TACHEOMETRY
This is the operation of measuring distances by means of stadia hairs.
Measuring the distances using stadia hairs involves setting the instruments at one end of the line being measured and a leveling staff is held vertically at the other end. The points where the stadia hairs cut the staff are read. The difference between the readings is the staff intercept, S. Assuming H is the horizontal distance between the instrument and staff, then
H = KS + (f + C)
Where K = constant multiplier (f +c) = additive constant
Note that K = f/i
Where f = focal length of the objective lens.
i= interval between stadia hairs
The equation above is applied to external focusing telescope, but when an anallactic lens is fitted is the telescope to bring the focal point on the vertical axis and therefore remove the need for additive constant.
H = KS.
But when the ends of the line being measured are on different levels such that the telescope has to be elevated of depressed through an angle of Ө0, the formulae above changes to:
H =KS Cos 2θ`and reduced level:
V = KS Cos Ө sin Ө+ HI – H
HI = height of instrument
h = staff reading
Occasionally, if θ exceeds 450, it is better to tilt the staff so that it is perpendicular to the line of sight. Short sight is therefore attached to the staff to enable this to be done accurately. The method is called normal staffing then the formulae becomes:
H = KS Cos θ+ h sin θ
V = KS sin θ+ HI –– h cos θ