Short Notes for Compass & Plane Table Surveying | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


 ? Compass Surveying ? Plane Table Surveying
CHAPTER HIGHLIGHTS
CoMPass Surveying
Introduction
Chain surveying can be used for relatively small and fl at 
areas. But when large areas are involved, any instrument 
which enables angles or directions of the survey lines are to 
be used. Compass survey is one such instrument in which 
directions of survey lines are measured with compass and 
lengths of lines are measured with a tape or chain. Used to 
run a traverse (open or close).
Types of Meridians
Meridian is any specifi ed direction where bearings (angles) 
are taken relative to that direction.
 1. True meridian: Line joining true north and true 
south. It always converges from North Pole to South 
Pole. Established by astronomical observations.
 2. Magnetic meridian: It is the direction shown by a 
freely fl oating and balanced magnetic needle, free 
from all other attractive forces. Established with 
magnetic compass.
 3. Arbitrary meridian: Any convenient direction 
towards a permanent and prominent mark or signal 
(example like top of a chimney). Used to determine 
the relative positions of lines in a small area.
Types of Bearings
Bearing is an angle between a meridian and survey line. 
 1. True bearing: True bearing of a line is horizontal 
angle between true meridian and the line. Since 
true meridian is fi xed through a point, true bearing 
is constant irrespective of time. (Also known as 
Azimuth).
 2. Magnetic bearing: Magnetic bearing of a line is the 
horizontal angle made with the magnetic meridian. 
Used for small areas and changes with time. Measured 
with magnetic compass. 
 3. Arbitrary bearing: Arbitrary bearing of a line is the 
horizontal angle made with any arbitrary meridian. 
Theodolite is used to measure it. 
System of Bearings
Whole Circle Bearing System (WCB)
or Azimuthal System
 • Bearing of a line is measured with magnetic north in 
clockwise direction. 
 • Bearings vary from 0°-360°.
 • Prismatic compass is graduated in this system. 
Compass and Plane
T able Surveying
Part III_Unit 12_Chapter 02.indd   1 5/31/2017   5:00:46 PM
Page 2


 ? Compass Surveying ? Plane Table Surveying
CHAPTER HIGHLIGHTS
CoMPass Surveying
Introduction
Chain surveying can be used for relatively small and fl at 
areas. But when large areas are involved, any instrument 
which enables angles or directions of the survey lines are to 
be used. Compass survey is one such instrument in which 
directions of survey lines are measured with compass and 
lengths of lines are measured with a tape or chain. Used to 
run a traverse (open or close).
Types of Meridians
Meridian is any specifi ed direction where bearings (angles) 
are taken relative to that direction.
 1. True meridian: Line joining true north and true 
south. It always converges from North Pole to South 
Pole. Established by astronomical observations.
 2. Magnetic meridian: It is the direction shown by a 
freely fl oating and balanced magnetic needle, free 
from all other attractive forces. Established with 
magnetic compass.
 3. Arbitrary meridian: Any convenient direction 
towards a permanent and prominent mark or signal 
(example like top of a chimney). Used to determine 
the relative positions of lines in a small area.
Types of Bearings
Bearing is an angle between a meridian and survey line. 
 1. True bearing: True bearing of a line is horizontal 
angle between true meridian and the line. Since 
true meridian is fi xed through a point, true bearing 
is constant irrespective of time. (Also known as 
Azimuth).
 2. Magnetic bearing: Magnetic bearing of a line is the 
horizontal angle made with the magnetic meridian. 
Used for small areas and changes with time. Measured 
with magnetic compass. 
 3. Arbitrary bearing: Arbitrary bearing of a line is the 
horizontal angle made with any arbitrary meridian. 
Theodolite is used to measure it. 
System of Bearings
Whole Circle Bearing System (WCB)
or Azimuthal System
 • Bearing of a line is measured with magnetic north in 
clockwise direction. 
 • Bearings vary from 0°-360°.
 • Prismatic compass is graduated in this system. 
Compass and Plane
T able Surveying
Part III_Unit 12_Chapter 02.indd   1 5/31/2017   5:00:46 PM
    
N
D
W
C
S
B
E
A
0
4
?
1
?
2
?
3
?
WCB system
Bearing of lines:
OA = q 1
;
OB = q 2
;
OC = q 3
;
OD = q 4
;
Quadrantal Bearing System (QB)
 • Bearing of a line is measured eastward or westward from 
north or south whichever is nearer.
