The document provides an extensive overview of compass surveying, detailing the definition of meridians, bearings, and azimuths. It explains different types of compasses, including the Brunton compass, and covers topics such as local attraction, magnetic declination, and errors in compass surveys. The document is aimed at understanding compass surveying techniques and their application in various surveying tasks.

1. 4. The Compass (7 hours)
4. The Compass
4.1 Introduction
4.2 The Brunton compass, The
bearings, azimuth
4.3 Local attraction, magnetic
declination, typical compass
problem.
4.4 Compass traversing, errors and
adjustment.
4.5 Traverse plotting

2. 4. The Compass
4.1 Introduction, definition of meridian, bearing and azimuth
Introduction:
The branch of surveying in which directions of survey lines are
determined by a compass and their lengths by chaining or taping
directly on the surface of the earth is called compass surveying.
It is adopted when the area is comparatively large and free from
magnetic effects.
Uses of Compass
• To find the magnetic bearing (direction) of a line.
• In reconnaissance.
• To fill the detail.
• To find the direction by navigators.
• To find the direction during the night marching.
• Rough engineering survey.

3. 4. The Compass
4.1 Introduction, definition of meridian, bearing and azimuth
Meridians and Bearings
A great circle, which passes through true north and true south is known as
meridian. The fixed direction on surface of the earth, with reference to
which, bearings of survey lines are expressed, is called a Meridian.
The horizontal angle between the reference meridian and the survey line
measured in a clockwise or anticlockwise direction is called Bearing.
Types of Meridian
a) True Meridian
b) Magnetic Meridian
c) Grid Meridian
d) Arbitrary Direction

4. 4. The Compass
a) True Meridian
• The line of intersection of the earth
surface by a plane containing North
Pole, South Pole and observer’s position
is called True Meridian or Geographical
Meridian.
• It represents the true north-south
direction at the plane.
• True meridian at a point is fixed and
does not change with time.
• It can be determined by astronomical
observations to the importance survey
work to determine the absolute position
of different points or lines.
4.1 Introduction, definition of meridian, bearing and azimuth

5. 4. The Compass
4.1 Introduction, definition of meridian, bearing and
azimuth
b) Magnetic Meridian
The direction indicates by a freely suspended and
properly balanced magnetic needle unaffected by local
attractive force is called Magnetic Meridian.
It can be determine by using magnetic compass or
needle.
Generally it is used in less precise survey work to fix
the location of points.

6. 4. The Compass
4.1 Introduction, definition of meridian, bearing and azimuth
c) Grid Meridian
Sometimes for preparing a map some state agencies assume several
lines parallel to the true meridian for particular zone, these lines are
known as grid line, and the central line is called grid meridian.
Grid meridian is the reference meridian for a country on a state survey
map. For survey of country the true meridian of central place is
regarded as the reference meridian. All other meridian in the country
is assumed parallel to the grid meridian. Generally rectangular grids
are plotted on the map.

7. 4. The Compass
4.1 Introduction, definition of meridian, bearing and azimuth
d) Arbitrary Direction
It is only suitable direction towards a permanent prominent work or
signal such as temple, elevated water tank, church, electric pole etc.
for better orientation; it is advisable to select an arbitrary median
roughly along the general direction of the true meridian. It is used to
determine, the relative position of the survey lines and station in small
area.
Sometimes for the survey of a
small area, a convenient
direction is assumed as a
meridian, is known as arbitrary
meridian

8. 4. The Compass
4.1 Introduction, definition of meridian, bearing and azimuth
Bearing
The horizontal angle measured in clockwise or anticlockwise direction
between the meridian and the survey line is termed as bearing.
Different types of bearings are defined based on different criteria.
Types of Bearing
A. Based on meridian
a)Azimuth or True Bearing
b)Magnetic Bearing
c)Grid Bearing
d)Arbitrary Bearing
B. Based on direction
a)Fore Bearing
b)Back Bearing
C. Based on designation
a)Whole Circle Bearing
b)Quadrantal Bearing (or Reduced
Bearing)
A
B
N
W
S
E
θ
θ
O

9. 4. The Compass
a) Azimuth or True Bearing
• The azimuth or true bearing of a line is
its horizontal angle from the North
direction of the true meridian measured
clockwise.
• The horizontal angle between the true
meridian and the survey line is called
True Bearing. The true bearing of a line
can be reestablished even after hundreds
of year because it does not change with
time. It is used in important survey work.
• In Figure, azimuth of a line OA is given
by NOA (= 52°), measured from the
North (Geographical) and that of line OB
is NOB (= 208°).

