# methods of measuring horizontal angles using theodolite

Upendra Kumar
 VERNIER THEODOLITE

There are three methods for a measure of an angle with the theodolite.
1. Direct method
2.Repetition method
3. Reiteration method

FOR MORE KNOWLEDGE:-

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Direct method

For the measure of the angle between C and D
i. Set the instrument at O and complete temporary adjustment of the instrument.

(ii) set the vernier A zero. For this step clamped the lower clamp screw and lose the upper clamp. Rotating the instrument in a horizontal plane until the index of the vernier (A) nearly coincides with the zero of the horizontal circle. Clamped the upper clamp and turn the upper slow motion or tangent screw until the oo zero into exact coincidence.
(iii)  Lose the lower clamp, turning the telescope to the approximately toward left-hand point C and sight over the top of the telescope. Tighten the lower clamp and make exact bisection withe the help of lower clamp screw. For error due to non vertically of ranging rod minimize use of verticle circle clamp and tad tangent screw coincidence of station mark. Check the setting of vernier (A). Read the vernier (A) and (B) and record it.
(iv) Unclamp the upper clamp and rotate the telescope clockwise until the line of sight is set nearly on the right-hand point (D). exact bisection make with the turning upper tangent screw.
(v) Read both vernier and record . Deduct the vernier (A) readings points D-C . and vernier (B) reading deduct by 180 °. Finally, mean the value of vernier A and B give the required angle COD.

TABLE 1

 Stn Object Angle Observation Reding on Vernier     A.               B Angle on Vernier      A.           B Mean  angle of Vernier Mean angle of observation O C D C OD Face left 0°0'0".      180°0'0" 60°20'20"    239°40'40" 60°20'20"   59°40'40" 60°0'30" O C D COD Face Right 0°0'0"          180°0'0" 59°40'20"        240°20'20" 59°40'20'     60°20'20" 60°0'20" 60°0'25"

Repetition method: - 1. Set the instrument at Complete temporary adjustment procedure. Set the Vernier A at 0°and Vernier B at 180°.
2. Upper clamp is fixed and lower clamp loosened turn the telescope to the ranging rod at C. Make complete bisection with the help of the lower clamp screw and lower tangent screw. Check the Vernier reading at Vernier A and Vernier B. Booked the readings as initial readings. Tighten the lower clamp loosened the upper clamp turn the telescope in clockwise direction and bisects ranging rod D. Complete accurate bisection with the help of the upper tangent screw. Read the Vernier’s reading and booked as final readings of first step of repetition.

3. Loosened the lower clamp screw and turn the telescope in anti-clockwise direction bisect the ranging rod at C. Clamped the lower clamp screw, and complete bisection at C with the help of lower tangent screw. Loosened the upper clamp screw and turn the telescope in clockwise direction and bisect the ranging at D, and complete bisection process. Read and write the readings as final readings of second steps of repetition. Repeat the upper procedure at least three times.

Then angle LCOD= accumulated angle / no. of times readings taken.

4. Change the face of instrument, and repeats the upper process.
Mean of the readings of both faces give the accurate reading of the LCOD.

TABLE 2

 Station Object Face Angle No.of reading Initial reading on Vernier Final reading on Vernier Angle on Vernier mean angle  on Vernier O C D Left COD 1. 2. 3. 0°0'0"           180°0'0" 60°0'40"         240°0'40" 120°20'40".      300°20'40" 60°0'40"     240°0'40" 120°20'40"   300°20'40" 180°20'40"   360°20'40" 60°6'53" 60°6'53" 60°6'53" O C D Right COD 1. 2. 3. 0°0'0"            180°0'0" 60°0'20"         240°20'0" 120°20'20"      300°20'20" 60°0'20" 240°20'0" 120°20'20"    300°20'20" 180°20'20"    360°20'20" 60°6'46" 60°6'46" 60°6'46"

 Mean angle of observation 60°6'49" Remark

Reiteration Method

In this method several angles are measured successively, and finally the horizon is closed. The final reading of the leading of the leading vernier should be the same as its initial reading. if not the discrepancy is equally distributed among all the measured angles.

procedure- (i) Set the instrument over O and level it correctly.
(ii) Set the vernier A to zero.
(iii) Direct the telescope to the  point A which is known as the referring object and bisect it accurately                                 by using the lower clamp and lower tangent screw. note the vernier readings.
(iv) Loosen the upper plate and turn the telescope clockwise until the point B is exactly bisected by                                   turning the upper tangent screw. read both verniers. the mean of the two vernier readings will                                     give the value of the angle AOB.
(v) Similarly , bisect C successively,and closed at A reading both verniers at each bisection.,at each                                   bisection.
(vi) Change the face of the instrument and do it same as the above.