 • Bearings vary from 0°-90°.
 • Observed by surveyors compass.
 • Bearings are called reduced bearings.
N
W
D
C
B
S
E
A
0
I
II III
IV
4
?
1
?
2
?
3
?
QB system
Bearings of lines: 
OA = Nq 1
E
OB = Sq 2
E
OC = Sq 3
W
OD = Nq 4
W 
Conversions of Bearings 
from One System to Other
Conversion of WCB into RB
Line
WCB 
Between (q)
Rule for RB 
or QB Quadrant
OA 0° and 90° WCB (q ) NE(I)
OB 90° and 180° 180° - WCB ( q ) SE (II)
OC 180° and 270° WCB (q ) - 180° SW (III)
OD 270° and 360° 360° - WCB ( q ) NW (IV)
Conversion of RB into WCB
Line RB Rule for WCB WCB Between
OA Nq 1
E RB 0° and 90°
OB Sq 2
E 180° - RB 90° and 180°
OC Sq 3
W 180° + RB 180° and 270°
OD Nq 4
W 360° - RB 270° and 360°
Fore and Back Bearing
 • The bearing of a line measured in the direction of pro-
gress of survey is called fore bearing (FB).
 • The bearing measured in the opposite direction of sur-
vey or in opposite direction to FB is called back bearing  
(BB).
Calculating BB from FB
 1. If FB is given in WCB:
    BB = FB + 180° if FB < 180°
    BB = FB - 180° if FB > 180°
 2. If FB is given in QB:
  To convert to BB, the value of the bearing remains 
same, except that ‘N’ substituted by ‘S’, ‘E’ substituted 
by ‘W’ and vice-versa.
Calculation of Included Angles  
from Bearings
Can be calculated by using diagrams.
 1. If WCB are given:
 (a) Bearing of two lines measured from common 
point
Included angle = FB of one line - FB of other line
Part III_Unit 12_Chapter 02.indd   2 5/31/2017   5:00:47 PM
Page 3


 ? Compass Surveying ? Plane Table Surveying
CHAPTER HIGHLIGHTS
CoMPass Surveying
Introduction
Chain surveying can be used for relatively small and fl at 
areas. But when large areas are involved, any instrument 
which enables angles or directions of the survey lines are to 
be used. Compass survey is one such instrument in which 
directions of survey lines are measured with compass and 
lengths of lines are measured with a tape or chain. Used to 
run a traverse (open or close).
Types of Meridians
Meridian is any specifi ed direction where bearings (angles) 
are taken relative to that direction.
 1. True meridian: Line joining true north and true 
south. It always converges from North Pole to South 
Pole. Established by astronomical observations.
 2. Magnetic meridian: It is the direction shown by a 
freely fl oating and balanced magnetic needle, free 
from all other attractive forces. Established with 
magnetic compass.
 3. Arbitrary meridian: Any convenient direction 
towards a permanent and prominent mark or signal 
(example like top of a chimney). Used to determine 
the relative positions of lines in a small area.
Types of Bearings
Bearing is an angle between a meridian and survey line. 
 1. True bearing: True bearing of a line is horizontal 
angle between true meridian and the line. Since 
true meridian is fi xed through a point, true bearing 
is constant irrespective of time. (Also known as 
Azimuth).
 2. Magnetic bearing: Magnetic bearing of a line is the 
horizontal angle made with the magnetic meridian. 
Used for small areas and changes with time. Measured 
with magnetic compass. 
 3. Arbitrary bearing: Arbitrary bearing of a line is the 
horizontal angle made with any arbitrary meridian. 
Theodolite is used to measure it. 
System of Bearings
Whole Circle Bearing System (WCB)
or Azimuthal System
 • Bearing of a line is measured with magnetic north in 
clockwise direction. 
 • Bearings vary from 0°-360°.
 • Prismatic compass is graduated in this system. 
Compass and Plane
T able Surveying
Part III_Unit 12_Chapter 02.indd   1 5/31/2017   5:00:46 PM
    
N
D
W
C
S
B
E
A
0
4
?
1
?
2
?
3
?
WCB system
Bearing of lines:
OA = q 1
;
OB = q 2
;
OC = q 3
;
OD = q 4
;
Quadrantal Bearing System (QB)
 • Bearing of a line is measured eastward or westward from 
north or south whichever is nearer.
 • Bearings vary from 0°-90°.
