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Now it is evident on looking at the beam from above that the surface exposed by the cutting plane, showing the nature of its material, will have two edges at b, c, parallel to each other and at right angles to the YP, and in length equal to that of the beam ; and at a an edge parallel to that at b, the surface between these latter edges being that untouched by the cutting plane, and therefore coloured green ; the lower edge of the beam at d, not being seen from above, will have no counterpart in the plan, and the two ends of the beam being square with its sides, and therefore parallel with the VP, will be represented in plan by lines in that position. Therefore, having drawn in in the YP of the sheet of paper, as at A, Sheet 2 the end elevation of the beam with its sides at the intended inclination to the HP, let fall from the points , b, c projectors perpendicular to the IL into the HP, set off on the projector let fall from a a distance from the IL equal to that the inner end of the beam is assumed to be from the YP which is arbitrary and from this point a", on the same projector, set off a distance a", ', equal to the length of the beam ; through a", a draw lines parallel to the IL cutting the projec- tors from , 5, c, in a", b", c", ', b', c f ; join these points by straight lines as shown, and the required projection is obtained. As the sur- face bounded by the parallel lines b", b', c", c, and b", c", b', c, is the plan of the section of the beam exposed after cutting, it is indicated by drawing lines with the 45 set-square, as shown. The projection of the sectional plan of the " carpenter's pencil," shown in elevation at B, Sheet 2, will present no difficulty to the student, as the procedure is clearly shown ; there is, however, one MECHANICAL AND ENGINEERING DRAWING 57