work
1. Instrumental
2. Personal
3. Natural
Instrumental Errors
These are due to:
1. Imperfect adjustment of the instrument.
2. Structural defects in instrument
3. Imperfections due to wear.
• Error due to imperfect adjustment of plate levels:
The error can be eliminated only by careful leveling
with respect to the altitude bubble if it is in adjust-
ment and can be eliminated by double sighting.
• Error due to line of collimation not being perpen-
dicular to the horizontal axis:
Error, e = b sec a b = Error in collimation
a = Inclination
This error can be eliminated by taking both face
observations.
• Error due to horizontal axis not being perpendicular to
the vertical axis:
Error, e = b tan a This error can be eliminated by taking both face
observations.
• Error due to non-parallelism of the axis of telescope level
and the line of collimation can be eliminated by taking
both face observations.
• Error due to eccentricity of inner and outer axes can
be eliminated by taking the mean of the two vernier
readings.
• Error due to imperfect graduations can be eliminated by
taking mean of several readings distributed over different
portions of the graduated circle.
• Error due to eccentricity of verniers can be eliminated
by reading both the verniers and taking the mean of the
two.
Personal Errors
1. Errors in manipulation:
(a) Inaccurate centering
(b) Inaccurate levelling
(c) Slip
(d) Manipulating wrong tangent screw.
2. Errors in sighting and reading:
(a) Inaccurate bisection of points observed.
(b) Mistakes in setting the vernier.
(c) Parallax: Due to parallax, accurate bisection is
not possible. Error can be eliminated by focusing
eye-piece and objective.
Natural Errors
1. Unequal atmospheric refraction due to high
temperature.
2. Unequal expansion of parts of telescope and circles
due to temperature change.
3. Unequal settlement of tripod.
4. Wind producing vibrations.
Double Sighting
Measurement of horizontal angle or vertical angle twice;
once with the telescope in normal condition and once
with the telescope in inverted condition is called double
sighting.
Traverse Surveying and
Omitted Measurements
1. Introduction: Traversing is that type of survey in
which a number of connected survey lines form the
framework and the directions and the lengths of the
survey lines are measured with the help of an angle
measuring instrument (compass or theodolite) and a
tape (or chain) respectively.
• When the lines form a circuit which ends at the
starting point, it is known as closed traverse.
Part III_Unit 12_Chapter 03.indd 3 5/31/2017 5:01:11 PM
Page 4
? Theodolite survey ? Traverse surveying and omitted
measurements
CHAPTER HIGHLIGHTS
THeodoLite Survey
Introduction
Horizontal angles can be measured by compass. But to get
precise readings and to measure horizontal and vertical angles
another instrument called theodolite is used. It can be used for
laying off horizontal angles, locating points on line, prolong-
ing survey lines, establishing grades, determining diff erence
in elevation, setting out curves, etc.
Theodolites
1. Transit theodolite or transit: In transit theodolite
the line of sight can be reversed by revolving the
telescope through 180° in the vertical plane and is
commonly used.
2. Non-transit theodolite: These are either plain
theodolites or Y-theodolites in which the telescope
cannot be transited.
Parts of Transit Theodolite
1. Telescope: It is mounted on a spindle known as
horizontal axis or trunnion axis and internal focusing
type is widely used.
2. V ertical circle: It is a circular graduated arc attached
to the trunnion axis of the telescope and operated by
means of vertical circle clamp and its corresponding
slow motion or tangent screw. The circle is graduated
from 0°–360° in clockwise or it is divided into four
quadrants.
3. Index frame (T-frame or vernier frame): It is
T -shaped frame consisting of a vertical leg known as
clipping arm and a horizontal bar known as vernier
arm or index arm whose two extremities are fi tted
with verniers to read vertical circle. Clip screw is
used for slight adjustment. Altitude bubble is placed
on the top of the index frame.
4. The standards (or A-frame): Two resembling letter
‘A ’ are mounted on the upper plates. The trunnion axis,
T-frames and the arm of vertical circle clamp are
attached to the A-frame.