 • Observed by surveyors compass.
 • Bearings are called reduced bearings.
N
W
D
C
B
S
E
A
0
I
II III
IV
4
?
1
?
2
?
3
?
QB system
Bearings of lines: 
OA = Nq 1
E
OB = Sq 2
E
OC = Sq 3
W
OD = Nq 4
W 
Conversions of Bearings 
from One System to Other
Conversion of WCB into RB
Line
WCB 
Between (q)
Rule for RB 
or QB Quadrant
OA 0° and 90° WCB (q ) NE(I)
OB 90° and 180° 180° - WCB ( q ) SE (II)
OC 180° and 270° WCB (q ) - 180° SW (III)
OD 270° and 360° 360° - WCB ( q ) NW (IV)
Conversion of RB into WCB
Line RB Rule for WCB WCB Between
OA Nq 1
E RB 0° and 90°
OB Sq 2
E 180° - RB 90° and 180°
OC Sq 3
W 180° + RB 180° and 270°
OD Nq 4
W 360° - RB 270° and 360°
Fore and Back Bearing
 • The bearing of a line measured in the direction of pro-
gress of survey is called fore bearing (FB).
 • The bearing measured in the opposite direction of sur-
vey or in opposite direction to FB is called back bearing  
(BB).
Calculating BB from FB
 1. If FB is given in WCB:
    BB = FB + 180° if FB < 180°
    BB = FB - 180° if FB > 180°
 2. If FB is given in QB:
  To convert to BB, the value of the bearing remains 
same, except that ‘N’ substituted by ‘S’, ‘E’ substituted 
by ‘W’ and vice-versa.
Calculation of Included Angles  
from Bearings
Can be calculated by using diagrams.
 1. If WCB are given:
 (a) Bearing of two lines measured from common 
point
Included angle = FB of one line - FB of other line
Part III_Unit 12_Chapter 02.indd   2 5/31/2017   5:00:47 PM
      
B
E
C
N
1
?
2
?
= a
2
?
1
? -
a
 (b) Bearings of two lines not measured from common 
point.
Included angle = BB of previous line - FB of next line.
 2. If QB or RB are given:
  In case of QB, it is easy to find included angle by 
drawing diagram.
N
B
C B
N
S
C
E W E
1
?
1
?
2
?
2
?
= a
2
?
1
? - = a
1
?
2
? -
a
a
N N
B
E
C
S S
2
?
180 - = a (           )
1
?
2
? -
a
E
B
C
W
1
?
1
?
2
?
180 - = a (           )
1
?
2
? -
a
Calculation of Bearings from Angles
 • Traverse in which included angles between successive 
lines are measured and the bearings of the lines can be 
calculated provided the bearing of any one line is also 
measured.
 • In a closed traverse, clockwise angles will be the interior 
angles if traverse is run in anti-clockwise direction.
Bearing of a line = Bearing of previous line + Included 
angle
 • If the sum is more than 180°, deduct 180°.
 • If the sum is less than 180°, add 180°.
Sum of included angles = (2n - 4)90°
NOTE
Where, n is number of included angles.
Magnetic Compass
 • It gives directly the magnetic bearings of lines.
 • Lines of force of earth’ s magnetic field run generally from 
south to north.
Dip
The angle which the lines of force make with the surface of 
earth is called the angle of dip or simply dip of the needle.
 • At 70° north latitude and 96° west longitudinal, dip will 
be 90° and it is called north magnetic pole. Similarly near 
south magnetic pole dip is 90° (i.e., at Poles)
 • Lines of force are parallel to the surface of the earth only 
at equator.
 • Dip of the needle is zero at equator and needle will remain 
horizontal.
Magnetic Declination
Magnetic declination = True bearing - Magnetic bearing
 • Mariners call declination by the name ‘variation’.
 • If the magnetic meridian is to the right side (eastern side) 
of the true meridian, declination is said to be eastern or 
positive.
 • If the declination is to the left side (western side) of the 
true meridian, it is said to be western or negative.
E
?
W
?
True
meridian
True
meridian Magnetic
meridian
Magnetic
meridian
Declination east Declination west
 • Isogonics line is the line drawn through the points of 
same declination.
