a. That the point of intersection of two given straight lines on the ground, and the corresponding point on the map, will be a given point on the map, if the corresponding lines on the map be ascertained to be correctly laid down in position. And,
b. That any two points being given or correctly determined, the straight line terminating in them will be a given line. Further,
c. That a straight line traced or drawn through given points, is given in position. It should be kept in view that lines may be more accurately traced, and to a greater distance, with the naked eye, when the party tracing is rather above than below the level of the field on which the trace shall be made.
It may be also seen that a point on the map which is the common point of intersection of three straight lines drawn through well-defined points in the detail will be a given point, if lines traced through the corresponding detail points on the ground be found to have a common point of intersection. And further, that the correct determination of two such points on the map determines, as already stated, the position of a straight line through these points. The determination, in the above manner, of three such common points of intersection correctly determines the representation of a given triangle. In the examination the sides of the triangle determined by intersections, as above, should be measured on the ground, to ascertain and verify the accuracy of the determinations of the angular points on the trace or map. The production of detail lines, and lines traced through plotted points, should be taken up in the chain measurements of the sides of this triangle. Through these verified points straight lines should be traced, and drawn in pencil, to well-defined points in the detail, such as the buttals of fences, the corners of houses and walls, gate piers, &c. On these lines the intersected and neighbouring detail should be examined by chain and scale measurements. In the measurement of the lines the internal and adjacent external detail should be very carefully examined, and corrected on the map where found in error. The examination of the detail should be carried forward by the production and intersection of given lines, and also by chain measurements from given points, to verify the position of the detail or other points on the map. This examination should be continued to the limits of the trace sheet. In remote parts of the trace and district, lines of verification should be drawn, traced on the ground and measured with the chain to verify the scale measurements by the examination. These lines should be long, and in situations affording few facilities for the accurate determination on the map of the position of the plotted detail by other modes of examination.
The straight line passing through the extremities, or other well-defined points in curved detail, should be regarded as a detail line, and the position of the intermediate curved detail verified by ordinates or tangents. Buildings and adjacent detail should be carefully examined by productions, &c., because of the greater difficulties these details usually present to the surveyor and plotter, and the consequent liability to small errors in the position of some of the plotted points, which affect the direction of lines determined on them.
Among the [Plates] appended to this work will be found several examples of map drawing suitable for reference. [Plate 16] shows the signs used on ordinary maps and charts. [Plates 29] and [30] contain signs used chiefly upon Indian and colonial maps; and [Plates 31] and [32] give the signs employed upon military maps, with a section and a plan of fortifications. These signs should be neatly drawn and their dimensions suited to the scale of the map, the same remark applying to these as to trees in elevation. [Plate 1] is a plan showing the principal characters of work used in mapping. This plan has been very carefully compiled and drawn to render it suitable as a plan of reference. [Plate 12] illustrates the construction and colouring of hills according to the several methods described in the preceding Sections. Other examples, with rocky cliffs, will be found on [Plate 14]. [Plate 18] contains a piece of the Ordnance map drawn to a scale of one inch to the mile, and furnishes an example of finished work. Upon the same [Plate] will be found a piece of chart showing soundings, intended as a reference for hydrographers and others engaged in marine surveys. And [Plate 28] shows the manner in which geological maps are prepared. The whole of these examples will be found worthy of careful study as specimens of the draughtsman’s art.
The Plates relating to this Section are Nos. [1], [10], [12], [14], [18], [28,] [29], [30], [31], and [32].
Section VI.—Mechanical and Architectural Drawings.
It is not within the scope of the present work to explain and to illustrate the principles according to which mechanical drawings are executed. These must be studied in special treatises on Projection. The several methods of giving expression and embellishment to this class of drawings have, however, been fully described, and the principles upon which these methods are founded carefully explained. It now remains for us to add a few general remarks and some detailed instructions on the practical application of these principles and methods.