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the one assumed in the diagram, its projected length in the VP would have been greater or less than eg, directly in proportion to its altered position with respect to the VP. If EF had been swung so far round on F until it had coincided with Ff, then its projection in the VP would be eg', or a line equal in length to the given line EF. 18. In the foregoing problems in this chapter, we have given all the positions which it is possible for a line to occupy with reference to its planes of projection, and we could at once proceed to the projection of plane figures, were it not necessary at this stage that the student should thoroughly understand the true significance of the line lettered IL in previous and all future diagrams throughout this work. This line, we have already shown, is the line of intersection of the two "planes of projection"; but it is much more than this. The VP and HP, being for all the future purposes of the student draughtsman represented by the one flat surface of his sheet of paper, with the IL either shown on it or assumed to be there, dividing its surface into two planes, it becomes when shown in on a drawing or explanatory diagram at one and the same time the representative, not only of the IL, but of the VP and HP as well, for it is a plan of the VP and an elevation of the HP, and as these it is a datum line from which heights above the HP, or distances from the VP, may be measured or set off. These facts, it will be seen, are verified by a reference to Fig. 72. Here the IL is for all the figures, a plan of the VP, showing the line Ab by its plan to be parallel to the VP, and in front of it, at a distance equal to Aa. Similarly C, the lower end of the line Cp, is shown touching the VP, while its upper end p, projected into t in the HP, stands out from the VP a distance equal to tt', and above the HP a