10. 4. The Compass
b) Magnetic Bearing
The horizontal angle between the
magnetic meridian and survey line is
called Magnetic Bearing. As magnetic
meridian slowly changes with time the
magnetic bearing also changes with time.
Hence it is used for less important survey
work.
c) Grid Bearing
The horizontal angle between the grid meridian and survey line is called
Grid Bearing. It is used in the survey of state.
d) Arbitrary Bearing
The horizontal angle between the arbitrary meridian and survey line is
called Arbitrary Bearing. It is used in the survey of small area.
4.1 Introduction, definition of meridian, bearing and azimuth
magnetic meridian

11. 4. The Compass
4.1 Introduction, definition of meridian, bearing and azimuth
B) Based on Direction
a) Fore Bearing (FB)
The bearings measured in the progress of
surveying i.e. in the forward direction of
survey lines is known as fore bearing or
Forward Bearing.
b) Back Bearing (BB)
The bearing measured in opposite to the
progress of surveying i.e. in backward
direction of survey line is known as Back
Bearing.
A
B C
D
A
B C
D
C
A
B
D
In WCB the difference between FB and BB should be exactly 180°
BB=FB+/-180°

12. 4.1 Introduction, definition of meridian, bearing and
azimuth
BB = FB ± 180
FB = BB ± 180
If BB or FB is less then 180. Than +180. if BB or FB is greater
then 180. Than -180 is required.
4. The Compass

13. 4. The Compass
4.1 Introduction, definition of meridian, bearing and azimuth
C. Based on Designation of Bearings or System of Bearing
a) Whole circle bearing (WCB)
b) Reduced Bearing (RB) or Quadrantal Bearing (QB)
a) Whole Circle Bearing (WCB)
Bearings measured from north in a clockwise direction are termed as
Whole Circle Bearing. The WCB system is also sometimes known as
azimuthal system. In this system bearing of line is measured from the
true north or magnetic north in clockwise direction. The value varies
from 0 degrees to 360 degrees. Referring to figure WCB of lines OA,
OB, OC and OD are α1, α 2, α 3 and α 4 respectively.
A
B
C
D
N
W
S
E
α1
α2
α
3
α4
I
II
IV
III

14. 4. The Compass
4.1 Introduction, definition of meridian, bearing and azimuth
b) Reduced Bearing (RB) or Quadrantal Bearing (QB)
The bearings measured either from the
north or from the south towards east or
west whichever is nearer is known as
Reduced Bearing. The values vary from 0
degrees to 90 degrees for a particular
quadrant. It is also known as Quadrantal
Bearing (QB).
A
B
C
D
N
W
S
E
I
II
IV
III

15. 4. The Compass
The Brunton compass
A Brunton Compass is a
specialized instrument used
widely by those needing to
make an accurate degree and
angle measurements in the
field. It is properly known as
the Brunton Pocket
Transit. David W. Brunton, a
Canadian Geologist invented it
in 1894.
4. The Compass
4.1 Introduction
4.2 The Brunton compass, The bearings, azimuth

16. 4. The Compass
The Brunton compass
Locate North, Set local declination
•Measure Bearings
•Measure Strike and Dip of planes
Strike: Direction of the line of intersection between a tilted plane and
a horizontal plane.
Dip: The maximum slope of a plane, measured from horizontal. The
dip direction is always perpendicular to strike.

17. 4. The Compass
4.2.1 Compass types, system of bearing, conversion from one system to another
Generally there are two types of compass used in compass surveying.
a) Prismatic Compass b) Surveyor Compass
a) Prismatic Compass
• Prismatic Compass comprises of a
magnetic needle attached to the
circular ring made up of aluminium.
• The needle is on the pivot and will
orient itself in the magnetic meridian
Therefore the north and south ends of
the ring will be in this direction.
• The line of sight is defined by the
objective vane and the eye slit, both
attached to the compass box.

18. 4.2.1 Compass types, system of bearing, conversion from one system to another
The object vane consist of a vertical hair attached to a suitable
frame while the eye slit consist of a vertical slit cut in to the upper
assembly of the prism unit, both being hinged to the box.
When an object is sighted, the sight vanes will rotate with respect to
the N-S end of ring through an angle which the line makes with the
magnetic meridian.
4. The Compass

19.  A triangular prism is fitted below the eye
slit, having suitable arrangement for
focusing to suit different eye sight.
 The readings increase in clockwise
direction from 0o at South end, 90o at West
end, 180o at North end and 270o at East
end.
 The object vane frame can be folded on
the glass lid which covers the top at box.
 The object vane presses against a bend
lever which lifts the needle of the pivot
and holds it against the glass lid.
 When bright objects are sighted, dark
glass may be interposed in to the line of
sight.
4. The Compass
4.2.1 Compass types, system of bearing, conversion from one system to another

20. 4. The Compass
4.2.1 Compass types, system of bearing, conversion from one system to another
b) Surveyor’s Compass
Surveyor’s compass is similar in construction to the prismatic
compass with a few modifications stated as below.
• 00 at north and south ends and 900 at
east and west ends in quadrant
bearing (QB) system.
• Diameter of circular ring is about
50mm to 200mm.
• No mirror is attached to the object
vane for sighting object at higher
elevation or depression.
• Readings are taken directly by seeing
through the eye vane consists of a
simple metal vane with a fine sight
hole. Sighting and taking reading
can’t be done simultaneously.

