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datum line as an axis, carrying with it all its points, the position of which with respect to the YP may always be easily determined, and from them the projections of the lines in which they lie may be found. 41. To find the projections of a compound curved line, or one no part of which would coincide with or lie in a plane, the process is some- what more difficult, as its appearance in two directions at right angles to each other must be known, or given, before a third view of it can be obtained. As an example Fig, 140 MECHANICAL AND ENGINEERING DRAWING 89 Let AB, No. 1 (Fig. 140), be the elevation of such a curved line, and ab, No. 2, another elevation of the same line, at right angles to the first. It is evident that such a line could not coincide with a plane, yet if the relation of any points in it with the planes of its projection be known, or can be determined, then the plan or horizontal projection of the line can be found. Let, then, the line ab, No. 2, be the front elevation of the line, the VP being behind it, and AB, No. 1, its side elevation, looking in the direction of the arrow x. Then the end A or a of the line is nearest the YP, or farthest from the eye ; and the end B or b the converse. To prove this, through A, No. 1, and b, No. 2, draw the lines Ap, cb, perpendicular to the IL ; then Ap will represent an end elevation or edge view of the YP looking in the direction of the arrow x and cb that of a plane at right angles to the YP. With the assistance of these as datum planes we can determine the distance of any point in the line AB from each of them, and thus obtain its horizontal projection. A line drawn through a series of points thus found will be the plan of the curved line sought.