—The lines chained over in a survey and recorded in the field-book are not usually the actual lines existing on the ground, but imaginary straight lines chosen for the purpose of referring other lines and points to them. They are, therefore, appropriately termed reference lines, and all points situate in them to which other lines are referred, in other words, all points in a reference line in which other reference lines intersect it, are termed reference points. Reference lines are generally made to form triangles for facility of computation, and these triangles enclose the area to be surveyed. But to determine the details included within them, it is necessary to form other and smaller triangles within the larger ones first laid down. The latter are, therefore, distinguished as Primary and the former as Secondary triangles, and the lines of which they are composed are called primary and secondary reference lines.
Plotted Points.
—In laying down a line of definite length upon paper, the positions of its extremities are determined and marked by pencil dots; such dots, or rather the points indicated by such dots, are termed plotted points. The line is drawn by joining the plotted points.
To Plot Reference Lines and Points.
—To plot a reference line of a given length when the position of neither of its extremities is given, a light dot must be made upon the paper in a convenient part to indicate the position of one extremity. The pencil-point mark should be as light and well defined as possible, and hence it is essential that the pencil used should be hard, and always kept pared to a fine conical point. The scale must then be applied, in the direction of the line to be drawn, with its zero point coincident with the plotted point. The scale should be lightly but firmly held in this position with the left hand. The distance of the other extremity of the line must then be found upon the scale, and the eye placed directly over the line of the graduation; this is necessary to the correct placing of the point, and it is well to train the eye to trace accurately the prolongation of the line of graduation upon the paper. A dot must be placed in the prolongation of this line and close to the edge of the scale, to mark the position of the other extremity. The reference line is then to be drawn between these two plotted points with a sharp chisel-pointed pencil. Reference lines, like reference points, should be well defined, but drawn as fine and light as possible. The degree of fineness and lightness should be such that when the detail is finely but firmly outlined, the reference lines and points may not be visible, except on a close inspection of the surface.
To plot secondary reference lines, as, for example, a number of offset lines, apply the scale so that its edge may be parallel to and almost over the pencil trace of the primary line and its zero point coincident with the point at which the line begins. Care must always be taken to place the zero of the scale at the beginning of the line, and not at the end of it. At the distances recorded in the field-book as those at which the offsets were taken, plot upon the line, in the manner described above, the points indicating the extremities of the offset lines. All other points, such as stations and intersection of fences, roads, and streams, should be plotted at the same time. Around all stations, a light, hand-drawn circle should be placed, and intersections marked by small cross lines. This being done, place the offset scale so that the zero may coincide with the plotted point in the reference line and the edge be perpendicular to the line. To bring the edge into this position, the end of the scale should be placed parallel to the reference line; this is, of course, assuming the scale to be perfectly rectangular, as it ought to be. The other extremities of the lines may then be plotted in the same manner as those of the primary lines.
To illustrate the foregoing remarks, let it be required to plot the following portion of a field-book.
| 00 | 1346 | or 000 Line 1. | ||||
| 75 | 1170 | |||||
| 96 | 1000 | |||||
| 05 | 650 | |||||
| 66 | 400 | |||||
| 00 | 000 | |||||
| Line 3. | From | 1946 | last. | |||
 | ||||||
| 1946 | 00 | |||||
| 1420 | 88 | |||||
| 1200 | 144 | |||||
| 1000 | 110 | |||||
| 600 | 75 | |||||
| 520 | 50 | |||||
| 000 | 00 | |||||
| Line 2. | From | 2504 | last. | |||
 | ||||||
| 2504 | 00 | |||||
| 2000 | 65 | |||||
| 1790 | 95 | |||||
| 1610 | 115 | |||||
| 1440 | 87 | |||||
| 1220 | 110 | |||||
| 1000 | ||||||
| 850 | 28 | |||||
| 420 | 100 | |||||
| Line 1. | 000 | 00 | or 1346 Line 3. | |||
| Begin at south corner and range N. | ||||||
Having laid down in a convenient part of the paper the beginning of Line 1, place the edge of the scale so that the zero may coincide with the plotted point and the edge be parallel to one of the meridians. Holding the scale firmly in this position, plot the distance 2504 links, and join the plotted points. Then, without removing the scale, plot upon this reference line the distances at which the secondary or offset lines were taken, that is at 420, 850, 1220, 1440, 1610, 1790, and 2000 links. In this case we have nothing but offsets; had there been stations or intersections of fences, roads, or streams, these would have had to be plotted at the same time, and distinguished by an appropriate mark. Line 2 begins at the end of Line 1, and returns on the left at an acute angle, as indicated by the arrow in the field-book. But as the magnitude of this angle is not known, the survey having been taken with the chain alone, the exact direction of Line 2 must be ascertained in the following manner. Take the length of the line in the compasses, and with this distance as a radius, strike an arc from the end of Line 1. Also with the length of Line 3 as a radius, strike an arc from the beginning of Line 1, at which point Line 3 closes, intersecting the former. The point of intersection will be the end of Line 2. Join this point to the end of Line 1, and plot the offset reference points upon this line in the manner already described for Line 1. Line 3 begins at the end of Line 2, and terminates at the beginning of Line 1; hence both extremities being determined, we have only to join these points, and to plot the offset reference points as before. Had a split line been taken for the sake of accuracy from the angle A C B to the base Line 1, the intersection of this line should have been plotted upon Line 1, and the position of the end of Line 2 found by striking an arc from this point also with a radius equal to the length of the split line. If the distances have been correctly measured in the field and correctly taken from the scale, the three arcs will intersect at the same point. If they do not so intersect, the error must be noted in an error-sheet, and corrected in the field before proceeding further. It may be remarked here that on account of the irregularities of the surface chained over, all measured lines are liable to be recorded a little too long. One link in ten chains may be allowed for this source of error. Assuming, however, that the primary reference lines “close” properly, the offset lines may be plotted in the manner already described, and the detail or boundary lines drawn in, which in the present instance are hedges. [Fig. 82] shows the survey as laid down in the foregoing notes.
When the survey has been made with the aid of an angular instrument, the method of plotting the primary reference lines differs somewhat from the foregoing. In this case, the paper should be first covered with a number of parallel straight lines ruled about an inch and a half apart to represent magnetic meridians. The first station may then be marked upon one of these meridians in a convenient part of the paper. To lay down the first reference line, apply the protractor to this meridian with its centre point coincident with the plotted point, and from the bearing recorded in the field-book, lay off the given angle. Join the two plotted points and produce the line indefinitely; and upon this line lay off a distance equal to the length of the measured line. The second reference line must be drawn in the same manner, from the end of the first, by laying off from that point the recorded angle. But as the end of the first line will probably not fall upon a meridian, the protractor will have to be moved up to the point by means of a parallel ruler adjusted to the nearest meridian. A more convenient and a more accurate method, however, is to make the left of the drawing represent the north while plotting, and to use the T-square instead of the parallel ruler. All subsequent lines are plotted in the same way. Instead of covering the paper with meridians before commencing to plot, it may, in some cases, be found more convenient to draw with the set and T squares a short meridian through the point as required.