5. Levelling head: It consists of two parallel triangular
plates known as plates. Its functions are:
(a) To support main part of instrument.
(b) To attach the theodolite to the tripod.
(c) To provide a means for leveling the theodolite.
6. Lower plate (or scale plate): Lower plate carries
a lower clamp screw and a corresponding tangent
screw to rotate the plate and fi x at any position. Size
of theodolite is represented by the size of scale plate.
7. Upper plate (or vernier plate): This is connected to
inner axis and carries two verniers and also an upper
clamp screw and a corresponding tangent screw.
• On clamping upper and unclamping the lower clamp,
instrument rotates on its outer axis without any relative
motion between the plates.
• Lower clamp is clamped and upper unclamped, instru-
ment rotates on inner axis with relative motion between
vernier and scale.
Theodolite, Traverse Survey
and Omitted Measurements
Part III_Unit 12_Chapter 03.indd 1 5/31/2017 5:01:10 PM
• For using any tangent screw, its corresponding clamp
screw must be tightened.
8. Plate levels: These are carried by the upper plates
which are perpendicular to each other with one of
them parallel to turnion axis. These help the telescope
to settle in exact vertical position.
9. Tripod: It is a stand on which theodolite is mounted
10. Plumb bob: It is tool a having a cone shaped weight
attached to a long thread. The weight is hanged using
thread from centre of tripod stand and centering of
the odilite is done.
11. Compass: Simpler theodolites may contain circular
compass box in the centre of upper plate. It is useful
when we select north as the reference meridian.
Definitions and Terms
1. Vertical axis: This is the axis about which the
instrument can be rotated in a horizontal plane.
Lower and upper plates rotate about this axis. It is
also known as azimuth axis.
2. Horizontal axis or trunnion axis: is the axis about
which the telescope and the vertical circle rotate in
the vertical plane.
3. Line of sight or line of collimation: is the line
passing through the intersection of the horizontal
and vertical cross-hairs and the optical centre of the
object glass and its continuation.
4. Axis of level tube or bubble line: It is a straight line
tangential to the longitudinal curve of the level tube at
its centre. It is horizontal when the bubble is central.
5. Transiting: also known as plunging or reversing. It is
the process of turning the telescope in vertical plane
through 180° about the trunnion axis.
6. Swinging the telescope: The process of turning the
telescope in horizontal plane. If rotated clockwise,
it is called right swing. If rotated in anticlockwise
direction, it is called left swing.
7. Face left observation: If the face of vertical circle
is to the left of the observer, the observation angle is
called as face left observation.
8. Face right observation: If the face of vertical circle
is to the right of the observer.
9. Telescope normal or direct: Telescope is said to be
normal when the face of the vertical circle is to the
left side and the bubble is up.
10. Telescope inverted or reversed: When face of
vertical circle is to the right and the bubble down.
11. Changing face: It is an operation of bringing the face
of the telescope from left to right and vice versa.
Adjustments in Theodolite
Temporary Adjustments of Theodolite
• Setting: The instrument to be set over the station, center-
ing by a plumb bob and approximate levelling with the
help of tripod legs.
• Levelling: Done using leveling screws or foot screws to
make the vertical axis truly vertical.
• Elimination of parallax: Parallax is a condition aris-
ing when the image formed by the objective is not in the
plane of the cross hairs.
It is done in two steps:
1. Focusing the eye-piece: For distinct vision of the
cross hairs.
2. Focusing the objective: Focusing screw is turned till
the image appears clear and sharp and is in the plane
of cross hairs.
Permanent Adjustments of Theodolite
1. Adjustment of plate level: To make the axis of plate
bubble perpendicular to the vertical axis when the
bubble is central.
2. Adjustment of line of sight: Line of sight should
coincide with optical axis of the telescope.
3. Adjustment of horizontal axis: Horizontal axis
should be perpendicular to the vertical axis. Spire test
is done.
4. Adjustment of altitude level and vertical index
frame: Clip and tangent screws are used for adjusting
vertical frame and levelling of altitude.
