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either from the right side or the left. As a rule, the rays of light are always assumed to come over the left shoulder of the draughtsman in jporo&Z lines, and to strike the planes of projection or the VP and HP of the drawing at an apparent angle of 45 with the IL, or inter- secting line of those planes. The actual direction of the rays is graphically shown in the diagram Fig. 133. Let VP and HP represent the two planes of projection, and the line IL the intersecting line dividing them. In these planes draw in ABCD to represent the elevation, and a'b'c'd' the plan of a cube. In the position shown, the front and back faces of the cube are parallel to the VP, and all the others perpendicular to it. Through C in the elevation, and c in plan, draw lines EC, ec' y making angles of 45 with the IL ; then EC and ec will represent the plan and elevation of a ray of light and the apparent direction in which it falls upon the VP and HP. The actual direction, or path of the ray, is from the upper anterior or front corner of the cube at A, to the lower posterior or back corner of the cube behind C. In other words, the ray of light is assumed to travel in a direction coinciding with the diagonal of the cube, drawn between point A and the point beyond C. To find the actual angle that this ray of light makes with the planes of projection : At point A in the elevation of the cube erect at A, a perpendicular to AC \ on this set off from A a length Ad equal to a side of the cube ; join d and C ; then the angle ACd is that made by the ray of light with the planes of projection VP and HP. For if the right-angled triangle dAC be supposed to turn on its base AC as a hinge until its plane coincides with AC, then the angular point d will coincide with A, and the hypothenuse dC of the triangle dAC