21. 4. The Compass
4.2.1 Compass types, system of bearing, conversion from one system to another
b) Surveyor’s Compass contd…
It is similar to prismatic compass except with a following
modifications.
✓ The graduated ring is directly attached to the circular box and not
with the magnetic needle.
✓ The magnetic needle floats freely over the pivot.
✓ No prism is attached to the eye vane and it is having a narrow
vertical slit

22. Difference
Surveyor’s compass
• The graduated ring and needle are free
to move w.r.t each other.
• Graduation are in QB system and
marked 0⁰ at north & south, 90⁰ at east
& west. East and West is interchanged.
• It measures or gives Q.B. of a line.
• Sighting and reading are not possible
simultaneously.
• The needle is of edge bar type.
• The graduation are engraved erect.
• It cannot be used without tripod.
Prismatic compass
• The graduated ring is attached to the
magnetic needle.
• Graduation are in WCB system and
marked 0⁰ at south and 180⁰ north,
90⁰ at west and 270⁰ is marked at east.
• It measures or gives W.C.B. of a line.
• Sighting and reading are possible
simultaneously.
• The needle is of broad type.
• The graduation are engraved inverted
• It may be used without tripod by
holding in hand.
Comparison between Prismatic Compass and Surveyor’s Compass.

23. 4. The Compass
4.2.1 Compass types, system of bearing, conversion from one system to another
Conversion from one System to Another of Bearing
Conversion of WCB into QB
A
B
C
D
N
W
S
E
A
B
C
D
N
W
S
E
α1
α2
α3
α4
I
IV
II
III
I
IV
II
III
Quadrant WCB (α) RB θ
I 0 to 90⁰ Nθ1E θ1 = α1
II >90⁰ to 180⁰< S θ2E θ2 = 180⁰ - α2
III >180⁰ to 270⁰< S θ3W θ3 = α3 - 180⁰
IV >270⁰ to 360⁰< N θ4W θ4 = 360⁰ - α4

24. 4.2.1 Compass types, system of bearing, conversion from one system to another
Conversion of QB into WCB
A
B
C
D
N
W
S
E
α1
α2
α3
α4
Quadrant RB (θ) WCB (α) WCB(α)
I Nθ1E 0 to 90⁰ α1 = θ1
II S θ2E >90⁰ to 180⁰< α2 = 180⁰ - θ2
III S θ3W >180⁰ to 270⁰< α3 = 180⁰ + θ3
IV N θ4W >270⁰ to 360⁰< θ4 = 360⁰ - α4
I
IV
II
III
A
B
C
D
N
W
S
E
I
IV
II
III
4. The Compass

25. Example:
4.1. Convert the following WCBs to QBs
(a) WCB of AB = 45°30’
(Ans N45°30’E)
(b) WCB of BC = 125°45’
(Ans 180- 125°45’ = S54° 15’E)
(c) WCB of CD = 265°45’
(Ans 265°45’- 180 = S85° 45’W)
(d) WCB of DA = 345°15’
(Ans 360 - 345°15’ = N14° 45’W)
A
B
C
D
N
W
S
E
α1
α2
α3
α4
I
IV
II
III
A
B
C
D
N
W E
I
IV
II
III
4.2. Convert the following QBs to WCBs
a) AB=S 30°30’ E
(Ans 180 - 30°30’ = 149°30’)
b) BC=N 40°30’ W
(Ans 360 - 40°30’ = 319°30’)
4. The Compass

26. Example:
4.3. Fore bearing of the following lines are given. Find back bearing
a) AB=S 40°30’ W
(Ans BB of AB = N40°30’E in QB Systm,
= 40°30’ in WCB System)
b) BC=S 30°30’ E
(Ans BB of BC= N30°30’W in QB System &
= N30°30’W = 360° - 30°30’
= 329°30’ in WCB System)
A
B
C
D
N
W
S
E
α1
α2
α3
α4
I
IV
II
III
C
N
W
S
E
II
IV
B
N
S
W E
B
III
I
A
N
S
W E
N
W
S
E
N
S
W E
N
S
W E
N
S
W E
B
A
C
4. The Compass

27. 4. The Compass (7 hours)
4.3 Local attraction, magnetic
declination, typical compass
problem.
4.4 Compass traversing, errors and
adjustment.
4.5 Traverse plotting

28. 4. The Compass
4.3 Errors in compass survey (local attraction and observational error)
Local Attraction:
Metallic objects and direct-current electricity, both of which cause a
local attraction, affect the main magnetic field. Due to these affect the
magnetic needle does not point to the magnetic north, when it is
under the influence of the external attractive forces. In the presence
of magnetic materials such as iron pipes, steel structures, iron poles,
posts, rails mineral deposits in the ground etc. the needle deflects
from its normal position. Hence

29. 4.3 Errors in compass survey (local attraction and observational error)
• Local attraction is the influence that prevents magnetic needle
pointing to magnetic north pole
• Unavoidable substance that affect are
✓Magnetic ore
✓Underground iron pipes
✓High voltage transmission line
✓Electric pole etc.
• Influence caused by avoidable magnetic substance doesn’t come
under local attraction such as instrument, watch wrist, key etc
4. The Compass

