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Tacheometric surveying. Tacheometer. Tacheometer is transit theodolite fitted with stadia diaphragm, and analltic lens.

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Tacheometer is transit theodolite fitted with stadia diaphragm, and analltic lens

Anallatic lens: Additional convex lens is provided between the eye piece and the object glass at a fixed distance from the object glass. The purpose of providing anallatic lens is to make additive constant (f+d) exactly zero.

Anallatic lens is provided in external focusing telescope, not required in internal focusing telescope.
  • Advantage
    • it simplifies the calculation by making the additive constant ‘0’.
    • Therefore, there is only one constant which is multiplying constant.
    • Distances are directly calculated by multiplying the difference of stadia hair readings by 100.
  • Disadvantage
    • Brightness of the image is much reduced due to absorption of light.
principle of tacheometry
Principle of tacheometry
  • The principle of techeometry is based on property of isoscales triangles, where the ratio of distance of the base from apex and length of the base is always constant.
  • D1/S1=D2/S2=D3/S3=f/I (multiplying constant)
    • F= focal length of object and
    • i= stadia intercept

The stadia readings with horizontal sight on a vertical staff held 50 m from a tacheometer were 1.285 m and 1.780 m. the focal length of the object glass was 25 cm. the distance between the object glass and the vertical axis of the tacheometer was 15 cm. calculate the stadia interval.

theory of anallatic lens
Theory of anallatic lens


  • S = staff intercept CD1
  • O= Optical centre of object glass
  • A= Optical centre of anallatic lens
  • V= vertical axis of inst.
  • P= Principal focus of the anallatic lens
  • f1 and f2= conjugate focal lengths of the object glass
  • f= focal length of object glass
  • f’= focal length of the anallatic lens
  • K= distance between object glass and anallatic lens
  • d= distance between optical centre of object glass and vertical axis of instrument
  • M=distance between optical centre of object glass and real image dc
  • i= length of real image dc, when anallatic lens is provided
  • I’= length of real image d3c3, when anallatic lens is not provided
  • D= distance between vertical axis of instrument and the staff

Home assignment (no need to submit):

    • How does the an anallactic lens work to reduce the additive constant to zero?
    • Illustrate the working of anallactic lens by a neat diagram and discuss the effect on constants using appropriate expression?
    • Derive the distance and elevation formulae for following cases of tachometry.
      • Inclined sight and staff vertical (for angle of elevation and depression both)
      • Inclined sight and staff normal (for angle of elevation and depression both)