This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.

55. Any line which lies in the picture plane will be its own perspective, and show the true length of the line (24 h). Such a line is called a Line of Measures.

In the last problem, the line ae, being in the picture plane, was a line of measures ; that is to say, its length could be laid off directly from the given data, and from this length the lengths of the remaining lines in the perspective drawing could be established. Fig. 20 shows a similar problem. The line ae lies in the picture plane, and apep is, therefore, a line of measures for the object.

56. Besides this principal line of measures, other lines of measures may easily be established by extending any vertical plane in the object until it intersects the picture plane. This intersection, since it lies in the picture plane, will show in its true size, and will be an auxiliary line of measures. All points in it will show at their true height above the plane of the ground. Thus, in Fig. 20, apep is the principal line of measures, and shows the true height of the block. If the rear vertical faces of the block are extended till they intersect the picture plane, these intersections (mpnp and oppp) will be auxiliary lines of measures, and will also show the true height of the block. It will be noticed in the figure that mpnp and oppp are each equal to apep. Either one of these lines could have been used to determine the vertical height of the perspective of the block. For illustration, suppose it is desired to find the height of the perspective, using the line oppp as the line of measures. Assume the vanishing points (vad and vab') for the two systems of horizontal edges in the block to have been established as in the previous case. Now extend the line be (in the diagram), which represents the horizontal projection of the face cbf, till it intersects HPP. From this intersection drop a vertical line of which will represent the intersection of the vertical face ebf with, the picture plane, and will be a line of measures for the face. pp, where this line of measures intersects VH1 will be the point where the lower horizontal edge (produced) of the face cbf intersects the picture plane. Measure off the distanceppop equal to the true height of the block, as given by the elevation. Two lines drawn through op and pp respectively, and vanishing at vad, will represent the perspectives of the upper and lower edges of the face cbf, produced. The perspective (bp), of the point 5, will be found on the perspective of the upper edge of the face cbf, vertically below the intersection of HPP with the horizontal projection of a visual ray drawn through the point b in the diagram. A vey-tical line through bp will intersect the lower horizontal edge of the face cbf in the point fp. Lines drawn respectively through bp and fp, vanishing at vab, will establish the perspectives of the upper and lower horizontal edges of the face abfe The points ap and ep will be found vertically under the points a and e in the diagram. The remainder of the perspective projection may now easily be determined.

57. The perspectives of any points on the faces of the block may be found by means of the diagram and one of the lines of measures.

Let the points gv, hv, kv, and lv in the given elevation, determine a square on the face abfe of the block. Let the points g, h, k, and l, represent the position of the square in the diagram. Extend the upper and lower horizontal edges of the square, as shown in elevation, until they intersect the vertical edge avev in the points tv and vv. To determine the perspective of the square, lay off on apep, which is a line of measures for the face abfe, the divisions tp and vp taken directly from the elevation. Two lines drawn through tv and vp respectively, vanishing at vab, will represent the perspectives of the upper and lower edges (produced) of the square. gp will be found on the perspective of the upper edge, vertically under the intersection of HPP with the horizontal projection of a visual ray drawn through the point g in the diagram. The position of kp may be established in a similar manner. Vertical lines drawn through gp and kp respectively, will complete the perspective of the square.

58. The auxiliary line of measures oppp might have been used instead of apep. In this case, oppp should be divided by the points wp and yp, in the same way that ae, in elevation, is divided by the points t and v. Through wp and yp, draw horizontal lines lying in the plane cbf, for which op pp is a line of measures. These lines will vanish at vad and intersect the vertical edge bpfp of the block. From these intersections draw horizontal lines lying in the plane abef, vanishing at vaband representing the upper and lower edges of the square. The remainder of the square may be determined as in the previous case.

POSTOFFICE AND COURTHOUSE, PIERRE, S. D.

J Knox Taylor, Supervising Architect, Treasury Department, Washington, D. C, Architect.

Plans Shown on Following Page.

First Floor- Assignment Plan;.

Second -Floor. .Assignment plan.

PLANS OF POSTOFFICE AND COURTHOUSE, PIERRE, S. D.

J. Knox Taylor, Supervising Architect, Treasury Department, Washington, D. C, Architect.

For Perspective View, See Preceding Page.

In a similar manner, the auxiliary line of measures mpnp might have been used to determine the upper and lower edges of the square. This construction has been indicated, and the student should follow it through.

59. It sometimes happens that no line in the object lies in the picture plane. In such a case there is no principal line of measures, and some vertical plane in the object must be extended until it intersects the picture plane, forming by this intersection an auxiliary line of measures. Fig. 21 illustrates such a ease. A rectangular block, similar to those shown in Figs. 19 and '20, is situated some distance behind the picture plane, as indicated by the relative positions of HPP and the diagram.

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