30. • Let Station A be affected by local attraction
• Observed bearing of AB = θ1
• Computed angle B = 1800 + θ1 – ß would not be right.
B
C
A
ß
θ1
B
4.3 Errors in compass survey (local attraction and observational error)
4. The Compass

31. Detection of Local attraction
• By observing the both bearings of line (F.B. & B.B.) and noting
the difference (1800 in case of W.C.B. & equal magnitude in
case of R.B.)
• We confirm the local attraction only if the difference is not
due to observational errors.
• If detected, that has to be eliminated/corrected
Two methods of elimination/correction
• First method (Correction by bearing)
• Second method (Correction by angle)
4.3 Errors in compass survey (local attraction and observational error)
4. The Compass

32. 4. The Compass
4.3 Magnetic declination and dip, variation in magnetic declination,
relation between true bearing, magnetic bearing and declination
Magnetic declination:
Magnetic declination is the horizontal angle
observed from the geodetic meridian to the
magnetic meridian. In other words, the angle
between magnetic meridian and true
meridian is known as a magnetic declination.
An east declination exists if the magnetic
meridian is east of geodetic north; a west
declination occurs if it is west of geodetic
north. East declinations are considered
positive and west declinations negative.

33. 4. The Compass
4.3 Magnetic declination and dip, variation in magnetic declination,
relation between true bearing, magnetic bearing and declination
Relation between true bearing, magnetic
bearing and declination:
True Bearing = Magnetic bearing ± Magnetic Declination
Take + when declination East
Take – when declination West

34. • First method
• Difference of B.B. & F.B. of each lines of traverse is checked,
they differ by correctly or not.
• The one having correct difference means that bearing
measured in those stations are free from local attraction
• Correction are accordingly applied to rest of station.
• If none of the lines have correct difference between F.B. & B.B.,
the one with minimum error is balanced and repeat the similar
procedure.
❖Diagram is good friend again to solve the numerical problem.
4.3 Errors in compass survey (local attraction and observational error)
4. The Compass

35. • Second method
• Based on the fact that the interior angle measured on the
affected station is right.
• All the interior angles are measured
• Check of interior angle
sum of interior angles = (2n-4) ×90°,
where n is number of traverse side
• Errors are distributed and bearing of lines are calculated with
the corrected angles from the lines with unaffected station.
4.3 Errors in compass survey (local attraction and observational error)
4. The Compass

36. 4. The Compass
4.3 Errors in compass survey (local attraction and observational error)
Correction For Local Attraction:
Method-I: FB & BB difference method
In this method, the correction at each station is found. From the fore
bearing and the back bearing of different lines, find the line whose FB
and BB differ exactly by 1800. There is no local attraction at both the
end stations of that line. All the bearings taken at these stations will be
free from local attraction and are therefore correct.
Line FB BB FB - BB
AB 239000’ 600 00’ 1790
BC 290030’ 1100 30’ 1800
CD 61015’ 2410 45’ 1800 30’
DA 141030’ 3200 30’ 1790 00’
A
B
D
C
C
As the FB and BB of the line BC differ by 1800, the stations B and C are free
from local attraction. Therefore, the BB of the line AB (=600) and the FB of
the line CD (=610 15’) are also correct.

37. 4. The Compass
4.3 Errors in compass survey (local attraction and observational error)
Correction For Local Attraction:
Method-II: Included angle method
For applying this method to a traverse, the included angles between
different lines are calculated from the observed bearings, starting from
the unaffected line (or most least affected line), the bearings of all
other lines are determined from the computed angles.
Line FB BB FB - BB
AB 239000’ 600 00’ 1790
BC 290030’ 1100 30’ 1800
CD 61015’ 2410 45’ -1800 30’
DA 141030’ 3200 30’ -1790 00’
A
B
D
C
if there is no line that is unaffected, take the line whose FB and BB differ
least from 1800. Find the mean bearings of that line by distributing half
the error to each of the FB and BB. Take that line as the unaffected line
and apply the above procedure.
1120 00’ 1780 30’

38. 4. The Compass
Calculation of angles from bearings and vice versa
CLOCKWISE TRAVERSE
BB of 1st – FB of 2nd = Interior Ang
FB of 2nd –BB of 1st =Exterior Angle
ANTICLOCKWISE TRAVERSE
FB of 2nd –BB of 1st =Interior Angle
BB of 1st – FB of 2nd = Exterior Angle
IF Calculated Angle value is negative
(less than 0) add 3600
and
greater than 3600 subtract 3600
TOTAL ANGLE =(2N±4)×90
Take +ve for Exterior Angle
Take -ve for interiror Angle

