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UNIT-4TACHEOMETRYQ1.what are the working method of tachometrylevelling.A1) The various tacheometric methods employ principle in different ways and differ one another in methods of observation and reduction, but maybe classified under two heads: (i) The stadia system. (ii) The tangential system. In the stadia system, observation is taken with the stadia wires of the tacheometer and in the tangential system the angles of elevation are measured from instrument station to the points with a theodolite and their tangents are used to determine horizontal of the telescope for necessary but stadia system needs only one and is more commonly used Q2. What are the basic principle of tacheometry levelling?A2) The underlying principle common to different methods of the tachometer is that horizontal distance between an instrument station and a point as well as the elevation of the point relative to the instrument can be determined from angle subtended at the instrument station by a known distance at the point and vertical angle from instrument to the point. Q3. What are the equation for horizontal line of sight of tacheometry levelling?A3) The principle of stadia tachometer is explained as follows: (Fig.)
Fig-1 principle of stadia tachometer Let O= the optical centre of the object-glass a, b and c= the bottom, top and central hairs at the diagram A, B and C= the points on the staff cut by three lines a b= I the interval between stadia lines. (ab is the length of the image of AB) AB=S=the staff intercept (the differences of the stadia hair readings) f= the focal length of object-glass i.e, the distance between the centre (O) to the principal focus (FG) of the lens. u – the horizontal distance from the optical centre (O) to the staff. v = the horizontal distance from the optical centre (O) to the image of the staff, u and v is called the conjugate focal length of the lens. d = the horizontal distance from the optical centre (O) to the vertical axis of the tachometer. D = the horizontal distance from the vertical axis of the instrument to the staff, 
Reference 1 The constant f/i is called the multiple constant and its value is usually 100, while constant (f+d) is called the additive constant and its value varies from 30 cm to 60 cm in case of the external focusing telescope, it is very small varying from 10 cm to 20 cm and is therefore often ignored. Q4.What is beman stadia arc?A4) It is the type of graduated arc attached to the vertical circle of an alidade or transit to make the computing elevation difference for inclined stadia sights simply. The arc, designed by W. M. Beaman of the U. S. Geological Survey, is that each division on the arc is equal to 100 (1/2 sin 2A), where A = vertical angle. the index is set exactly on graduation and difference in height along an inclined line of sight is obtained by multiplying the stadia intercept by the number of Beaman arc divisionsQ5.Explain substance bar? A5) A subtense bar (fig. is a horizontal staff with targets fixed at a known distance apart. It is about 4m long having a small spirit level and a quick levelling head. A sight rule, provided at its centre, can be placed along the line of sight by viewing the telescope of the theodolite thought the vanes. The bar is mounted on a tripod and is placed at right angles to the line of sight for making observations. After levelling and aligning, it is clamped using a clamp screw. Q6.Explain moving hiar and tangential method of tacheometry levelling?A6) The Tangential System of Tacheometry: This method is used when the telescope is not fitted with a stadia diagram. In this method, the telescope is directed towards staff to which the horizontal and vertical distances are to be measured and two vertical angles to two vanes or targets on the staff at a known distance (S) apart are taken. The horizontal and vertical distances are then calculated as follows: Case 1:When both the observed angles are angles of elevation:
Fig-6 When both the observed angles are angles of elevationIn fig, let O=The instruments station. O’=The position of the instruments axis P= The staff station. ∠AO’Q= θ1= vertical angle to the upper vane. ∠BO’Q= θ2 =” “ “ lower AB=S=the staff intercept. BQ=V= the horizontal distance from the inst, axis to the lower vane. O’Q=D= the horizontal distance from the inst. station O to the staff station P PB= h= the height of the lower vane above the foot of the staff.
Refrence-7 Case II:When both the observed angles are angles of depression: (Fig. 10.11).
Refrence-8 Case III.When one of the observed angles is the angle of elevation and the other an angle of depression:
Refrence-9Q7.Write stadia reduction formulas?A7) stadia work we are concerned with finding two values as follows: (1) horizontal distance from the centre of the instrument to the stadia rod and (2) vertical distance, or elevation difference, between the centre of instrument and middle-hair reading on the rod. To obtain these values, you must use stadia reduction formulas.Stadia Formula for Horizontal Sights.— For a horizontal sight, the distance that we need to determine the horizontal distance between the centre of the instrument and stadia rod. This distance is found by adding the stadia distance to instrument constant as follows:Write ks for the stadia distance and (f + c) for instrument constant. Then the formula for computing horizontal distances when sights are horizontal becomes the following:H=ks +(f+c)Where:h=horizontal distance from the centre of the instrument to a vertical stadia rodk=stadia constant, usually 100s=stadia intervalf + c =instrument constant (zero for internally focusing telescopes; approximately 1 foot for externally focusing telescopes)f =focal lengths of the lensc=distance from the centre of the instrument to the centre of the lensQ8.Explain anallatic lens in external focusing telecscope?A8) An additional convex lens, called an analytic lens, is provided in an external focusing telescope between the eyepiece and object-glass at a fixed distance from the later, to eliminate the additive constant, (f+d), from the distance formula: 
to simplify the calculation work. The analytic lens is seldom placed in internal focussing telescope since the value of the additive constant is only a few centimetres and can be neglected. The disadvantage of the analytics a lens is a reduction in the brilliancy of the image due to increasing observation of light. The value of the additive constant, (δ+d) can be made equal to zero by bringing the apex (G) of geometric angle AGB (Fig. 10. 4) into exact coincidence with the centre on\f the instrument. The theory of analytic lens is explained as follows:
Fig-5 analytic lens Let, S = the staff intercept AB. i = the length of the image of AB i.e. the actual stadia interval when the analytic lens is interposed. i = the length ba of the image of AB when no analytic lens was provided. O = the optical centre of the object-glass. O = the optical centre of the analytic lens e = the distance between the optical centre of the object-glass and the analytic lens. f = to cel length of object-glass. f’ = focal length of the analytic lens. F = Principle focus of the analytic lens. G = the centre of the instrument. d = the distance from the centre of the object-glass top the vertical axis of the instrument. D – the distance from the vertical axis of the instrument to the staff. f1and f2 = the conjugate focal length of the object-glass.k = the distance from the optical centre of the object-glass to the actual image b a.(k— e) and (f2 —e) = the conjugate focal length of the analytic lens.The ray of light from A and B are refracted by the object-glass to meet at F. The analytic lens is so placed that F is its principal focus. Thus ray of light would become parallel to the axis of the telescope after passing through the analytic lens and give actual image b an of the staff intercept AB. 