Part III_Unit 12_Chapter 02.indd   3 5/31/2017   5:00:47 PM
Page 4


 ? Compass Surveying ? Plane Table Surveying
CHAPTER HIGHLIGHTS
CoMPass Surveying
Introduction
Chain surveying can be used for relatively small and fl at 
areas. But when large areas are involved, any instrument 
which enables angles or directions of the survey lines are to 
be used. Compass survey is one such instrument in which 
directions of survey lines are measured with compass and 
lengths of lines are measured with a tape or chain. Used to 
run a traverse (open or close).
Types of Meridians
Meridian is any specifi ed direction where bearings (angles) 
are taken relative to that direction.
 1. True meridian: Line joining true north and true 
south. It always converges from North Pole to South 
Pole. Established by astronomical observations.
 2. Magnetic meridian: It is the direction shown by a 
freely fl oating and balanced magnetic needle, free 
from all other attractive forces. Established with 
magnetic compass.
 3. Arbitrary meridian: Any convenient direction 
towards a permanent and prominent mark or signal 
(example like top of a chimney). Used to determine 
the relative positions of lines in a small area.
Types of Bearings
Bearing is an angle between a meridian and survey line. 
 1. True bearing: True bearing of a line is horizontal 
angle between true meridian and the line. Since 
true meridian is fi xed through a point, true bearing 
is constant irrespective of time. (Also known as 
Azimuth).
 2. Magnetic bearing: Magnetic bearing of a line is the 
horizontal angle made with the magnetic meridian. 
Used for small areas and changes with time. Measured 
with magnetic compass. 
 3. Arbitrary bearing: Arbitrary bearing of a line is the 
horizontal angle made with any arbitrary meridian. 
Theodolite is used to measure it. 
System of Bearings
Whole Circle Bearing System (WCB)
or Azimuthal System
 • Bearing of a line is measured with magnetic north in 
clockwise direction. 
 • Bearings vary from 0°-360°.
 • Prismatic compass is graduated in this system. 
Compass and Plane
T able Surveying
Part III_Unit 12_Chapter 02.indd   1 5/31/2017   5:00:46 PM
    
N
D
W
C
S
B
E
A
0
4
?
1
?
2
?
3
?
WCB system
Bearing of lines:
OA = q 1
;
OB = q 2
;
OC = q 3
;
OD = q 4
;
Quadrantal Bearing System (QB)
 • Bearing of a line is measured eastward or westward from 
north or south whichever is nearer.
 • Bearings vary from 0°-90°.
 • Observed by surveyors compass.
 • Bearings are called reduced bearings.
N
W
D
C
B
S
E
A
0
I
II III
IV
4
?
1
?
2
?
3
?
QB system
Bearings of lines: 
OA = Nq 1
E
OB = Sq 2
E
OC = Sq 3
W
OD = Nq 4
W 
Conversions of Bearings 
from One System to Other
Conversion of WCB into RB
Line
WCB 
Between (q)
Rule for RB 
or QB Quadrant
OA 0° and 90° WCB (q ) NE(I)
OB 90° and 180° 180° - WCB ( q ) SE (II)
OC 180° and 270° WCB (q ) - 180° SW (III)
OD 270° and 360° 360° - WCB ( q ) NW (IV)
Conversion of RB into WCB
Line RB Rule for WCB WCB Between
OA Nq 1
E RB 0° and 90°
OB Sq 2
E 180° - RB 90° and 180°
OC Sq 3
W 180° + RB 180° and 270°
OD Nq 4
W 360° - RB 270° and 360°
Fore and Back Bearing
 • The bearing of a line measured in the direction of pro-
gress of survey is called fore bearing (FB).
 • The bearing measured in the opposite direction of sur-
vey or in opposite direction to FB is called back bearing  
(BB).
Calculating BB from FB
 1. If FB is given in WCB:
    BB = FB + 180° if FB < 180°
    BB = FB - 180° if FB > 180°
 2. If FB is given in QB:
  To convert to BB, the value of the bearing remains 
same, except that ‘N’ substituted by ‘S’, ‘E’ substituted 
by ‘W’ and vice-versa.
Calculation of Included Angles  
from Bearings
Can be calculated by using diagrams.
 1. If WCB are given:
 (a) Bearing of two lines measured from common 
point
Included angle = FB of one line - FB of other line
Part III_Unit 12_Chapter 02.indd   2 5/31/2017   5:00:47 PM
      
B
E
C
N
1
?
2
?
= a
2
?
1
? -
a
 (b) Bearings of two lines not measured from common 
point.
Included angle = BB of previous line - FB of next line.