39. Example:4.1 Calculate correct bearing of all line from the given observation below.
FB BB
Line d m d m
AB 122 15 302 15
BC 66 30 243 45
CD 308 0 132 30
DA 198 15 15 30
FB BB FB - BB
Line d m d m Deg Min
AB 122 15 302 15 -180 0
BC 66 30 243 45 -177 15
CD 308 0 132 30 175 30
DA 198 15 15 30 182 45
Solution:
Calculation of Interior Angles:
Int. Ang. B = FB of BC – BB of AB
= 660 30’–3020 15’ = -2350 45’
= 1240 15’
Int. Ang. C = FB of CD – BB of BC
= 3080 00’–2430 45’ = 640 15’ B
A
D
C
+ 3600
Int. Ang. D = FB of DA – BB of CD
= 1980 15’–1320 30’ = 650 45’
Int. Ang. A = FB of AB – BB of DA
= 1220 15’–150 30’ = 1060 45’
Now, sum of internal angle
= ∡A+ ∡B + ∡C+∡D=361ᵒ 00’
True Angle = (2N-4)×90° = 360ᵒ
Total error, e = 361ᵒ 00’ - 360ᵒ = +1° 00’
Correction, c = - 1° 00’
Correction in each angle= -60’/4=-15’
B
A
D
C

40. Example:4.1 Calculate correct bearing of all line from the given observation given
below table
FB BB FB - BB
Line d m d m d m
AB 122 15 302 15 -180 0
BC 66 30 243 45 -177 15
CD 308 0 132 30 175 30
DA 198 15 15 30 182 45
Solution:
Corrected internal angles:
Int. Ang. A = 1060 45’– 15’ = 1060 30’
Int. Ang. B = 1240 15’– 15’ = 1240 00’
Int. Ang. C =640 15’ – 15’ = 640 00’
Int. Ang. D =650 45’– 15’ = 650 30’
Now, sum of internal angle
= ∡A+ ∡B + ∡C+∡D=360ᵒ 00’
B
A
D
C
Calculation of Correct Bearing
From the observation difference of FB and
BB of line AB is exactly 1800, so station A and
B are free from local attraction.
Taking BB of AB (302° 15’) is correct Bearing
Now,
Correct FB of BC = BB of AB +Corr. ∡B
= 302° 15’+ 124° 00’
= 426° 15’ (<360°)
= 426° 15’ - 360° = 66° 15’

41. Example:4.1 Calculate correct bearing of all line from the observation given below
table.
FB BB FB - BB
Line d m d m d m
AB 122 15 302 15 -180 0
BC 66 30 243 45 -177 15
CD 308 0 132 30 175 30
DA 198 15 15 30 182 45
Solution:
Corrected internal angles:
Int. Ang. A = 1060 45’– 15’ = 1060 30’
Int. Ang. B = 1240 15’– 15’ = 1240 00’
Int. Ang. C =640 15’ – 45’ = 640 00’
Int. Ang. D =650 45’– 15’ = 650 30’
Now, sum of internal angle
= ∡A+ ∡B + ∡C+∡D=360ᵒ 00’
B
A
D
C
A
Correct BB of CD = FB of CD ± 180°
= 310° 15’ - 180° = 130° 15’
Correct FB of DA = BB of CD + Corr. ∡D
= 130° 15’ +650 30’ = 195° 45’
Correct BB of DA = 195° 45’-180° = 15° 45’
Correct FB of AB = BB of DA + Corr. ∡A
= 15° 45’ + 1060 30’ = 1220 15’
Correct BB of AB = 1220 15’ + 180°
= 302° 15’ which is Correct bearing
Correct BB of BC = FB of BC ± 180°
= 66° 15’+ 180° =246° 15’
Correct FB of CD = BB of BC +Corr. ∡C
= 246° 15’+ 64° 00’= 310° 15’

42. 4. The Compass
Line
FB BB
Obs. Ang. Corrn.
Corrected
Ang.
Corrected Bearing
d m d m FB BB
AB 122 15 302 15 A 106° 45’ - 15’ 106° 30’ 122° 15’ 302° 15’
BC 66 30 243 45 B 124° 15’ - 15’ 124° 00’ 66° 15’ 246° 15’
CD 308 0 132 30 C 64° 15’ - 15’ 64° 00’ 310° 15’ 130° 15’
DA 198 15 15 30 D 65° 45’ - 15’ 65° 30’ 195° 45’ 15° 15’

43. Example:4.2 Calculate true bearing of all line from the observation given below
table. If declination of AB is 30 W.
FB BB
Line d m d m
AB 66 30 243 45
BC 308 0 132 30
CD 198 15 16 30
DA 122 15 302 15
Solution:
Calculation of Correct Bearing
From the observation difference of FB
and BB of line DA is exactly 1800, so
station A and D are free from local
attraction. Hence FB of AB, BB of AD, FB
of DA and BB of CD is correct.
Now, FB of AB (66° 30’) is correct
Bearing.
BB of AB = FB of AB ± 180°
= 66° 30’ + 180° = 246° 30’
A
D
C
B
But observe BB of AB = 243° 45’
∴ Difference =246°30’- 243° 45’= + 2° 45’
Correct FB of BC = Obs. FB of BC + 2° 45’
= 308°+ 2° 45’ = 310° 45’
Correct BB of BC = 310° 45’ - 180°
= 130° 45’
But observe BB of BC = 132° 30’
∴ Difference =130°45’- 132° 30’ = -1° 45’
Correct FB of CD = Obs. FB of CD - 1° 45’
= 198° 15’- 1° 45’ = 196° 30’
Correct BB of CD =196° 30’ - 180°
= 16° 30’ = Obs. BB of CD
FB BB FB - BB
Line d m d m d m
AB 66 30 243 45 -179 15
BC 308 0 132 30 179 30
CD 198 15 16 30 181 45
DA 122 15 302 15 -180 00

