**Eg:**

The following observations were made in a tacheometric surveying. A tacheometer was set up at the intermediate point on line AB.

Multiplying constant (f /i) = 100, additive constant (f +d) = 0.1

Calculate the horizontal distance AB & RL of station B. RL of station A is 465m.

**Calculation:**

**horizontal distance**

D = (f/i ) S cos²Î¸ + (f +d ) cosÎ¸

Now,

D1 = = (f/i ) S1 cos²Î¸1 + (f +d ) cosÎ¸1

Here,

S1 = staff intercept at station A = 2.425

Î¸1 = Vertical angle = 6°30'

D1 = [(100 ✕ 2.425 ✕ cos² 6°30') + ( 0.1 ✕ cos6°30')]

= [239.39 + 0.0993]

** D1 ** = **239.49 m.**

Similarly,

D2 = [(100 ✕ 1.950 ✕ cos² 9°15') + ( 0.1 ✕ cos9°15')]

= [189.962 + 0.0987]

** D2** = **190.06 m.**

Formula for **vertical distance**

V = [(f/i ) S sin2Î¸ /2 + (f +d ) sinÎ¸]

Now,

V1 = [(f/i ) S1 sin2Î¸1 /2 + (f +d ) sinÎ¸1]

= [ {100 ✕ 2.425 ✕ sin(2 ✕ 6°30') /2} + (0.1 ✕ sin6°30')]

=[ 27.275 + 0.0113]

**V1 = 27.29 m.**

Similarly,

V2 = [(f/i ) S2 sin2Î¸2 /2 + (f +d ) sinÎ¸2]

= [ {100 ✕ 1.95 ✕ sin(2 ✕ 9°15') /2} + (0.1 ✕ sin9°15')]

=[ 30.937 + 0.0161]

**V2 = 30.95 m.**

**RL of a central axis of the instrument at station P**

= [RL at station A + axial hair reading of staff at A - V1]

= [ 465m. + 2.150 - 27.29]

= **439.86m.**

**Find: ðŸ‘‡**

**1**. **Horizontal distance AB**

= [D1 +D2]

= [239.49m. + 190.06m.]

= **429.55m.**

**2**. **RL of station B**

= [RL of instrument axis at P + V2 - axial hair reading of staff at B]

= [ 439.86m. + 30.95m. - 1.865]

= **468.945m.**

**Thank you for going through these calculation steps❤. Have a good day ðŸ˜„.**