The following are the five main methods of plotting a traverse survey: 1. By Parallel Meridians through Each Station 2. By Included Angles 3. By Central Meridian or Paper Protractor 4. By Rectangular Co-Ordinates 5. By Chords.

#### Method # 1. By Parallel Meridians through Each Station:

Having fixed suitably, the position of the starting point say A, draw a line representing the magnetic meridian. Then with a protractor plot the bearing of line AB (θ1) (fig 5 .22), and cut AB according to the scale. Then at B, draw a line parallel to the previous line representing the meridian and plot the bearing of BC (θ2) and measure its length with the scale. Repeat the whole process until all the lines are drawn. If the traverse is a closed one, last line should end at the starting point. If it does not, discrepancy is said to be the closing error.

This method is defective because the error in plotting the direction of one line is earned forward in whole of the traverse.

#### Method # 2. By Included Angles:

Draw the meridian at the starting station A and plot the bearing of line AB (θ1) (Fig. 5.23) and measure length AB to the scale. Then at B, draw the angle ABC with the help of a protractor and cut off length BC to the scale. Repeat the process at each of the succeeding stations.

The liability of a cumulative error in protracting the angles is similar to that in the first method but still this is preferred to the first because:

(i) The necessity and inconvenience of drawing parallel meridians and

(ii) The liable error in the parallelism between all meridian lines are eliminated.

#### Method # 3. By Central Meridian or Paper Protractor:

In this method, a point say O is selected just in the centre of the paper and a line representing the meridian is drawn through it. Then with the protractor stationed at O, bearing of all the lines are plotted with reference to this meridian as shown in fig 5.24. The position of the starting station say A is suitably selected on the sheet and the line AB is drawn parallel to the respective line and its length is cut off to scale. Proceed similarly until all the lines are drawn.

The method is preferred to both the above method because the direction of all the lines are plotted from a single setting of the protractor and the possible error in placing the protractor at every station is avoided. But still the error may accumulate from incorrect drawing of parallel lines.

#### Method # 4. By Rectangular Co-Ordinates:

This method is generally used for plotting precise work, mainly a theodolite traverse, both closed and open.

In this method, the position of different points are plotted on a plan with reference to two lines yy1 (y-axis) and xx1 (x-axis) which are respectively parallel and perpendicular to the meridian (Fig. 5.25). These reference lines are called the axes of the co-ordinates, and the point of their intersection O, called the origin.

The origin may either be any traverse station or entirely outside the traverse. The distance of a point from each of the axes are called its co-ordinates.

If the length and bearing of a line are known, its projection on the y-axis and x-axis may be calculated and then plotted.

This method is the most accurate of all the methods of plotting because the use of protractor is entirely done away and each point is plotted independent of the others. The error of plotting do not, therefore, accumulate.

#### Method # 5. By Chords:

In this method, the angle between the various lines are plotted by geometrical construction with the aid of table of natural sines. The chord of an angle is twice the size of half the angle. Various mathematical tables give the lengths of chords of angles corresponding to unit radius.

For plotting a traverse, a line representing meridian is drawn through the starting station say A. With A as centre and 10 units as radius, draw an arc B1B2 cutting the meridian in B1 (fig 5.26). The chord length B1B2 for the angle B1AB2 (the bearing of AB) is obtained from the table of chords or calculated by the relation, chord B1B2 = 2x 10.sin θ1 θ2. From B1, measure the chord distance B1B2, thus marking the point B2 on the arc. Join A and B2, which represents the direction of AB.