44. 4. The Compass
FB BB FB - BB Corrected Bearing
Line d m d m d m FB BB
AB 66 30 243 45 -179 15 66° 30’ 246° 30’
BC 308 0 132 30 179 30 310° 45’ 130° 45’
CD 198 15 16 30 181 45 196° 30’ 16° 30’
DA 122 15 302 15 -180 00 122° 15’ 302° 15’

45. 4. The Compass
4.5 Errors in compass survey (local attraction and observational error)
Example: The following FB and BB were observed in a traverse survey,
where local attraction was suspected. Compute the corrected bearing
of the all the traverse line.
Line FB BB
AB 191030' 13000'
BC 69030' 246030'
CD 32015' 210030'
DE 262045' 80045'
EA 230015' 53000'
Solution: Since no line has a difference of 1800 in
its FB and BB, first included angles are to be
calculated.
So interior angle at A=FB of AB – BB of EA
=191030'- 53000' =138030'
B
E
C
A
D
Line
Obs FB Obs FB
Line
Bearing Diff.
° ' ° ' ° '
AB 191 30 13 0 AB 178 30
BC 69 30 246 30 BC -177 0
CD 32 15 210 30 CD -178 -15
DE 262 45 80 45 DE 182 0
EA 230 15 53 0 EA 177 15
Interior angle at B = 69030'-13000' = 56030'
Interior angle at C = 32015'- 246030' = -214015‘
Interior angle at C = 3600 - 214015' = 145045'
Interior angle at D = 262045'- 210030' = 52015'

46. 4. The Compass
4.5 Errors in compass survey (local attraction and observational error)
By observing it is found that AB has the least difference from 1800 in
its FB and BB, so first of all error is distributed equally in its FB and BB.
Difference=191030'-13000'=178030'
Error= 178030'-180000'= - 01030', negative error, correction must be positive
So corrected FB of AB = 191030'+ (01030')/2 = 192015'
And corrected BB of AB = 192015' -180000'=12015'
Line
Observed FB
(WCB)
Observed FB
(WCB) Line
Bearing Diff. Observed HA
Corre
ction
Corrected
HA
° ' ° ' ° ' Stn. ° ' (-) ° '
AB 191 30 13 0 AB 178 30 A 138 30 -30' 138 0
BC 69 30 246 30 BC -177 0 B 56 30 -30' 56 0
CD 32 15 210 30 CD -178 -15 C 145 45 -30' 145 15
DE 262 45 80 45 DE 182 0 D 52 15 -30' 51 45
EA 230 15 53 0 EA 177 15 E 149 30 -30' 149 0
542 30 540 0

47. B
E
A
D
4.5 Errors in compass survey (local attraction and observational error)
Corrected BB of AB = 192015' -180000'=12015'
Again,
Corrected FB of BC = Corrected FB of AB+ interior angle at B±1800 or -5400
OR
Corrected FB of BC = BB of AB + interior angle at B)
=12015'+56000'=68015'
Corrected FB of CD = BB of BC +angle C
=68015‘+1800 +145015‘-360°= 33030'
Corrected FB of DE = BB of CD+ angle D
=33030'+1800 +51045'= 265015'
Corrected FB of EA = BB of DE + angle E
=265015'-1800 +149000'= 234015'
Corrected FB of AB = BB of EA+ angle A
=234015'-1800 +138000'= 192015', Hence checked
4. The Compass
C
Corrected
HA
° '
138 0
56 0
145 15
51 45
149 0
540 0

48. 4. The Compass
4.5 Errors in compass survey (local attraction and observational error)
Again corrected FB of BC= Corrected FB of AB+ interior angle at B±1800
or -5400 =192015'+56000'-1800 =68015'
Corrected FB of CD = FB of BC +angle C± 1800 or -5400
68015'+145015'-1800 = 33030'
Corrected FB of DE = FB of CD+ angle D±1800 or -5400
33030'+51045'+1800 = 265015'
Corrected FB of EA = FB of DE + angle E ± 1800 or -5400
265015'+149000'-1800 = 234015'
Corrected FB of AB = FB of EA+ angle A ± 1800 or -5400
234015'+138000'-1800 = 192015', hence checked
`
Line
Observed
FB (WCB)
Observed
FB (WCB) Line
Bearing
Diff.
Observed HA
Corr
ectio
n
Corrected
HA
Corrected
FB
Corrected
BB
° ' ° ' ° ' Stn. ° ' (-) ° ' ° ' ° '
AB 191 30 13 0 AB 178 30 A 138 30 -30' 138 0 192 15 12 15
BC 69 30 246 30 BC -177 0 B 56 30 -30' 56 0 68 15 248 15
CD 32 15 210 30 CD -178 -15 C 145 45 -30' 145 15 33 30 213 30
DE 262 45 80 45 DE 182 0 D 52 15 -30' 51 45 265 15 85 15
EA 230 15 53 0 EA 177 15 E 149 30 -30' 149 0 234 15 54 15
542 30 540 0