Operations done with Theodolite
Measurement of Horizontal Angle
Repetition Method Used to measure horizontal angle to a
finer degree of accuracy than that obtained with the least
count of vernier.
Errors eliminated:
1. Errors due to eccentricity of verniers and centres are
eliminated by taking both vernier readings.
2. Errors due to in adjustment of line of collimation and
the trunnion axis are eliminated by taking both face
readings.
3. Error due to inaccurate graduations are eliminated by
taking the readings at different parts of the circle.
4. Errors due to inaccurate bisection of the object,
eccentric centering, etc., may be to some extent
counter-balanced in different observations.
5. Errors due to slip, displacement of station signals and
want of verticality of the vertical axis, etc., are not
eliminated since they are all cumulative.
Direction Method or Reiteration Method This is also
known as method of series and is suitable for the measure-
ment of the angles of a group having a common vertex point
and finally the horizon is closed such that sum of angles
equal to 360°.
1. Measurement of vertical angles.
2. Measuring magnetic bearing of a line.
Part III_Unit 12_Chapter 03.indd 2 5/31/2017 5:01:11 PM
3. Measuring direct angles and deflection angles.
4. To prolong a straight line.
5. To locate point of intersection of two straight lines.
6. To lay off a horizontal angle.
7. To lay off an angle by repetition.
Fundamental Lines and Their
Desired Relations
1. Vertical axis
2. Horizontal axis (trunnion or transit axis)
3. Line of collimation (line of sight)
4. Axis of plate level
5. Axis of altitude level
When the theodolite is in proper adjustment:
• The axis of the plate level must lie in a plane perpendicu-
lar to the vertical axis.
• The line of collimation must be perpendicular to the hori-
zontal axis at its intersection with the vertical axis.
• Horizontal axis must be perpendicular to vertical axis.
• Axis of altitude level (telescope level) must be parallel to
line of collimation.
• Vertical circle vernier must read zero when the line of
collimation is horizontal.
Sources of Error in Theodolite Work
1. Instrumental
2. Personal
3. Natural
Instrumental Errors
These are due to:
1. Imperfect adjustment of the instrument.
2. Structural defects in instrument
3. Imperfections due to wear.
• Error due to imperfect adjustment of plate levels:
The error can be eliminated only by careful leveling
with respect to the altitude bubble if it is in adjust-
ment and can be eliminated by double sighting.
• Error due to line of collimation not being perpen-
dicular to the horizontal axis:
Error, e = b sec a b = Error in collimation
a = Inclination
This error can be eliminated by taking both face
observations.
• Error due to horizontal axis not being perpendicular to
the vertical axis:
Error, e = b tan a This error can be eliminated by taking both face
observations.
• Error due to non-parallelism of the axis of telescope level
and the line of collimation can be eliminated by taking
both face observations.
• Error due to eccentricity of inner and outer axes can
be eliminated by taking the mean of the two vernier
readings.
• Error due to imperfect graduations can be eliminated by
taking mean of several readings distributed over different
portions of the graduated circle.
• Error due to eccentricity of verniers can be eliminated
by reading both the verniers and taking the mean of the
two.
Personal Errors
1. Errors in manipulation:
(a) Inaccurate centering
(b) Inaccurate levelling
(c) Slip
(d) Manipulating wrong tangent screw.
2. Errors in sighting and reading:
(a) Inaccurate bisection of points observed.
(b) Mistakes in setting the vernier.
(c) Parallax: Due to parallax, accurate bisection is
not possible. Error can be eliminated by focusing
eye-piece and objective.
Natural Errors
1. Unequal atmospheric refraction due to high
temperature.
2. Unequal expansion of parts of telescope and circles
due to temperature change.
3. Unequal settlement of tripod.
4. Wind producing vibrations.
Double Sighting
Measurement of horizontal angle or vertical angle twice;
once with the telescope in normal condition and once
with the telescope in inverted condition is called double
sighting.
