Fig. 23 shows the plan and elevation of a pedestal resting on the ground and against a vertical wall. This is an application of the preceding problem in finding the shades and shadows of one object upon another. The profile of the cornice moulding on the left, at A, can be used as a profile projection in finding the shadows of those mouldings on themselves and upon the front face B, of the pedestal. By drawing the profile projections of the rays tangent to this profile of mouldings, it will be seen what edges are shade lines and where their• shadoWs will fall on the surface of B. 'The line avbv can be assumed to be the profile projection of the front face of B, and being a line is used as the ground line for finding the shadow on B. As this collection of mouldings is parallel to the V plane their shades and shadows will be parallel in the elevation. Otherwise the shadows of this pedestal are found in a manner similar to the preceding problem.
51. Problem VIII. To find the shadow of a chimney on a sloping roof.
Fig. 23a shows in elevation and side elevation the chimney and roof. The chimney itself being made up of prisms with their planes parallel or perpendicular to the V plane, its light and shade faces can be determined at once, as in Problem V. It will be evident from the figure that the top, front, and left-hand faces of the chimney in elevation will be in light. The remaining faces will be in shade, and the shade lines will be therefore, yd, on the back, de, and Lx. Not all of bx and yd will cast shadows for the shadow of the flat band, running around the upper part of the chimney, will cause a portion of these two lines yd and bx to be in shadow and such portions cannot cast any shadows. (See Problem VI—the shadow of one object upon another.) It is evident that, to find the shadow of the shade line of the chimney upon the sloping roof, we must have for a ground line a projection of the roof which, is a line. The roof in elevation is projected as a plane, but the side elevation (or in other words the profile .projection) shows the roof projected as a line in the lino /tPgP. This line will be then the ground line for finding the shadow of any point in the chimney on the roof. For example, take the point b. If we draw the profile projection of the ray through the point bP until it intersects the ground line 11PgP, and draw from •this point of intersection a horizontal line across until it intersects the vertical projection of the ray drawn through bv, this last point of intersection bs, will be the shadow of b upon the roof.
In a similar manner the shadow of any point or line in the chimney can be found on the roof.
Before completing the shadow of the chimney upon the roof let us consider the shadow of the flat band on the main part of the chimney. This band projects the.same amount on all sides. On the left-hand and front faces it will cast a shadow on the chimney proper. Only the shadow on the front face will be visible in elevation. To find this, draw the profile projection • of the ray through the point gP until it intersects the line aPvP, the profile projection of the front face. From this point y,P draw a horizontal line across until it meets the vertical projection of the ray drawn through qv. From qv, the shadow of qvwv on the front face will be parallel to gvwv, for that line is parallel to that face; therefore draw givz,v.
Now that the on the chimney itself have been determined, its shadow on the roof can found as explained in the first part of this problem. A portion of the shade line of the flat band, zvwv, wvav, etc., falls beyond the chimney on the roof, as shown by the line zsle., tow-, etc.
52. It is to be noted in the shadow on the roof that: (a) The shadows of the vertical edges of the make angles with a horizontal line equal to the angle of the slope of the roof (in this case 60°).
(b) The horizontal edges which • are parallel to V cast shadows which are parallel to these same edges in the chimney.
(c) The horizontal edges which are perpendicular to V cast shadows which snake angles of 45° with a horizontal line.
53. The above method would also be used in finding shad ows on sloping surfaces when the objects are given in elevation and side elevation, as, for example, a dormer window.
54. Problem IL ' To find the shades and shadows of a hand rail on a flight of steps and on the.ground.
Fig: 24 shows the plan and elevation of a flight of four steps situated in front of a vertical wall, with a solid hand rail on either side, the hand rails being terminated by rectangular posts. At a smaller scale is shown a section through the steps and the slope of the hand rail.
This problem amounts to finding the shadow of a broken that is to say, the shade line, on a series of planes. Each of the planes requires its own ground line, which in the case of each plane will be that projection of the plane which is a line. Since the planes of the steps and rails, with exception, are all parallel or perpendicular to the co-ordinate planes we can determine at once what planes are in light and what in shadow and thus deter mine the shade line.