49. 4.6 Field work and field book maintaining
• Field work consists of following steps
Steps:
1. Reconnaissance
2. Marking and Fixing survey station
3. First Compass traversing then only detailing
4. Bearing measurement & distance measurement
• Bearing verification should be done if possible
5. Details measurement
• Offsetting
• Bearing and distance
• Bearings from two points (Intersection by Compass)
• Bearing from one points and distance from other point
4. The Compass
C
B
E
D
A b1
b3
b4
b2
w1
w2

50. 4. The Compass
Field book
• Make a sketch of traverse at first
and observation and
measurement is carried out then
reading and recording as per
given field book below
C
B
E
D
A b1
b3
b4
b2
w1
w2
Line Distance
Bearing
Diff (FB-BB) Remarks
FB BB
AB
BC
CD
DE
EA
Field book for Traversing
4.6 Field work and field book maintaining

51. 4. The Compass
Field book
• Make a sketch of field with all
details and traverse in large size C
B
E
D
A b1
b3
b4
b2
w1
w2
Instrument Station Sighted to Distance Bearing Remarks
E B1 L1 (E-b1) θx
E b4 L2 (E-b4) θy
D b2
D b3
Field book for Detailing
4.6 Field work and field book maintaining

52. 4.7 Computation and plotting a traverse
4. The Compass
Methods of plotting a traverse
The following methods are commonly used for plotting the compass
traverse.
1. Parallel meridian method
2. Included angle method
3. Method of tangents
4. Method of chords
5. Rectangular co-ordinate method

53. 4.7 Computation and plotting a traverse
4. The Compass
1. Parallel meridian method
i) Fixing the starting station (say A), a line
representing the meridian is drawn
through A
ii) The bearing of the first line AB is then
plotted with a protractor.
iii) The length of the line AB is marked off with
a scale. Thus, the point B is located.
iv) The meridian line is drawn at the station B,
and the process is repeated to locate the
station C.
v) Likewise, all other points are located.
B
A
D
C
N
N
N
N

54. 4.7 Computation and plotting a traverse
2. Included angle method
4. The Compass
i) The meridian line is drawn only through the starting point; say A
ii) The bearing of the line AB is plotted and its length is laid off with
a scale, as in the parallel meridian method. Thus the point B is
located.
iii) At the point B, the included angle ABC is plotted with a
protractor and the length BC is measured off with a scale.
iv) Thus the point C is fixed. The process is repeated till the last line
has been drawn.
B
A
D
C
N

55. 4.7 Computation and plotting a traverse
3. Method of tangents
4. The Compass
i) The starting point A is fixed and the meridian
line is drawn at A.
ii) a suitable length (say 100mm) is marked off
the meridian as AB1
iii) A perpendicular is erected at B1 and a
distance B1B2 equal to 100 tan α1 is marked
off.
where α1 is the reduced bearing of the line AB.
iv) The line joining the points A and B2 gives the direction of the line AB.
A distance equal to the length of AB is scaled off and thus the point B
is fixed.
iv. The process is repeated at the point B and continued at other points
till the last line has been drawn.
This method is commonly used for plotting an open traverse.
B
A
D
C
N
B1
B2
α

56. 4.7 Computation and plotting a traverse
4. Method of Chords
4. The Compass
In this Method, the geometrical construction is done making use of the chord
lengths. The position of the point A is fixed and the meridian line is drawn through
A. With A as the centre and a convenient radius (say, 5cm), an arc (c1) is drawn.
With 0 as the centre and a radius equal to (2×5sin (θ/2)), an arc is swung cutting
the arc c1. The line joining point A and the points of intersection of two arc gives
the direction of the line AD. The length AD is scaled off. The process is repeated at
the station B and all other stations.
A
θ0
(2×5×sin 450/2)
= 3.82 cm
(For θ =45)
D
B
r B
A
D
θ rsinθ/2
θ/2
θ/2
Chord r’ = 2rsinθ/2
B
N
0
c1

57. 4.7 Computation and plotting a traverse
5. Rectangular co-ordinate method
• Survey station are plotted by their co-ordinates.
• Very accurate method of plotting
• Closing error is balanced prior to plotting-Biggest
advantage
C
B
A
D
E
4. The Compass
N
E

