Locate a Point at the intersection of two (intersecting) lines:
(i) Set up the instrument at point C; sight the point D and drive the two pegs at the points c and d located on the line CD (which intersects the line AB).
(ii) Drive nails in the centre of the two pegs driven at the points c and d and stretch a wire or string having its two ends held by the said two nails.
(iii) Set up the instrument at the point A and sight the point B. Set a point P where the LOS cuts the stretched wire or string; that newly established point P will be point lying at the intersection of two lines AB and CD.
Horizontal and Vertical Measurement of a Building (using a Theodolite):
Horizontal Measurement of a Building is taken by using the already explained method of (iv) Establishing a line beyond an obstruction e.g. building
Vertical Measurement of a Building is taken by the following method:
Let “H” be the height of a building above a certain Datum e.g. Bench Mark (BM) / Theodolite Station.
“h” is the height of the building above the theodolite’s horizontal axis.
“h1” is the height of the theodolite’s horizontal axis from (i.e. above) the BM.
“h2” is the height of the theodolite’s horizontal axis from (i.e. above) the ground of the building (we suppose that the ground of the building is a little higher than the ground of the theodolite station i.e. h1 > h2 )
“” is the angle observed at the theodolite station, made between the theodolite’s horizontal axis and top-most edge of the building.
“D” is the horizontal distance measured between the theodolite station and nearest base of the building. Now: h = D.tan and H = h + h1 = D.tan + h1
Thus H gives the height of the building above the BM.
Height of the theodolite’s horizontal axis Ht = RL of BM + h1
Total height of the building from its ground = h + h2
Errors in the Theodolite Surveying:
The errors in Theod Surveying are of Four Types: (i) Instrumental Error (ii) Natural Error and (iii) Personal Error (iv) Mistake (Carelessness)
(i) Instrumental Errors: Imperfect adjustment, imperfect LOS, imperfect Horizontal and / or Vertical Axis, eccentricity of the verniers / V.C, imperfect coincidence of verniers, non-adjustment of vertical vernier, etc.
(ii) Natural Errors: Mostly due to Local Attraction; others are due to temperature, wind, rain, refraction and invisible settlement (sinking) of tripod due to soft ground.
(iii) Personal Errors: Inaccurate centering, inaccurate levelling, inaccurate adjustment of the levelling screws, inaccurate use of tangent screws, inaccurate or wrong setting and / or reading of the verniers, inaccurate sighting, inaccurate bisection, etc
(iv) Mistakes: Mostly due to misreading or mis-noting; Reading or noting down the vernier or values wrongly, reading the wrong vernier, turning the wrong tangent screw, sighting the wrong target (if there are a number of targets / ranging rods), not recording (+) / (-) sign for Vertical Angles, missing the right or left deflection angle or missing the opposite face e.g. Face Right
Tacheometry is a branch of Angular Surveying in which the horizontal and vertical distances of the points are obtained by optical means (measured with an optical instrument “Tacheometer”) as opposed to the ordinary slower process of taking the measurements by tape or chain.
 
This Method is:
Rapid and convenient.
Best adapted in obstacles such as steep and broken ground, deep ravines, stretches of water or swamps and so on which make the chaining difficult or impossible,
The primary objective of tacheometry is the preparation of contour-maps or plans requiring both the horizontal as well as vertical control. Also,
Tacheometry (in Greek it means “Quick Measure”) is a system of rapid surveying, by which the positions, both horizontal and vertical, of the points on the earth surface are determined without using a chain or tape or a separate leveling instrument.

Uses of Tacheometry:
  
Survey work in difficult terrain where the direct methods are inconvenient
Detail filling
Checking of already measured distances
Hydrographic surveys and
Establishing secondary control
The instruments required for carrying out Tacheometric surveying:

