[Larger illustration] (75 kB).

In a convenient part of the paper draw the straight line N S to represent the magnetic meridian, and plot upon it the first station A. Set the protractor with its centre accurately placed over this point and its 360th and 180th divisions coinciding with the meridian. Holding the instrument securely in this position, lay off around it all the bearings as entered in the field-book, numbering them in the order in which they were taken. Against each of these numbers it is well to place the page of the field-book on which the measurement of the angle and the survey of the line are entered. The plotting must now be commenced by laying down the first line through the first bearing and determining its length from the recorded measurements. The direction of the second line has next to be transferred from the first station A to the extremity of the first line, or the second station B. This is accomplished by means of the parallel ruler, by placing the edge of the ruler through the plotted point and the point marked as bearing 2, and extending it till the same edge intersects the point B. A line is then to be drawn from this point and its length laid off from the field-book as before. The direction of the third line will then be transferred from the first angular point to the end of the second line, or station C, in the same manner. This will be continued for all the lines in the traverse, and if all the measurements have been correctly laid down, not only will the last line pass through the point A, but it will be of the same length as the chained line. Also the bearings taken from A to E and H will pass through these latter stations. These proof line bearings should be laid down at the same time as the reference line bearings, from which they should be distinguished by some sign. The directions of the reference lines should be consecutively transferred, and the length of each line should be plotted in its proper place before the direction of the next is transferred. To ensure the work closing properly, great care must be taken to plot the points accurately and to draw the pencil lines fine.

Fig. 84.

The degree of accuracy to be attained will depend in a great measure upon the extent of the traverse. With long lines the difficulties increase, and with a great number of angles the chances of error are multiplied. If the angles are carefully taken, it is probable that seconds have been read off in several instances, and these if neglected, especially upon long chain lines, may lead to an error of some importance. Also when the lines are long, the parallel ruler becomes practically useless, and some other system has to be adopted. One way of overcoming these difficulties is to draw a parallel to the first meridian through every third or fourth angle; in such a case, great care must be observed in drawing the parallels. A more easily practicable method, however, is to use the T-square in the manner already described. If the left-hand edge of the drawing board be made the north, the blade will determine meridional lines, and by laying the straight side of a semicircular protractor against the edge of the blade, its zero will be adjusted to the fixed line of direction. The first bearing having been laid down, the line is drawn and made the scale length of the chain line; the blade of the square is then pushed to the station thus found, and the next bearing set off. This operation is repeated until all the lines have been laid down. If the work closes properly, the plotting of the secondary lines may be proceeded with.

The most accurate method of plotting a traverse is by rectangular co-ordinates, or, as it is usually termed, Northings, Southings, Eastings, and Westings, because the position of each station is plotted independently, and is not affected by the errors committed in plotting previous stations. This method consists in assuming two fixed lines or axes crossing each other at right angles at a fixed point, computing the perpendicular distances or co-ordinates of each station from those two axes, and plotting the position of each station by means of the T and set squares and a linear scale. The meridian is usually made to represent one of the axes, and in this case the co-ordinates parallel to one axis will be the distances of the stations to the north or south of the fixed point, and those parallel to the other axis will be their distances to the east or west of the same point. Let N S, [Fig. 84], represent the meridian, and A B the first bearing taken, and the first line measured. The angle in this case is N A B = θ. If θ is an acute angle, the second station B is to the north of the first station A; if it is an obtuse angle, B is to the south of A. If the angle θ lies to the right of the meridian, B is to the east of A; if to the left, to the west. Thus it will be seen that if the northernly and easternly directions are considered positive, the southernly and westernly directions will be negative. From the foregoing it is manifest that the co-ordinates of B are as follows:—

Northing A a = b B (or if negative, southing) = A B × cos. θ.
Easting A b = a B (or if negative, westing) = A B × sin. θ.

To plot the point B, draw through the point A, with the aid of the T-square, a horizontal line. Multiply the chained length of the line A B by the sine of the angle N A B as entered in the field-book, and set off this distance along the horizontal line. From the point thus determined, erect, with the aid of the set square, a perpendicular, which will be parallel to the meridian. Multiply the chained length of A B by the cosine of the angle N A B, and set off this distance along the perpendicular line. The point thus determined will be the position of the second station B, which may then be joined to A by a straight line.

Fig. 85.