58. 4. The Compass
Graphical method of distribution of error and permissible precision.
Error
When a close traverse is plotted. The starting and finishing points may
not be coincide. The distance by which the traverse fails to close is said
to the error. such an error may occur due to mistakes made in
measurement of lengths and bearings of the lines or because of an
error in plotting. If the closing error exceeds a certain permissible limit
,the field work should be repeated, but when it is within permissible
level.it is adjusted geographically.
The errors may be classified as
a) Instrumental errors
b) Personal errors
c) Errors due to natural causes
A
D
A’
C
e
E
B

59. 4. The Compass
4.8 Graphical method of distribution of error and permissible precision.
1. Instrumental error
A
D
A’
C
e
E
B
The errors occur due to the faults or wrong
adjustments of the instrument itself They may be
due to the following reasons:
a) The needle not being perfectly straight.
b) improper balancing weight
c) vanes not being perfectly straight and vertical
hair being loose or too thick
d) graduated circle not being horizontal
e) Pivot being bent
f) Sluggish needle
g) Blunt pivot point
h) Plane of sight not being vertical
i) Line of sight not passing through the center of
graduated ring

60. 4. The Compass
4.8 Graphical method of distribution of error and permissible precision.
2. Personal error
it may be due to the following reasons:
a) Carelessness in reading and recording
b) Inaccurate centering
c) Inaccurate leveling of the compass box
d) Inaccurate bisection of signals
A
D
A’
C
e
E
B
3. Errors due to natural causes
The errors due to external or natural forces include the following:
a) Variation in declinations
b) Earthquake
c) Magnetic changes in the atmosphere due to clouds and storms.
d) Local attraction at the site of work due to proximity of the local
attractive forces
e) Irregular variations due to magnetic storms etc.

61. 4. The Compass
4.8 Graphical method of distribution of error and permissible precision.
Permissible Error:
If the misclosure is with in the permissible limit. It is to adjusted otherwise if misclosure is
large or out of permissible limit then work must be repeated. Standard deviation in angular
measurement generally taken equal to 0.5 to 1 times (1 is preferred) the least count of the
instrument used in measuring the angles.
Estimated 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛, 𝑆𝐷 = 𝐿𝑒𝑎𝑠𝑡 𝐶𝑜𝑢𝑛𝑡 (𝐿𝐶) ×1.0
𝑃𝑒𝑟𝑚𝑖𝑠𝑠𝑖𝑏𝑙𝑒 𝐿𝑖𝑚𝑖𝑡 = 𝑆𝐷 × 𝑁𝑜𝑏 𝑜𝑓 𝑆𝑒𝑡𝑢𝑝 𝑜𝑓 𝑖𝑛𝑠𝑡𝑟𝑢𝑚𝑒𝑛𝑡 (𝑁)
𝑃𝑒𝑟𝑚𝑖𝑠𝑠𝑖𝑏𝑙𝑒 𝐿𝑖𝑚𝑖𝑡 = 𝐿𝐶 × 𝑁
Limit of closing Error
Difference of FB and BB = 180° ±2×LC
Angular Error of Closer ≤(30’ × 𝑁 {Permissible Limit = LC 𝑁}
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐶𝑙𝑜𝑠𝑖𝑛𝑔 𝐸𝑟𝑟𝑜𝑟 =
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡𝑟𝑎𝑣𝑒𝑟𝑠𝑒

62. Graphical method of distribution of error and permissible precision.
In plotting a closed traverse, it sometimes to happens that the starting end
points do not coincide and a certain gap or distance remains between these
two points. This distance is referred to as the closing error or the error of
closure.
As shown in figure, the traverse AB1C1D1E1A1 is plotted and A does not
coincide with A1. Hence, the distance AA1 is the closing error and it is
adjusted graphically as follows.
a) A horizontal line is drawn to a difference scale representing the
length of all the lines of the traverse.
b) join the points A and a to get the line Aa.
c) Draw A1a parallel to AA1
d) Draw parallel lines bB1, cC1, dD1 and eE1.
e) At point B1 on the plotted traverse draw a parallel line B1B equal and
parallel to bB1.
f) repeat the procedure at all the stations and get the corrected closed
traverse ABCDE.
• it may be noted that line A1a can be also drawn perpendicular to AA1.
But in that case, the other parallel lines will represent the closing gear in
magnitude only and not in direction. Hence. the direction of closing
error will have to be obtained from the plotted traverse.
A
a
A1
b
B1
c
C1
d
D1
e
E1
e
A
D1
A1
C1
e
E1
B1
E
D
C
B
A
D1
A1
C1
e
E1
B1

63. Class Note and Assignment

64. Example:4.9 Calculate True bearing of all line from the observation given below
table if declination of Line BC is 2° 30’ W
a) Included angle method and
b) Bearing correction method
FB BB
Line d m d m
AB 302 15 122 15
BC 16 30 198 15
CD 132 30 308 0
DA 243 45 66 30
A
B
C
D

65. Instruments for Compass Surveying
Prismatic Compass
Tripod
Chain
Tape
Arrows and Ranging rods