Refrence-2The negative sign is used in (ii) since b ‘a’ and ba are on the same side of the analytic legs.
Refrence-3 now the conditions that D should be proportional to S requires that the 2nd and 3rd terms in (v) are equal to zero so that 
Refrence-4 In this condition, the apex G of the tacheometric angle AGB exactly coincides with the instruments
Refrence-5 In this condition, the apex G of the tacheometric angle AGB exactly coincides with the instruments 
Refrence-6Q9.Explain levelling by stadia?A9) Levelling by Stadia: Levelling by stadia tachometer is an indirect and rapid method of levelling. It is suitable where the country is rough and precision needed is not great. The transit should preferably be provided with a sensitive control level for vertical vernier so that error may be readily eliminated. The method of running a line of levels by this method is as follows: (i) Set up transit at a convenient point. (ii) Take a backsight on the staff held at a B.M., first by observing stadia interval and then by measuring the vertical angle to some arbitrarily chosen mark on the staff. (iii) Establish a change point in advance of transit, and take similar observations, the vertical angle is measured with horizontal cross-hair set on the same mark as before. (iv) Move trait to a new point in advance of change point and repeat the process. (v) Record stadia distance and vertical angles and also staff reading which is used as an index when vertical angles are measured.
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Reference 1 The constant f/i is called the multiple constant and its value is usually 100, while constant (f+d) is called the additive constant and its value varies from 30 cm to 60 cm in case of the external focusing telescope, it is very small varying from 10 cm to 20 cm and is therefore often ignored. Q4.What is beman stadia arc?A4) It is the type of graduated arc attached to the vertical circle of an alidade or transit to make the computing elevation difference for inclined stadia sights simply. The arc, designed by W. M. Beaman of the U. S. Geological Survey, is that each division on the arc is equal to 100 (1/2 sin 2A), where A = vertical angle. the index is set exactly on graduation and difference in height along an inclined line of sight is obtained by multiplying the stadia intercept by the number of Beaman arc divisionsQ5.Explain substance bar? A5) A subtense bar (fig. is a horizontal staff with targets fixed at a known distance apart. It is about 4m long having a small spirit level and a quick levelling head. A sight rule, provided at its centre, can be placed along the line of sight by viewing the telescope of the theodolite thought the vanes. The bar is mounted on a tripod and is placed at right angles to the line of sight for making observations. After levelling and aligning, it is clamped using a clamp screw. Q6.Explain moving hiar and tangential method of tacheometry levelling?A6) The Tangential System of Tacheometry: This method is used when the telescope is not fitted with a stadia diagram. In this method, the telescope is directed towards staff to which the horizontal and vertical distances are to be measured and two vertical angles to two vanes or targets on the staff at a known distance (S) apart are taken. The horizontal and vertical distances are then calculated as follows: Case 1:When both the observed angles are angles of elevation:
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to simplify the calculation work. The analytic lens is seldom placed in internal focussing telescope since the value of the additive constant is only a few centimetres and can be neglected. The disadvantage of the analytics a lens is a reduction in the brilliancy of the image due to increasing observation of light. The value of the additive constant, (δ+d) can be made equal to zero by bringing the apex (G) of geometric angle AGB (Fig. 10. 4) into exact coincidence with the centre on\f the instrument. The theory of analytic lens is explained as follows:
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Refrence-2The negative sign is used in (ii) since b ‘a’ and ba are on the same side of the analytic legs.
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Refrence-4 In this condition, the apex G of the tacheometric angle AGB exactly coincides with the instruments
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Refrence-6Q9.Explain levelling by stadia?A9) Levelling by Stadia: Levelling by stadia tachometer is an indirect and rapid method of levelling. It is suitable where the country is rough and precision needed is not great. The transit should preferably be provided with a sensitive control level for vertical vernier so that error may be readily eliminated. The method of running a line of levels by this method is as follows: (i) Set up transit at a convenient point. (ii) Take a backsight on the staff held at a B.M., first by observing stadia interval and then by measuring the vertical angle to some arbitrarily chosen mark on the staff. (iii) Establish a change point in advance of transit, and take similar observations, the vertical angle is measured with horizontal cross-hair set on the same mark as before. (iv) Move trait to a new point in advance of change point and repeat the process. (v) Record stadia distance and vertical angles and also staff reading which is used as an index when vertical angles are measured. 
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