Traverse Surveying and
Omitted Measurements
1. Introduction: Traversing is that type of survey in
which a number of connected survey lines form the
framework and the directions and the lengths of the
survey lines are measured with the help of an angle
measuring instrument (compass or theodolite) and a
tape (or chain) respectively.
• When the lines form a circuit which ends at the
starting point, it is known as closed traverse.
Part III_Unit 12_Chapter 03.indd 3 5/31/2017 5:01:11 PM
This is suitable for locating the boundaries of
lakes, woods etc., and for the survey of large areas.
• If the lines of survey ends at a point other than the
starting point it is said be an open traverse. This is
suitable for surveying a long narrow strip of land
as required for a road or canal or the coastline.
Methods of Traversing
1. Chain traversing
2. Chain and compass traversing (loose needle method)
3. Transit type traversing
(a) By fast needle method
(b) By measurement of angles between the lines
4. Plane table traversing
Traverse surveying is not limited to any particular geometri-
cal figure as in the case of chain surveying which has sys-
tem of connected triangles.
Chain Traversing
• In this, traversing is done with the chain and tape.
Directions of the lines are fixed entirely by linear or tie
measurements known as chain angles.
• Not suitable for accurate work and generally chain tra-
versing is not used if an angle measurement instrument
such as compass or theodolite are available.
Chain and Compass Traversing
Linear measurements are done with the help of chain or
tape and the bearings are measured with compass. Both FB
and BB are observed at each station.
Transit Type Traversing
1. Fast needle method:
• Magnetic bearings of traverse lines are measured
by a theodolite fitted with a compass with refer -
ence to the direction of magnetic meridian estab-
lished at the first station.
• In direct method with transiting, telescope will be
normal at one station and inverted at the next station.
• Direct method without transiting is the most satis-
factory method in which 180° correction is neces-
sary only at 2nd, 4th and 6th station and so on. Add
180° if the reading of vernier < 180°. Subtract 180°
if it is more than 180°.
2. Direct observation of angles: Angles are directly
measured with theodolites. Traversing is done by:
(a) Included angles
(b) Deflection angles
• Deflection angle is the angle, which a survey
line makes with the prolongation of the pre-
vious line. More suitable for survey of roads,
railways, pipe-lines, etc.
• If the direction of progress is counter-
clockwise and the angles measured clockwise
are directly the interior angles.
• If the direction of progress is clockwise and
hence the angles measured clockwise are exte-
rior angles.
Checks in Closed Traverse
Two kinds of errors are involved in traversing.
Linear Error
This shall be rectified by measuring each survey line for
second time. Preferably in the reverse direction on different
dates and by different parties.
Angular Error
1. Traverse by included angles:
• If the interior angles are measured, sum of interior
angles = (2N – 4) 90°.
• If the exterior angles are measured, sum of exterior
angles = (2N + 4) 90°.
N = Number of sides of the traverse.
2. Traverse by deflection angles:
S Deflection Angles = 360°
[Right hand deflection angles as ‘ +’, Left hand deflec-
tion angles as ‘–’]
3. Traverse by direct observation of bearings: Last line
FB = (Last line BB measured at the initial station ± 180°).
Plotting a Traverse Survey
Angle and Distance Method
This method is suitable for small surveys. Distance between
stations are laid off to scale and angles are plotted by one of
the following methods:
1. By protractor
2. By the tangent of the angle
3. By the chord of the angle
Coordinate Method
This method is the most practical and accurate one for plot-
ting traverse or any other extensive system of horizontal
control. Survey stations are plotted by calculating their co-
ordinates. Advantage of this method is that the closing error
can be eliminated by balancing prior to plotting.
1. Dependent or consecutive co-ordinates (latitude
or departure):
• Latitude (L) of a survey line may be defined as its
co-ordinate length measured parallel to an assumed
meridian direction.
• Latitude is positive when measured northward
(upward) and is termed as northing. It is nega-
tive when measured southward (downward) and is
termed as southing.