 2. If QB or RB are given:
  In case of QB, it is easy to find included angle by 
drawing diagram.
N
B
C B
N
S
C
E W E
1
?
1
?
2
?
2
?
= a
2
?
1
? - = a
1
?
2
? -
a
a
N N
B
E
C
S S
2
?
180 - = a (           )
1
?
2
? -
a
E
B
C
W
1
?
1
?
2
?
180 - = a (           )
1
?
2
? -
a
Calculation of Bearings from Angles
 • Traverse in which included angles between successive 
lines are measured and the bearings of the lines can be 
calculated provided the bearing of any one line is also 
measured.
 • In a closed traverse, clockwise angles will be the interior 
angles if traverse is run in anti-clockwise direction.
Bearing of a line = Bearing of previous line + Included 
angle
 • If the sum is more than 180°, deduct 180°.
 • If the sum is less than 180°, add 180°.
Sum of included angles = (2n - 4)90°
NOTE
Where, n is number of included angles.
Magnetic Compass
 • It gives directly the magnetic bearings of lines.
 • Lines of force of earth’ s magnetic field run generally from 
south to north.
Dip
The angle which the lines of force make with the surface of 
earth is called the angle of dip or simply dip of the needle.
 • At 70° north latitude and 96° west longitudinal, dip will 
be 90° and it is called north magnetic pole. Similarly near 
south magnetic pole dip is 90° (i.e., at Poles)
 • Lines of force are parallel to the surface of the earth only 
at equator.
 • Dip of the needle is zero at equator and needle will remain 
horizontal.
Magnetic Declination
Magnetic declination = True bearing - Magnetic bearing
 • Mariners call declination by the name ‘variation’.
 • If the magnetic meridian is to the right side (eastern side) 
of the true meridian, declination is said to be eastern or 
positive.
 • If the declination is to the left side (western side) of the 
true meridian, it is said to be western or negative.
E
?
W
?
True
meridian
True
meridian Magnetic
meridian
Magnetic
meridian
Declination east Declination west
 • Isogonics line is the line drawn through the points of 
same declination.
Part III_Unit 12_Chapter 02.indd   3 5/31/2017   5:00:47 PM
    
 • Agonic line is the line made up of points having zero 
declination.
 • ‘Magnetic declination’ at a place is not constant but var-
ies from time to time.
Variations in Declination
 1. Diurnal variation:
 • It is the daily variation and more in day and less 
at night.
 • Considerably more in summer than in winter.
 • More at magnetic poles and less at equator.
 • Amount of variation changes year to year.
 2. Annual variation: Variation which has an yearly 
period is known as annual variation. Varies from 
place to place.
 3. Secular variation:
 • It follows the roller coaster (sine-curve) and swings 
like a pendulum.
 • It is variation over a very long period, i.e., approxi-
mately 250 years.
 • Most important in the works of surveyor.
 4. Irregular variation: These variations are due to 
magnetic storms, earthquakes and other solar influences.
Determination of True Bearing
True bearing = Magnetic bearing ± Declination
Use ‘+’ if the declination is to the East.
Use ‘-’ if the declination is to the West. 
SOLVED EXAMPLES
Example 1
What is the true bearing of the line AB. If magnetic bearing 
= 39°25' and magnetic declination is 4°21' E.
(A) 35°4' (B) 43°46'
(C) 30°43' (D) 48°7'
Solution
True bearing is wrt true meridian  
E
A
B
TM
MM
39°25' 4°21'
}
 (for WCB only)
From diagram we can say,
True bearing = Magnetic bearing + Magnetic declination
TB = 39°25' + 4°21'
 = 43°46'.
Hence, the correct answer is option (B).
Example 2
The magnetic bearing of a line AB is S35°24' W. 
Calculate the true bearing if the declination is 5°10' E.
(A) S40°34' E (B) S30°14' E
(C) S40°34' W (D) S30°26' W
Solution
W
B
E
A
TM
TM
MM
MM
35°24'
5°10'
5°10'
From diagram,
TB = MB + Declination
 = S35°24' W + 5°10'
 = S40°34' W.
Hence, the correct answer is option (C).
Comparison of Prismatic Compass and Surveyor’s 
Compass
Object Prismatic Compass Surveyor’s Compass
Bearing WCB (0° to 360°) QB (0°-90°)
Graduations Inverted readings, as 
we have to see them 
through prism
Erect readings
Needle Broad type—filled to 
the bottom of 
aluminium ring.
