Generally, horizontal distances are measured by direct methods, i.e. laying of chains or tapes on ground. These methods are not always convenient if ground is undulating, rough, difficult and inaccessible. Under se circumstances, indirect methods are used to obtain distances. One such method is ?Tacheometry?.

In this method, distance between upper hair and lower hair, i.e. stadia interval i, on diaphragm of lens system is fixed. The staff intercepts, refore, changes according to distance D and vertical angle ?.

Accuracy is main plus point in case of Simpson?s rule. Due to involvement of odd number of sides and also procedure, accuracy levels in this process are good enough for producing good result.

The area of segment can be found out by using,
A = (2/3)*(O1-(O0+O2/2)). On substitution, we get
A = (2/3)*(45.76-(119.65+32.87/2))
A = -20.34 Sq. m (negative sign has no significance)
A = 20.34 sq. m.

We know that, area by mid-ordinate can be given as, A = d*?O. from this, value of d can be calculated as,
d = A/?O
d = 543.89 / 223.98
d = 2.42m.

The results obtained by Simpson?s rule are more accurate when compared to all cases. The results obtained by using Simpson?s rule are greater or smaller than those obtained by using trapezoidal rule according as curve of boundary is concave or convex towards base line.

The area from offsets can be calculated by using certain rules which include Mid-ordinate rule, Average ordinate rule, Trapezoidal rule, Simpson?s one-third rule, of which mid-ordinate and average ordinate rules come under ordinate rules set.

The magnifying power of eyepiece is also greater than for an ordinary transit to produce a clearer image of staff held far away.

A tacheometer is similar to an ordinary transit odolite, generally a vernier odolite itself, fitted with two stadia wires in addition to central cross-hair. The stadia diaphragm has three horizontal hairs viz., a central horizontal hair and upper and lower stadia hairs.

From geometry, D=1/2 x s x cot ?/2, where, s = distance between targets of subtense bar, and ? = apex angle subtended by targets at O. As ? is small tan ?/2 = ?/2, D = s/?.