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NOTE. - The true length of any line-which extends in front of the picture plane will be shorter than the perspective, of the line.

105. Having determined the perspective of any line, as dreP, its true length may be determined by drawing measure lines through d" and cr. The distance intercepted on VH, by these measure lines will show the true length of the line. Thus, ereP vanishes at Its. measure point must therefore be mab. Two lines drawn from mab, and passing through a" and dl' respectively, will intersect VH, in the points and The distance between and is the true length of c"d". This distance will be found equal to arb„ which is the true measure for the opposite and equal side (aPbP) of the rectangle.

In a similar manner, the true length of bre may be found by drawing measure lines from fled through bP and el' respec tively. will show the true length of a"b", and should be equal to ard„ which is the true length of the opposite and equal side (a"d") of the rectangle.

106. The perspective (e) of a point on one of the rear edges of the card may be determined in either of the following ways: 1st. From which is the intersection with VH, of the measure line through b", lay off on VII„ to the left (§103), the distance bee, equal to the bow" taken from the given plan. A measure line through vanishing at mad, will intersect erbr at the point w''.

2d. In the given plan draw a line through mu, parallel to a"b", intersecting a"dg in the point On make aPm, equal to as given in the plan. A measure line through w„ vanish ing at mad, will determine tv, on ardy. From m„ a line parallel to avbP (vanishing at vab) will determine, by its intersection with bPcP, the position of wr..

107. In making a perspective by the method of perspective plan, it is generally customary to assume VH and HPP co incident. That is to say, the coordinate planes are supposed to be in the position shown in Fig. 9, instead of being drawn apart as indicated in Fig. 9a. This arrangement simplifies the construc tion somewhat.

This is illustrated in Fig. 28, which shows a complete prob lem in the method of perspective plan. Compare this figure with Fig. 27, supposing that, in Fig. 27, HPP with all its related horizontal projections could be moved downward, until it just coincides with VH." The point n would coincide with e",.h, with and the arrangement would be similar to that shown in Fig. 28. All the principles involved in the construction of the meas ures, points, etc., would remain unchanged.

108. The vanishing points in Fig. 28 have first been assumed, as indicated at vab and ed. As the plan of the object is rectangular, SPH may be assumed at any point on a semicircle constructed with vabvad as diameter. By assuming SPH in this manner, lines drawn from it to va" and vad respectively must be at right angles to one another, since any angle that is just con tained in a semicircle must be a right angle. These lines show by the angles they make with HPP, the angles that the vertical' walls of the object in perspective projection will Make with the picture plane (§102).

109. mad and ma'' have been found, as explained in § 97, in accordance with the rule given in § 98.

should next be assumed at some distance below VII, to represent the vertical trace of the horizontal plane on which the perspective plan is to he made (§ 91).

The position of al' (on may now be assumed, and the perspective plan of the object constructed from the given plan, exactly as was done in the case of the rectangular card in Fig. 27.

110. having constructed the complete perspective plan, every point in the perspective projection of the object will be found vertically above the corresponding point in the perspective plan.

VII, is the vertical trace of the plane on which the perspec tive projection is supposed to rest. is found on VH, verti cally over e in the perspective plan. thPe,P is a vertical line of measures for the object, and shows the true height given by the elevation.

To find the height of the apex (k,P) of the roof, imagine a horizontal line parallel to the line ab to pass through tW apex, and to be extended till it intersects the picture plane. A line drawn through kr, vanishing at eb, will represent the perspective plan.of this line, and will in the point nt, which is the perspective plan of the point where the horizontal line through tl c apex intersects the picture plane. The vertical dis tance von„ laid off from VII„ will show the true height of the point k above the ground. /r,P will be found vertically above kr, and on the line through n, vanishing at The student should find no difficulty in following the construction for the remainder of the figure.

111. Fig. 29 illustrates another example of a similar nature to that in Fig. 28. The student should follow carefully through the construction of each point and line in the perspective plan and in the perspective projection. The problem offers no. especial difficulty.

Plate VI. should now be solved.