Use of analytic lens in tacheometric surveying
Tacheometry is a branch of angular surveying in which the horizontal and vertical distances of points are obtained by instrumental observation. The instrument usually employed in tacheometry is a tacheometer and a levelling staff. A tacheometer in a general sense, is a transit Theodolite having a stadia telescope i.e. a telescope fitted with a stadia diaphragm, i.e. a telescope equipped with two horizontal hairs called stadia hairs in addition to the regular cross- hairs.
The formula for calculating horizontal distance from Instrument to measure point is D = (f/i) S. Cos(squire)θ + (f+d) Cosθ
The vertical component V = (f/i) . S . (Sin2θ/2) + (f+d) Sinθ
Where f/i is multiplying constant and (f+d) is additive constant.
The values of f/i and (f+d) are usually marked on a card attached to the inside of box by the maker. Multiplying constant value is usually 100 and additive constant (f+d) value varying from 30 to 60 cm in the case of an external focusing telescope and in the case of an internal focusing telescope it varies from 8 to 20 cm.
The object of providing an additional convex lens, called an anallatic lens, in the telescope is to eliminate the additive constant (f+d). That means (f+d) will be zero.
The benefit of that is at the time of calculation (f+d)Cosθ and (f+d)Sinθ will be Zero.