(1) A Tacheometer (2) A Stadia Rod.Tacheometer is a Theodolite fitted with a Stadia Diaphragm.
Stadia Diaphragm is a circular or elliptical piece of high quality transparent glass equipped with three horizontal hairs and one vertical hair.
The Tacheometer with the Anallatic Lens is famous because its ‘Additive Constant’ is zero. Anallatic Lens is a one concave lens introduced between the eye-piece and the object-piece of the tacheometer to eliminate the additive constant of the instrument. Hence, it simplifies the calculations.
Additive Constant is needed (to be added to a figure) due to “Abberation”;
Abberation and types of Abberation (Four Types: Optical Ab, Spherical Ab, Chromatic Ab, Defocal Ab.)
Stadia Rod Measurement is also known as “Levelling”.
Anallatic (or Anallactic) Lens: It is a convergent lens i.e. bi-convex lens placed between the Object (objective lens) and Diaphragm of the telescope to bring the apex of the triangle having the stadia rod as its base, into the center of the telescope, so as to permit the distance to be measured directly.
Types of Lenses: (1): Convex Lens: (i) Bi-convex Lens (ii) Plano-convex Lens (iii) Concavo-convex Lens. (2): Concave Lens: (i) Bi-concave Lens (ii) Plano-concave Lens (iii) Concavo-convex Lens.

Chief Characteristics of Lenses according to their (above-mentioned) types
Stadia Rod and Marking on it: Two black rectangles in the centre (of width of rod), a white E under it, two black rectangles (placed towards the right edge of rod) under it, a black reverse E just under the above-said rectangles, are painted on the Stadia Rod in a vertical line; Height of one “E” or height of gap between the two “Es” (containing the said two black rectangles) is = 0.005 m = 5 mm. Stadia Rod is 3 or 5 m long with 5 or 15 cm wide, respectively
Methods of Tacheometric Survey:(1) Stadia Hair Method(2) Tangential Method (1) Stadia Hair Method: As the name suggests, theodolite with the Stadia Diaphragm (Three Types of Stadia Diaphragms: Normal, Columnar and Cross-type) is used to find out the Staff Intercept between the lower and upper hairs; central hair reading also is taken.Staff Intercept: It is the difference between the readings of upper hair and that of the lower hair
When the Staff Intercept is more than the whole length .
For inclined sights, readings are taken by usually keeping the staff either vertical or normal to the line of sight.
Stadia Hair Method is the most common method i.e. mostly used in Tacheometric Surveying
Subtense Method

This method is similar to the fixed hair method except that the stadia interval is variable.
hairs so as to set them against the two targets on the staff.

Thus, in this case, is kept fixed while the stadia interval, i.e., the distance between the stadia hairs is variable.

As in this case of fixed hair method, inclined sights can also be taken.
Tangential Method
In this method, the two short stadia hairs are not used, the readings are taken against the horizontal cross-hair.

To measure the staff intercept, two targets of the instruments are, therefore, necessary.

This necessitates the measurement of vertical angles twice for one single observation.
Stadia Hair Method: (a) Fixed Hair Method: In this method, the stadia hairs of the diaphragm are kept fixed i.e. at a constant distance apart and the Staff Intercept varies with the horizontal and vertical position of the staff with respect to the Theodolite. The reading of all the three cross hairs is taken.

Fixed Hair Method: There are Three Cases in this method:
Line of Sight is horizontal w.r.t the ground and Staff is held vertical i.e. LOS ll ground and LOS  staff
Line of Sight is inclined to the staff and staff is held vertical i.e. LOS  ground and LOS  staff
Line of Sight is inclined (w.r.t the ground) and staff is held normal to LOS i.e. LOS  ground and LOS is  staff

The telescopes used in Tacheometric Surveying are of Three Types:
External Focusing Telescope
Internal Focusing Telescope
External Focusing Anallatic Telescope i.e. fitted with Anallatic Lens  known as Possor’s Telescope
 A telescope mostly used for Tacheometric Surveying is an External Focusing Anallatic Telescope

Measuring Rods used in Tacheometric Surveying are of two types:
(i) Levelling Rods (ii) Stadia Rods.
Levelling Rod is also known as Levelling Staff.
Levelling Rods used for the longer distances i.e. more than 100 m are special types of rods and are known as Stadia Rods. Stadia Rods are stronger, longer, wider with larger, thicker and sharper figures / markings painted on the rods and they are usually multi-piece rods: Types: Foldable Type, Sliding Type, Telescopic Type and Multiple-V Type.
For smaller distances i.e. up to 100 m, the rods are graduated in 5 mm. And for longer distances, these are graduated in 1 cm