Part III_Unit 12_Chapter 03.indd 4 5/31/2017 5:01:11 PM
Page 5
? Theodolite survey ? Traverse surveying and omitted
measurements
CHAPTER HIGHLIGHTS
THeodoLite Survey
Introduction
Horizontal angles can be measured by compass. But to get
precise readings and to measure horizontal and vertical angles
another instrument called theodolite is used. It can be used for
laying off horizontal angles, locating points on line, prolong-
ing survey lines, establishing grades, determining diff erence
in elevation, setting out curves, etc.
Theodolites
1. Transit theodolite or transit: In transit theodolite
the line of sight can be reversed by revolving the
telescope through 180° in the vertical plane and is
commonly used.
2. Non-transit theodolite: These are either plain
theodolites or Y-theodolites in which the telescope
cannot be transited.
Parts of Transit Theodolite
1. Telescope: It is mounted on a spindle known as
horizontal axis or trunnion axis and internal focusing
type is widely used.
2. V ertical circle: It is a circular graduated arc attached
to the trunnion axis of the telescope and operated by
means of vertical circle clamp and its corresponding
slow motion or tangent screw. The circle is graduated
from 0°–360° in clockwise or it is divided into four
quadrants.
3. Index frame (T-frame or vernier frame): It is
T -shaped frame consisting of a vertical leg known as
clipping arm and a horizontal bar known as vernier
arm or index arm whose two extremities are fi tted
with verniers to read vertical circle. Clip screw is
used for slight adjustment. Altitude bubble is placed
on the top of the index frame.
4. The standards (or A-frame): Two resembling letter
‘A ’ are mounted on the upper plates. The trunnion axis,
T-frames and the arm of vertical circle clamp are
attached to the A-frame.
5. Levelling head: It consists of two parallel triangular
plates known as plates. Its functions are:
(a) To support main part of instrument.
(b) To attach the theodolite to the tripod.
(c) To provide a means for leveling the theodolite.
6. Lower plate (or scale plate): Lower plate carries
a lower clamp screw and a corresponding tangent
screw to rotate the plate and fi x at any position. Size
of theodolite is represented by the size of scale plate.
7. Upper plate (or vernier plate): This is connected to
inner axis and carries two verniers and also an upper
clamp screw and a corresponding tangent screw.
• On clamping upper and unclamping the lower clamp,
instrument rotates on its outer axis without any relative
motion between the plates.
• Lower clamp is clamped and upper unclamped, instru-
ment rotates on inner axis with relative motion between
vernier and scale.
Theodolite, Traverse Survey
and Omitted Measurements
Part III_Unit 12_Chapter 03.indd 1 5/31/2017 5:01:10 PM
• For using any tangent screw, its corresponding clamp
screw must be tightened.
8. Plate levels: These are carried by the upper plates
which are perpendicular to each other with one of
them parallel to turnion axis. These help the telescope
to settle in exact vertical position.
9. Tripod: It is a stand on which theodolite is mounted
10. Plumb bob: It is tool a having a cone shaped weight
attached to a long thread. The weight is hanged using
thread from centre of tripod stand and centering of
the odilite is done.
11. Compass: Simpler theodolites may contain circular
compass box in the centre of upper plate. It is useful
when we select north as the reference meridian.
Definitions and Terms
1. Vertical axis: This is the axis about which the
instrument can be rotated in a horizontal plane.
Lower and upper plates rotate about this axis. It is
also known as azimuth axis.
2. Horizontal axis or trunnion axis: is the axis about
which the telescope and the vertical circle rotate in
the vertical plane.
3. Line of sight or line of collimation: is the line
passing through the intersection of the horizontal
and vertical cross-hairs and the optical centre of the
object glass and its continuation.
4. Axis of level tube or bubble line: It is a straight line
tangential to the longitudinal curve of the level tube at
its centre. It is horizontal when the bubble is central.
5. Transiting: also known as plunging or reversing. It is
the process of turning the telescope in vertical plane
through 180° about the trunnion axis.
6. Swinging the telescope: The process of turning the
telescope in horizontal plane. If rotated clockwise,
it is called right swing. If rotated in anticlockwise
direction, it is called left swing.
