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Let ABC, No. 1 (Fig. 140a), be the elevation of the combined line. Being parallel to the YP, every part of it is equi-distant from it. Its plan, in this position, will be the straight line ab', No. 2, parallel to the IL, its length being determined by projectors from A and B in the 90 FIRST PRINCIPLES OF elevation. Produce BC, No. 1 the straight part of the line verti- cally to c', and let c'C be assumed as an axis round which the curved line can be turned through any given angle ; and also as a datum line from which measurements may be taken. In AB the curved part of the line take any convenient points 1, 2, 3, 4; and through them and A draw projectors parallel to the IL, to meet the axis, or datum line, in c', 1', 2', 3', 4'. Now, suppose ABC to rotate on the axis line c'BC, from its normal position parallel to the VP through any given angle ; then its plan at that angle will still be a straight line, but it will be at an angle with the IL or with its plan when in its first position equal to that it has been turned through. Let this angle be one of 60. Then to find its elevation in this new position, proceed as directed in solving Problem 45 by first projecting over on to db in plan the points in the curve, transferring them by arcs to a"b', and from thence by projectors into the upper plane, cutting those drawn through A, 1, 2, 3, 4, B, in the points shown ; then a line through a' and these points to B will be the elevation of the curve in its new position. Next, let this newly-found elevation of the combined line be inclined to the HP in such a way that the axial line and with it the part BC of the combined line makes an angle of 45 with the HP or IL ; and let its plan when in that position be required.