Edge bar type—also 
acts as an index.
Scale Free to float along with 
the broad type mag-
netic needle
Attached to the box
Sighting 
at object 
and taking 
bearing
Done simultaneously Sighting is to be 
done first and then 
the surveyor has to 
read the northern end 
of the needle
Tripod Not essential Essential
Part III_Unit 12_Chapter 02.indd   4 5/31/2017   5:00:47 PM
Page 5


 ? Compass Surveying ? Plane Table Surveying
CHAPTER HIGHLIGHTS
CoMPass Surveying
Introduction
Chain surveying can be used for relatively small and fl at 
areas. But when large areas are involved, any instrument 
which enables angles or directions of the survey lines are to 
be used. Compass survey is one such instrument in which 
directions of survey lines are measured with compass and 
lengths of lines are measured with a tape or chain. Used to 
run a traverse (open or close).
Types of Meridians
Meridian is any specifi ed direction where bearings (angles) 
are taken relative to that direction.
 1. True meridian: Line joining true north and true 
south. It always converges from North Pole to South 
Pole. Established by astronomical observations.
 2. Magnetic meridian: It is the direction shown by a 
freely fl oating and balanced magnetic needle, free 
from all other attractive forces. Established with 
magnetic compass.
 3. Arbitrary meridian: Any convenient direction 
towards a permanent and prominent mark or signal 
(example like top of a chimney). Used to determine 
the relative positions of lines in a small area.
Types of Bearings
Bearing is an angle between a meridian and survey line. 
 1. True bearing: True bearing of a line is horizontal 
angle between true meridian and the line. Since 
true meridian is fi xed through a point, true bearing 
is constant irrespective of time. (Also known as 
Azimuth).
 2. Magnetic bearing: Magnetic bearing of a line is the 
horizontal angle made with the magnetic meridian. 
Used for small areas and changes with time. Measured 
with magnetic compass. 
 3. Arbitrary bearing: Arbitrary bearing of a line is the 
horizontal angle made with any arbitrary meridian. 
Theodolite is used to measure it. 
System of Bearings
Whole Circle Bearing System (WCB)
or Azimuthal System
 • Bearing of a line is measured with magnetic north in 
clockwise direction. 
 • Bearings vary from 0°-360°.
 • Prismatic compass is graduated in this system. 
Compass and Plane
T able Surveying
Part III_Unit 12_Chapter 02.indd   1 5/31/2017   5:00:46 PM
    
N
D
W
C
S
B
E
A
0
4
?
1
?
2
?
3
?
WCB system
Bearing of lines:
OA = q 1
;
OB = q 2
;
OC = q 3
;
OD = q 4
;
Quadrantal Bearing System (QB)
 • Bearing of a line is measured eastward or westward from 
north or south whichever is nearer.
 • Bearings vary from 0°-90°.
 • Observed by surveyors compass.
 • Bearings are called reduced bearings.
N
W
D
C
B
S
E
A
0
I
II III
IV
4
?
1
?
2
?
3
?
QB system
Bearings of lines: 
OA = Nq 1
E
OB = Sq 2
E
OC = Sq 3
W
OD = Nq 4
W 
Conversions of Bearings 
from One System to Other
Conversion of WCB into RB
Line
WCB 
Between (q)
Rule for RB 
or QB Quadrant
OA 0° and 90° WCB (q ) NE(I)
OB 90° and 180° 180° - WCB ( q ) SE (II)
OC 180° and 270° WCB (q ) - 180° SW (III)
OD 270° and 360° 360° - WCB ( q ) NW (IV)
Conversion of RB into WCB
Line RB Rule for WCB WCB Between
OA Nq 1
E RB 0° and 90°
OB Sq 2
E 180° - RB 90° and 180°
OC Sq 3
W 180° + RB 180° and 270°
OD Nq 4
W 360° - RB 270° and 360°
Fore and Back Bearing
 • The bearing of a line measured in the direction of pro-
gress of survey is called fore bearing (FB).
 • The bearing measured in the opposite direction of sur-
vey or in opposite direction to FB is called back bearing  
(BB).
Calculating BB from FB
 1. If FB is given in WCB:
    BB = FB + 180° if FB < 180°
    BB = FB - 180° if FB > 180°
 2. If FB is given in QB:
  To convert to BB, the value of the bearing remains 
same, except that ‘N’ substituted by ‘S’, ‘E’ substituted 
by ‘W’ and vice-versa.
