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Upendra Kumar

                                              WHAT IS THE TACHEOMETRY SURVEY

A tachometry is a branch of angular measurement in which the horizontal and vertical distances of points are obtained by instrumental observation, chaining being thus entirely eliminated. The accuracy of the tacheometer is less than that of chaining, but it is far more rapid in a rough and difficult country where ordinary leveling is tedious chaining is difficult and slow.

                                  PRINCIPLE OF TECHEOMETRY

The principle of techeometry is based on the property of the isosceles triangle where the ratio of the distance of the base from the apex and the length of the base is always constant.


Here O₁a₁a₂,O₁b₁b₂ and O₁c₁c₂ are the isosceles triangles and its base distance from the apex is D₁, D₂ and D₃. The length of the bases or staff intercept is S₁S₂and S₃.
According to the law of isosceles triangle 
D₁/S₁=D₂ /S₂=D₃/S₃= f/i 
Where f =focal length of the objective and i= stadia intercept
f/i is called the multiplying constant.

                                            THEORY OF THE TACHEOMETRY


O= Optical center of object-glass.

A₁,A₂,C= Reading on the staff.

a₁,a₂ and c₁=Bottom, top and central hair on the diaphragm.

a₁,a₂=i= length of the image.

A₁,A₂= staff intercept.

F= Focus

V= Vertical of the instrument.

f= Focal length of the object-glass.

d= distance between the optical center and the vertical axis of the instrument.

u= Distance between optical center and staff.

v=Distance between optical center and image.

In the triangle a₁Oa₂=A₁OA₂

i/s=v/u                                                                                                     (1)

or v= iu/s

we know that property of lenses

1/v+1/u=1/f                                                                                              (2)

putting the value of v in equation (2)

     or           1/iu/s+1/u=1/f

     or             {1/u{s/i+1}=1/f

      or            u= {s/i+1}f                                                                           (3)

      D=           u+d

      D=          {s/i+1}f +d

      = s/if+f+d

       = {f/i}*s+(f+d)

Where f/i is called multiplying constant and is value for analatic lenses =100

 (f+d) is called additive constant and its value is given by tacheometre manufacture.


There are two types of instruments used in the tachometer survey.

1. Tachometer:- Tacheometer is also a transits theodolite having a stadia telescope. A telescope fitted with a stadia diaphragm is called a stadia telescope. If any telescope equipped with two horizontal hairs called stadia hairs to the regular hairs. The additional hairs are equidistant from the central one and are also known as stadia lines. The types of stadia diaphragm


The telescope used in the tacheometer is in anallatic telescope or telescope fitted with an anallatic lense. The value of constant f/i should be 100.
2. Stadia rod.

Stadia rod is used in tacheometric surveying may be folding and 5 cm to 15 cm wide and 3m to 4m to long. It is graduated in meters, decimeters, and centimeters.

Generally, three kinds of the telescope are used in stadia measurement.
1. The external-focusing telescope:-In the external-focusing telescope the diaphragm is to the outer tube and the objective to the inner tube. By turning the focussing screw the distance between the objective and diaphragm altered to form a real image on the plane of the crosshairs.
2. The internal-focusing telescope:-In the internal focussing telescope, the eyepiece, and objective do not move. A double concave lens is fitted with a rack and pinion arrangement between objective and eyepiece. if the focussing screw is turned a real image is formed on the plane of the cross-hair.
3. The anallatic telescope:-The telescope fitted with anallatic telescope is called anallatic telescope.


1. Stadia Method.

2. Tangential Method.

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