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The chief methods by which the relative directions of lines may be determined are: 1. Theodolite Traversing by Directs Observation of Angles 2. Theodolite Traversing by Direct Observation of Bearings.

**Method # 1. Theodolite Traversing by Directs Observation of Angles: **

In this method, the angles between the successive lines are measured, and the bearing of the starting line is observed. The bearings of the remaining lines are then found from the observed bearing and the measured angles.

**This method includes: **

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1. Traversing by the method of included angles.

2. Traversing by the method of direct angles.

3. Traversing by the method of deflection angles.

**1. Traversing by the Method of Included Angles:**

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In a closed traverse, the angles measured are either interior or exterior according as the traverse is run in a counter-clockwise direction (Fig. 9.15) or in a clockwise direction as in (Fig., 9.16) but in both the cases the result is the same. The common practice is to run a closed traverse in the counter- clockwise direction. The angles can be measured by repetition that is why, any desired degree of accuracy can be obtained in this method.

**Procedure:**

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In running the traverse ABCDEFG, set up the theodolite at first station A and observe the bearing of the line AB. Then measure the angle GAB. Shift the instrument to each of the successive stations B, C etc. and measure and angles ABC, BCD etc. Measure the lines AB, BC etc. and the take the necessary offsets to locate the required details.

**2. Traversing by the Method of Direct Angles:**

This method is commonly used for open traverses. In running the traverse as shown in fig. 9.17., set up the theodolite at the starting station. A and observe the bearing of line AB. Shift the theodolite to B. Set the vernier A to zero, take a back sight on the preceding station A.

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Unclamp the upper plate, turn the telescope clockwise, take a fore sight on the following station C, and read both verniers. The mean of the two vernier readings is the required direct angle ABC. Take other angles in the similar manner. Chain the lines AB, BC etc, and take the necessary offsets in the usual way.

**3. Traversing by the Method of Deflection Angles:**

This method is used for open traverses. This is much suitable when the survey lines make** **small deflection angles with each other as in the case of surveys for roads, railways, pipe lines etc. In running a traverse as in figure 9.18 set up the theodolite at the starting station A and observe the bearing of line AB. Shift the instrument to station B, set the vernier A to zero and take a back sight on A.

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Then transit the- telescope, loosen the upper clamp, turn the telescope clockwise and take a fore sight on C. Read both verniers, the mean of these readings is the required deflection angle of BC from AB. Also note down its direction. In this case, it is α_{1} R (i.e. α_{1} Right). Then set up the theodolite at each of the successive stations C, D, E, etc., and observe the deflection angles, and record them in the field-book. Chaining and offsetting is done in the usual manner.

**Method # 2. Theodolite Traversing by Direct Observation of Bearings: **

This is also called fast needle method. There are three methods of observing bearings directly in the field.

1. Direct method in which the telescope is transited.

2. Direct method in which the telescope is not transited.

3. Back bearing method.

**1. Direct Method in Which the Telescope is Transited (Fig. 9.19): **

(i) Set up the transit at A and level it. Set the vernier A to zero. Point the telescope to the magnetic north as indicated by the magnetic needle attached to the transit by using the lower clamp and tangent screw.

(ii) Loosen the upper clamp and bisect B exactly by using the upper clamp and its tangent screw. Read the vernier A which gives the bearing of AB say 50°. If the traverse is closed one, then observe also the back bearing of the last line (EA). This will serve as a check.

(iii) Shift the instrument and set it up at B. Check whether the vernier A still reads the bearing of AB i.e. 50°. If due to slip the readings differs, correct it with the upper tangent screw.

(iv) Using the lower clamp and tangent screws, back sight on A.

**(v) Transit the Telescope:**

The line of sight is thus directed towards AB produced and the vernier A still reads the bearing of AB. Loosen the upper clamp, turn the telescope, and bisect C exactly by using the upper clamp and tangent screw.

(vi) Read vernier A, which now gives the bearing of line BC, say, 115°.

(vii) With the vernier A clamped at 115°, transfer the instrument to C and repeat the process.

(viii) As a check upon the accuracy of work in a closed traverse, the back bearing of the last line (EA) observed in step (ii) at the first station A and its fore bearing taken at the last station (E) must differ exactly by 180°.

It should be noted that in this method, the telescope is transited for alternate back and fore readings.

**Alternative Method: **

In this method, the process is same as above except that at each station, the telescope is transited before a back sight is taken on the preceding line and therefore for each fore bearing the telescope is normal and for each back bearing it is inverted.

**2. Direct Method in Which the Telescope is Not Transited (Fig. 9.19):**

This method is preferable in the case of non-transit instruments or in the case of transit instruments having poor adjustment.

The procedure is similar to that followed in the first method except that the telescope at B is not transited after the back sight is taken on A, but rotated in a horizontal plane to sight C. The orientation thus becomes out by 180° and so a correction of 180° has to be applied to the reading of the vernier A taken at B.

Subtract 180° if the reading is more than 180°, and add 180°, if the reading is less than 180°. At C, the orientation becomes out by 360°, and is therefore correct, i.e. there is no need of applying the correction of 180°. Therefore, this correction is necessary only at even instrument-stations i.e. 2nd 4th, 6th and so on.

**3. Back Bearing Method. (Fig. 9.19): **

(i) Set up the instrument at A and observe the fore bearing of line AB.

(ii) Shift the instrument and set it up at B.

(iii) Set the vernier A to back bearing of AB.

(iv) With the vernier A kept clamped at the same reading, back-sight on A by using the lower clamp and its tangent screw. As the vernier A is set to the back bearing of AB and the line of sight is directed towards BA, the instrument is in correct orientation.

(v) Unclamp the upper plate and turn the telescope until C is sighted. Bisect C exactly by using the upper clamp and its tangent screw.

(vi) Read the vernier A which gives the bearing of BC.

(vii) Repeat the process at each of the subsequent stations.

Out of the three methods discussed above, the second is the best.