Table of Contents
Aim:
To determine the gradient of the line joining the given staff stations A and B and to find the RL of station B.
Instruments Required:
Theodolite, Tape, Peg, Target Levelling staff
Procedure:
 Set up the instrument approximately between the given objects and do the initial adjustments.
 Direct the telescope towards the staff at A and note the central hair reading h_{o}. Find the vertical angles by bisecting the staff at two points in the target leveling staff. The vertical angles may be both at elevation or both at depression or one elevation and one depression.
 Now turn the horizontal plate clockwise and sight towards B. Note the horizontal angle .
 Take the vertical angles at B and find the target distance S.
Take
RL of BM at A = 100.000m
S = m (Target distance)
_{1} & _{2} = Vertical angle to upper and lower targets respectively. h_{1} = Height of lower target above foot of ranging rod
h_{0} = Height of instrument above datum line
V = Level difference between A and B = D tan _{2}
R.L of H.I = R.L. of B.M. + h_{0}
R.L. of B = R.L. of H.I + V h_{1}
Let X = Horizontal distance between A and B Then, from the above figure,
X^{2} = D ^{2} + D ^{2} – 2D D cos
1 2 1 2
where D_{1} =
S1
tan_{1} tan _{2}
and D_{2} =
S2
tan_{1} tan _{2}
, = horizontal angle bet’ A and B
Gradient between A and B = V
X
Practical Applications:
 This method is adopted in obstacles such as steep & broken ground, deep ravines, stretches of water or swamp and so on, which makes chaining difficult or impossible.
 This method is adopted when the theodolite is not provided with a stadia diaphragm.
 This method is also used when the staff is too far from the instrument and it is difficult to read the staff.
TANGENTIAL TACHEOMETRY – TABULAR COLUMN
Staff reading (central hair) at A = h_{o} = m
Face : Left Swing : Left  
Inst at  Sight to  Position of vane  Vertical angle  Horizontal angle  
C  D  Mean  A  B  Mean  
 ‘  “  ‘  “   ‘  “   ‘  “  ‘  “   ‘  “  
P  A  Top vane  0  0  0  0  0  0  0  0  
Bottom vane  
B  Top vane  
Bottom vane  
Face : Right Swing : Right  
P  A  Top vane  0  0  0  0  0  0  0  0  
Bottom vane  
B  Top vane  
Bottom vane 
Result :

 The horizontal distance between A and B ( X ) =
 The horizontal angle between A and B ( ) =
 The RL of B =
 The gradient of the line joining A and B =