Calculation of Included Angles  
from Bearings
Can be calculated by using diagrams.
 1. If WCB are given:
 (a) Bearing of two lines measured from common 
point
Included angle = FB of one line - FB of other line
Part III_Unit 12_Chapter 02.indd   2 5/31/2017   5:00:47 PM
      
B
E
C
N
1
?
2
?
= a
2
?
1
? -
a
 (b) Bearings of two lines not measured from common 
point.
Included angle = BB of previous line - FB of next line.
 2. If QB or RB are given:
  In case of QB, it is easy to find included angle by 
drawing diagram.
N
B
C B
N
S
C
E W E
1
?
1
?
2
?
2
?
= a
2
?
1
? - = a
1
?
2
? -
a
a
N N
B
E
C
S S
2
?
180 - = a (           )
1
?
2
? -
a
E
B
C
W
1
?
1
?
2
?
180 - = a (           )
1
?
2
? -
a
Calculation of Bearings from Angles
 • Traverse in which included angles between successive 
lines are measured and the bearings of the lines can be 
calculated provided the bearing of any one line is also 
measured.
 • In a closed traverse, clockwise angles will be the interior 
angles if traverse is run in anti-clockwise direction.
Bearing of a line = Bearing of previous line + Included 
angle
 • If the sum is more than 180°, deduct 180°.
 • If the sum is less than 180°, add 180°.
Sum of included angles = (2n - 4)90°
NOTE
Where, n is number of included angles.
Magnetic Compass
 • It gives directly the magnetic bearings of lines.
 • Lines of force of earth’ s magnetic field run generally from 
south to north.
Dip
The angle which the lines of force make with the surface of 
earth is called the angle of dip or simply dip of the needle.
 • At 70° north latitude and 96° west longitudinal, dip will 
be 90° and it is called north magnetic pole. Similarly near 
south magnetic pole dip is 90° (i.e., at Poles)
 • Lines of force are parallel to the surface of the earth only 
at equator.
 • Dip of the needle is zero at equator and needle will remain 
horizontal.
Magnetic Declination
Magnetic declination = True bearing - Magnetic bearing
 • Mariners call declination by the name ‘variation’.
 • If the magnetic meridian is to the right side (eastern side) 
of the true meridian, declination is said to be eastern or 
positive.
 • If the declination is to the left side (western side) of the 
true meridian, it is said to be western or negative.
E
?
W
?
True
meridian
True
meridian Magnetic
meridian
Magnetic
meridian
Declination east Declination west
 • Isogonics line is the line drawn through the points of 
same declination.
Part III_Unit 12_Chapter 02.indd   3 5/31/2017   5:00:47 PM
    
 • Agonic line is the line made up of points having zero 
declination.
 • ‘Magnetic declination’ at a place is not constant but var-
ies from time to time.
Variations in Declination
 1. Diurnal variation:
 • It is the daily variation and more in day and less 
at night.
 • Considerably more in summer than in winter.
 • More at magnetic poles and less at equator.
 • Amount of variation changes year to year.
 2. Annual variation: Variation which has an yearly 
period is known as annual variation. Varies from 
place to place.
 3. Secular variation:
 • It follows the roller coaster (sine-curve) and swings 
like a pendulum.
 • It is variation over a very long period, i.e., approxi-
mately 250 years.
 • Most important in the works of surveyor.
 4. Irregular variation: These variations are due to 
magnetic storms, earthquakes and other solar influences.
Determination of True Bearing
True bearing = Magnetic bearing ± Declination
Use ‘+’ if the declination is to the East.
Use ‘-’ if the declination is to the West. 
SOLVED EXAMPLES
Example 1
What is the true bearing of the line AB. If magnetic bearing 
= 39°25' and magnetic declination is 4°21' E.
(A) 35°4' (B) 43°46'
(C) 30°43' (D) 48°7'
Solution
True bearing is wrt true meridian  
E
A
B
TM
MM
39°25' 4°21'
}
 (for WCB only)
From diagram we can say,
True bearing = Magnetic bearing + Magnetic declination
TB = 39°25' + 4°21'
 = 43°46'.
Hence, the correct answer is option (B).
Example 2
The magnetic bearing of a line AB is S35°24' W. 
Calculate the true bearing if the declination is 5°10' E.