7. Face left observation: If the face of vertical circle
is to the left of the observer, the observation angle is
called as face left observation.
8. Face right observation: If the face of vertical circle
is to the right of the observer.
9. Telescope normal or direct: Telescope is said to be
normal when the face of the vertical circle is to the
left side and the bubble is up.
10. Telescope inverted or reversed: When face of
vertical circle is to the right and the bubble down.
11. Changing face: It is an operation of bringing the face
of the telescope from left to right and vice versa.
Adjustments in Theodolite
Temporary Adjustments of Theodolite
• Setting: The instrument to be set over the station, center-
ing by a plumb bob and approximate levelling with the
help of tripod legs.
• Levelling: Done using leveling screws or foot screws to
make the vertical axis truly vertical.
• Elimination of parallax: Parallax is a condition aris-
ing when the image formed by the objective is not in the
plane of the cross hairs.
It is done in two steps:
1. Focusing the eye-piece: For distinct vision of the
cross hairs.
2. Focusing the objective: Focusing screw is turned till
the image appears clear and sharp and is in the plane
of cross hairs.
Permanent Adjustments of Theodolite
1. Adjustment of plate level: To make the axis of plate
bubble perpendicular to the vertical axis when the
bubble is central.
2. Adjustment of line of sight: Line of sight should
coincide with optical axis of the telescope.
3. Adjustment of horizontal axis: Horizontal axis
should be perpendicular to the vertical axis. Spire test
is done.
4. Adjustment of altitude level and vertical index
frame: Clip and tangent screws are used for adjusting
vertical frame and levelling of altitude.
Operations done with Theodolite
Measurement of Horizontal Angle
Repetition Method Used to measure horizontal angle to a
finer degree of accuracy than that obtained with the least
count of vernier.
Errors eliminated:
1. Errors due to eccentricity of verniers and centres are
eliminated by taking both vernier readings.
2. Errors due to in adjustment of line of collimation and
the trunnion axis are eliminated by taking both face
readings.
3. Error due to inaccurate graduations are eliminated by
taking the readings at different parts of the circle.
4. Errors due to inaccurate bisection of the object,
eccentric centering, etc., may be to some extent
counter-balanced in different observations.
5. Errors due to slip, displacement of station signals and
want of verticality of the vertical axis, etc., are not
eliminated since they are all cumulative.
Direction Method or Reiteration Method This is also
known as method of series and is suitable for the measure-
ment of the angles of a group having a common vertex point
and finally the horizon is closed such that sum of angles
equal to 360°.
1. Measurement of vertical angles.
2. Measuring magnetic bearing of a line.
Part III_Unit 12_Chapter 03.indd 2 5/31/2017 5:01:11 PM
3. Measuring direct angles and deflection angles.
4. To prolong a straight line.
5. To locate point of intersection of two straight lines.
6. To lay off a horizontal angle.
7. To lay off an angle by repetition.
Fundamental Lines and Their
Desired Relations
1. Vertical axis
2. Horizontal axis (trunnion or transit axis)
3. Line of collimation (line of sight)
4. Axis of plate level
5. Axis of altitude level
When the theodolite is in proper adjustment:
• The axis of the plate level must lie in a plane perpendicu-
lar to the vertical axis.
• The line of collimation must be perpendicular to the hori-
zontal axis at its intersection with the vertical axis.
• Horizontal axis must be perpendicular to vertical axis.
• Axis of altitude level (telescope level) must be parallel to
line of collimation.
• Vertical circle vernier must read zero when the line of
collimation is horizontal.
Sources of Error in Theodolite Work
1. Instrumental
2. Personal
3. Natural
Instrumental Errors
These are due to:
1. Imperfect adjustment of the instrument.
2. Structural defects in instrument
3. Imperfections due to wear.
• Error due to imperfect adjustment of plate levels:
The error can be eliminated only by careful leveling
with respect to the altitude bubble if it is in adjust-
ment and can be eliminated by double sighting.
