62. Having found the perspective of the main part of the house, the porch (without its roof) may be considered as a second rectangular block, no vertical edge of which lies in the picture plane. It may be treated in a manner exactly similar to that of the block shown in Fig. 21, § 59. We may consider that the rear vertical face of the block, which forms the porch of the house (g,q ), has been extended until it intersects the picture plane in the line ae, giving a line of measures for this face, just as in Fig. 21 the nearest vertical face of the block was extended until it intersected the picture plane in the line of measures mn.

On epap, make evcv equal to the true height of the vertical wall of the porch, as given by the elevation. A line through C'P, vanishing at vab, will be the perspective of the upper horizontal edge of the rear face of the block which forms the porch. The line through ep, vanishing at vab, which forms the lower edge of the front face of the main body of the house, also forms the lower edge of the rear face of the porch. Through the point h in the diagram, draw a visual ray, and through the intersection of this visual ray with HPP drop a vertical line. Where tins vertical line crosses the upper and lower horizontal edges of the rear face of the porch, will establish the points gp and hp respectively. Having found the vertical edge gphp, the remainder of the perspective of the porch (except the roof) can be found without difficulty, the horizontal edges of the porch vanishing at either vab or vad, according to the system to which they belong. Each vertical edge of the porch will be vertically below the point where HPP is crossed by a visual ray drawn through the point in the diagram which represents that edge. The fact that the porch projects, in part, in front of the picture plane, as indicated by the relation between the positions of the diagram and HPP, makes absolutely no difference in the construction of the perspective projection.

All of the vertical construction lines have not been shown in the figure, as this would have made the drawing too confusing. The student should be sure that he understands how every point in the perspective projection has been obtained, and, if necessary, should complete the vertical construction lines with pencil.

63. Having found the perspective of the vertical walls of the main body of the house, and of the porch, the next step will be to consider the roof of the main part of the house.

Imagine the horizontal line tw, which forms the ridge of the roof, to be extended until it intersects the picture plane. This is shown on the diagram by the extension of the line tw until it intersects HPP. From this intersection drop a, vertical line, as indicated in the figure. This vertical line may be considered to be the line of measures for an imaginary vertical plane passing through the ridge of the house, as indicated by the dotted lines in the plan and elevations of the house. On this line of measures, lay off the distance nm measured from VH2 (or VH2), equal to the true height of the ridge above the ground as given by the elevations of the house. A line drawn from the point m, vanishing at vab, will represent the ridge of the house, indefinitely extended. From the points t and w in the diagram draw visual rays. From the intersections of these visual rays with HPP drop vertical lines which will establish the positions of tp and wp on the perspective of the ridge of the roof. Lines drawn from tp and wp to the corners of the vertical walls of the house, as indicated, will complete the perspective of the roof.

To find the perspective of the porch roof, draw a visual ray through the point y on the diagram, and from its intersection with HPP drop a vertical. Where this vertical crosses the line apbp will give yp, one point in the perspective of the ridge of the porch. The perspective of the ridge will be represented by a line through yp, vanishing at vad. The point zp in the ridge will be vertically below the intersection of HPP with the visual ray drawn through the point z on the diagram. Lines drawn from yY and zp to the corners of the vertical walls of the porch, as indicated, will complete the perspective of the porch roof.

f>4. The perspective of the chimney must now be found. It will be seen that the chimney is formed by a rectangular block; and if it is supposed to extend down through the house, and rest upon the ground, it will be a block under exactly the same conditions as the one shown in Fig. 21, § 59. In order to find its perspective, extend its front vertical face, as indicated on the diagram, till it intersects HPP. A vertical line dropped from this intersection will be a line of measures for the front face of the chimney, and the distance ps, laid off on this line from VH1 (or VII.,), will show the true height of the top of the chimney above the ground, as given on the elevation. The distance so, measured from the point s on the line of measures, will be the true vertical height of the face of the chimney that is visible above the roof. Lines through s and o, vanishing at vab, will represent the horizontal edges of the front visible face of the chimney. The vertical edges of this face will be found vertically below the points where HPP is crossed by the visual rays drawn through the horizontal projections of these edges on the diagram.

Having determined the perspective of the front face of the chimney, the perspectives of the remaining edges may he found as in the cases of the rectangular blocks already discussed From the point r in the diagram, where the ridge of the roof intersects the left hand vertical face of the chimney, draw a visual ray intersecting HPP, and from this intersection drop a vertical line to the perspective of the ridge of the house, giving the perspective (rp) of the point where the ridge intersects the left hand face of the chimney. A line drawn from rp to the nearest lower corner of the front face of the chimney will be the perspective of the intersection of the plane of the roof with the left hand face of the chimney.

65. The problem of finding the perspectives of the windows and door is exactly similar to that of finding the perspective of the square hgkl on the surface of the block shown in Fig. 20.

It will be noticed that the intersection with the picture plane of the left hand vertical face of the porch gives a line of measures (§ 55 and § 59, note) for this face. This line may be used conveniently in establishing the height of the window in the porch.

At this point in the course the student should solve Plate III.