(A) S40°34' E (B) S30°14' E
(C) S40°34' W (D) S30°26' W
Solution
W
B
E
A
TM
TM
MM
MM
35°24'
5°10'
5°10'
From diagram,
TB = MB + Declination
 = S35°24' W + 5°10'
 = S40°34' W.
Hence, the correct answer is option (C).
Comparison of Prismatic Compass and Surveyor’s 
Compass
Object Prismatic Compass Surveyor’s Compass
Bearing WCB (0° to 360°) QB (0°-90°)
Graduations Inverted readings, as 
we have to see them 
through prism
Erect readings
Needle Broad type—filled to 
the bottom of 
aluminium ring.
Edge bar type—also 
acts as an index.
Scale Free to float along with 
the broad type mag-
netic needle
Attached to the box
Sighting 
at object 
and taking 
bearing
Done simultaneously Sighting is to be 
done first and then 
the surveyor has to 
read the northern end 
of the needle
Tripod Not essential Essential
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Adjustments of Prismatic Compass
 1. Temporary adjustments: Made at every setup of 
instrument
 (a) Centering (over the station): Done by adjusting 
legs of tripod and using plumb bob.
 (b) Leveling: With the help of ball and socket over 
the tripod leveling is done.
 (c) Focusing the prism: Prism is moved until 
graduations are clearly seen.
 2. Permanent adjustments: These are related to the 
instrument and its parts and done when the relations 
between parts are disturbed.
Local Attraction
 • This is a term used to denote the influence of any mag-
netic materials like magnetite in ground, wire carrying 
electric current, steel structures, chains, steep tapes, etc., 
 • If BB – FB ? 180°, then the station has local attraction.
Plane Table Surveying
Introduction
Plane table surveying is a graphical method of survey in 
which the field observations and plotting proceed simul-
taneously. This is most suitable in magnetic areas and for 
small scale maps.
Instruments Used
 1. Plane table: Three distinct types of tables are used. 
 (a) The traverse table: Consists of a small drawing 
board mounted on a tripod. Table is levelled by 
adjusting tripod legs, usually by eye estimation. 
 (b) Johnson table: Consists of a drawing board 
usually 45 × 60 cm or 60 × 75 cm. The head 
consists of a ball and socket joint.
 (c) Coast survey table: This table is superior to the 
above two types and is used for work of high 
precision.
 2. Alidade: It is a straight edge with some form of 
sighting device.
 (a) Plain alidade: Consists of a metal or wooden 
rule with two vanes at the ends. The working 
edge against which lines are drawn is also known 
as ‘beveled edge or edge’.
   It is not very much suitable on hilly area since 
the inclination of the line of sight is limited. 
 (b) Telescopic alidade:
 • Used when it is required to take inclined sights. 
 • Accuracy and range of sights are increased by 
its use. 
 3. Plumbing fork: It is used in large work and is meant 
for centering the table over the point or station 
occupied by the plane table when the plotted position 
of point is already known on the sheet. 
 4. Spirit level: For confirming if the table is properly 
levelled or not. It may be of tabular variety or circular 
type. 
 5. Compass: For orienting the plane table to magnetic 
north. Generally a trough compass is used. 
 6. Drawing paper: Of superior quality for mapping.
Working Operations
 1. Fixing: Fixing table to the tripod.
 2. Setting:
 (a) Levelling the table
 (b) Centering
 (c) Orientation
 3. Sighting the points
Orientation
The process of putting the plane table into some fixed direc-
tion so that the line representing a certain direction on the 
plan is parallel to that direction on the ground. 
This is essential to be fulfilled when more than one 
instrument station is to be used. 
 1. Orientation by trough compass: This is used: 
 • Where speed is more important than accuracy.
 • When there is no second point for orientation 
 • In certain resection problems.
 2. Orientation by back sighting: There are two cases 
in this orientation.
  Case 1: When it is possible to set the plane table 
on the point already plotted on the sheet by way of 
observation from previous station.
  Case 2: When it is not possible to set the plane table 
on the point already plotted. This method is known as 
resection.
Methods of Plane T abling
 1. Radiation.
 2. Intersection.
 3. Traversing.
 4. Resection.
The first two methods are generally employed for locating 
the details while the other two methods are used for locating 
the plane table stations.
Radiation
 • In this method, a ray is drawn from instrument station 
towards the point, distance is measured between station 
and point, and the point is located plotting to some scale 
on the drawing sheet.
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