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pencil, a hollow wooden tube, and the lower end of a square post. Their projections are all obtained in the same way as those just explained, numbered 1, 1, so there is 110 necessity for their demonstration. The actual rendering of the true projections of the four objects chosen for illustrating the subject of this chapter will now be given with the sheet of drawing-paper as one plane surface. To obtain the correct projection of the four objects shown in the diagram Fig. 96, we must assume that we have their exact models before us, and are able to draw in the VP on the sheet of paper a full-size view of each of their ends such, in fact, as are shown at A, B, C, D, Fig. 97. Each of these views is an end elevation, or vertical projection, of the " original object " or model, and will be found to agree with those shown in the diagram Fig. 96, on the " Vertical Plane of Projection," and numbered 1, 2, 3, 4. The height of these views above the IL on the sheet of paper is immaterial ; but whatever it is, it should be understood that the objects represented by A, B, C, D are the same height above the HP as these end views of them are above the IL of the VP and HP. Having these end views given, and knowing by measurement the length of the models, we can find their "plans" or projections in the HP. Now A, B, C, D are the front end views of objects in front of the VP, and as the objects are a given length, their back ends must either be assumed to touch the VP, or to be a given distance- from it. Assume them to be as in the diagram Fig. 96 viz., a certain distance from the VP ; in this case the ends will all be in a straight line that distance from the IL, for, as before shown, the IL is a " plan " of the VP. Taking, then, the IL as a datum line, set off from it the