• Error due to line of collimation not being perpen-
dicular to the horizontal axis:
Error, e = b sec a b = Error in collimation
a = Inclination
This error can be eliminated by taking both face
observations.
• Error due to horizontal axis not being perpendicular to
the vertical axis:
Error, e = b tan a This error can be eliminated by taking both face
observations.
• Error due to non-parallelism of the axis of telescope level
and the line of collimation can be eliminated by taking
both face observations.
• Error due to eccentricity of inner and outer axes can
be eliminated by taking the mean of the two vernier
readings.
• Error due to imperfect graduations can be eliminated by
taking mean of several readings distributed over different
portions of the graduated circle.
• Error due to eccentricity of verniers can be eliminated
by reading both the verniers and taking the mean of the
two.
Personal Errors
1. Errors in manipulation:
(a) Inaccurate centering
(b) Inaccurate levelling
(c) Slip
(d) Manipulating wrong tangent screw.
2. Errors in sighting and reading:
(a) Inaccurate bisection of points observed.
(b) Mistakes in setting the vernier.
(c) Parallax: Due to parallax, accurate bisection is
not possible. Error can be eliminated by focusing
eye-piece and objective.
Natural Errors
1. Unequal atmospheric refraction due to high
temperature.
2. Unequal expansion of parts of telescope and circles
due to temperature change.
3. Unequal settlement of tripod.
4. Wind producing vibrations.
Double Sighting
Measurement of horizontal angle or vertical angle twice;
once with the telescope in normal condition and once
with the telescope in inverted condition is called double
sighting.
Traverse Surveying and
Omitted Measurements
1. Introduction: Traversing is that type of survey in
which a number of connected survey lines form the
framework and the directions and the lengths of the
survey lines are measured with the help of an angle
measuring instrument (compass or theodolite) and a
tape (or chain) respectively.
• When the lines form a circuit which ends at the
starting point, it is known as closed traverse.
Part III_Unit 12_Chapter 03.indd 3 5/31/2017 5:01:11 PM
This is suitable for locating the boundaries of
lakes, woods etc., and for the survey of large areas.
• If the lines of survey ends at a point other than the
starting point it is said be an open traverse. This is
suitable for surveying a long narrow strip of land
as required for a road or canal or the coastline.
Methods of Traversing
1. Chain traversing
2. Chain and compass traversing (loose needle method)
3. Transit type traversing
(a) By fast needle method
(b) By measurement of angles between the lines
4. Plane table traversing
Traverse surveying is not limited to any particular geometri-
cal figure as in the case of chain surveying which has sys-
tem of connected triangles.
Chain Traversing
• In this, traversing is done with the chain and tape.
Directions of the lines are fixed entirely by linear or tie
measurements known as chain angles.
• Not suitable for accurate work and generally chain tra-
versing is not used if an angle measurement instrument
such as compass or theodolite are available.
Chain and Compass Traversing
Linear measurements are done with the help of chain or
tape and the bearings are measured with compass. Both FB
and BB are observed at each station.
Transit Type Traversing
1. Fast needle method:
• Magnetic bearings of traverse lines are measured
by a theodolite fitted with a compass with refer -
ence to the direction of magnetic meridian estab-
lished at the first station.
• In direct method with transiting, telescope will be
normal at one station and inverted at the next station.
• Direct method without transiting is the most satis-
factory method in which 180° correction is neces-
sary only at 2nd, 4th and 6th station and so on. Add
180° if the reading of vernier < 180°. Subtract 180°
if it is more than 180°.
2. Direct observation of angles: Angles are directly
measured with theodolites. Traversing is done by:
(a) Included angles
(b) Deflection angles
• Deflection angle is the angle, which a survey
line makes with the prolongation of the pre-
vious line. More suitable for survey of roads,
railways, pipe-lines, etc.
• If the direction of progress is counter-
clockwise and the angles measured clockwise
are directly the interior angles.
• If the direction of progress is clockwise and
hence the angles measured clockwise are exte-
rior angles.
Checks in Closed Traverse
Two kinds of errors are involved in traversing.
Linear Error
This shall be rectified by measuring each survey line for
second time. Preferably in the reverse direction on different
dates and by different parties.
Angular Error
1. Traverse by included angles:
• If the interior angles are measured, sum of interior
angles = (2N – 4) 90°.
• If the exterior angles are measured, sum of exterior
angles = (2N + 4) 90°.
N = Number of sides of the traverse.
2. Traverse by deflection angles:
S Deflection Angles = 360°
[Right hand deflection angles as ‘ +’, Left hand deflec-
tion angles as ‘–’]
3. Traverse by direct observation of bearings: Last line
FB = (Last line BB measured at the initial station ± 180°).
Plotting a Traverse Survey
Angle and Distance Method
This method is suitable for small surveys. Distance between
stations are laid off to scale and angles are plotted by one of
the following methods:
1. By protractor
2. By the tangent of the angle
3. By the chord of the angle
Coordinate Method
This method is the most practical and accurate one for plot-
ting traverse or any other extensive system of horizontal
control. Survey stations are plotted by calculating their co-
ordinates. Advantage of this method is that the closing error
can be eliminated by balancing prior to plotting.
1. Dependent or consecutive co-ordinates (latitude
or departure):
• Latitude (L) of a survey line may be defined as its
co-ordinate length measured parallel to an assumed
meridian direction.
• Latitude is positive when measured northward
(upward) and is termed as northing. It is nega-
tive when measured southward (downward) and is
termed as southing.
Part III_Unit 12_Chapter 03.indd 4 5/31/2017 5:01:11 PM
• Departure (D) of survey line may be defined as its
co-ordinate length measured at right angles to the
meridian direction.
• Departure of the line is positive when measured
eastward and is termed as easting. It is negative
when measured westward and is termed as westing.
From the figure,
L = + lcos q D = + lsin q I
D = l sin?
(+, -) (+, +)
(-, +) (-, -)
L = l cos?
?
2. Independent co-ordinates: Total latitude and
departure of any point with respect to a common
origin are known as independent co-ordinates or total
co-ordinates of the point.
Closing Error
If a closed traverse is plotted according to the field measure-
ments, the end point of the traverse will not coincide exactly with
the starting point owing to the errors in the field measurements
of angles and distances. This error is known as closing error.
Closing error,
eL D =+ () () SS
22
Direction of closing error, tand =
?
?
D
L
Relative error of closure
=
Error of closure
Perimeter of traverse
=
e
p
p
e
=
1
d
Closing
error
SL
SD
• For a closed traverse, SL = SD = 0
SOLVED EXAMPLES
Example 1
A closed traverse was conducted round an obstacle and the
following observations were made and length and bearing
of DA have been omitted. Calculate length and bearing of
the line DA.
Line Length (m) Bearing
AB 201.0 85°20'
BC 240.0 22°40'
CD 194.0 220°0'
DA ? ?
(A) 190.23 m and 242°2'
(B) 87.85 m and 180°28'
(C) 56.71 m and 136°6'
(D) 49.67 m and 44°24'
Solution
Given closed traverse ? SL = SD = 0
Latitude of AB = AB cos q
= +201cos 85°20'
Departure of AB = AB sin q = +201 sin 85°20'
Line Latitude (m) Departure (m)
+ – + –
AB 16.35 200.33
BC 221.46 92.49
CD 148.6 124.7
Sum 237.81 148.6 292.82 124.7
SL ' = 89.21 SD ' = 168.12
Latitude of DA = –SL' = –89.21 m
Departure of DA = –SD' = –168.12 m
Since both latitude and departure are negative. DA lies in
SW Quadrant. (IIIQ)
tan q =
Departure
Latitude
=
168.12
89.21
= 1.88
q = 62°2'
Bearing of DA = S62°2'W = 242°2'
Length of DA =
Latitude
cos ?
=
° '
89 21
62 2
.
cos( )
=190.23 m.
Hence, the correct answer is option (A).
Part III_Unit 12_Chapter 03.indd 5 5/31/2017 5:01:12 PM
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