1. The drawings of which an architect makes use can be divided into two general kinds: those for designing the building and illustrating to the client its scheme and appearance; and "working drawings" which, as their name implies, are the drawings from which the building is erected. The first class includes "studies," "preliminary sketches," and "rendered drawings." Working drawings consist of dimensioned drawings at various scales, and full-sized details.

2. It is in the drawings of the first kind that "shades and shadows" are employed, their use being an aid to a more truthful and realistic representation of the building or object illustrated. All architectural drawings are conventional; that is to say, they are made according to certain rules, but are not pictures in the sense that a painter represents a building. The source of light casting the shadows in an architectural representation of a building is supposed to be, as in the "picture" of a building, the sun, but the direction of its rays is fixed and the laws of light observed in nature are also somewhat modified. The purpose of the architect's drawing is to explain the building, therefore the laws of light in nature are followed only to the extent in which they help this explanation, and are, therefore, not necessarily to be followed consistently or completely. The fixed direction of the sun's rays is a further aid to the purpose of an architectural drawing in that it gives all the drawings a certain uniformity.

3. Definitions. A clear understanding of the following terms is necessary to insure an understanding of the explanations which follow.

4. Shade: When a body is subjected to rays of light, that portion which is turned away from the source of light and which, therefore, does not receive any of the rays, is said to be in shade. See Fig. 1.

5. Shadow: When a surface is in light and an object is placed between it and the source of light, intercepting thereby some of the rays, that portion of the surface from which light is thus excluded is said to be in shadow.

6. In actual practice distinction is seldom made between these terms "shade" and "shadow," and "shadow" is generally used for that part of an object from which light is excluded.

7. Umbra: That portion of space from which light is excluded is called the umbra or invisible shadow.

(a) The umbra of a point in space is evidently a line.

(b) The umbra of a line is in general a plane.

(c) The umbra of a plane is in general a solid.

(d) It is also evident, from Fig. 1, that the shadow of an object upon another object is the intersection of the umbra of the first object with the surface of the second object. For example, in Fig. 1, the shadow of the given sphere on the surface in light is the intersection of its umbra (in this case a cylinder) with the given surface producing an ellipse as the shadow of the sphere.

8. Ray of light: The sun is the supposed source of light in "shades and shadows," and the rays are propo-gated from it in straight lines and in all directions. Therefore, the ray of light can be represented graphically by a straight line. Since the sun is at an infinite distance, it can be safely assumed that the rays of light are all parallel.

9. Plane of light: A plane of light is any plane containing a ray of light, that is, in the sense of the ray lying in the plane.

10. Shade line: The line of separation between the portion of an object in light and the portion in shade is called the shade line.

11. It is evident, from Fig. 1, that this shade line is the boundary of the shade. It is made up of the points of tangency of rays of light tangent to the object.

12. It is also evident that the shadow of the object is the space enclosed by the shadow of the shade line. In Fig. 1, the shade line of the given sphere is a great circle of the sphere. The shadow of this great circle on the given plane is an ellipse. The portion within the ellipse is the shadow of the sphere.

FIG-1.

Notation

13. In the following explanations the notation usual in orthographic projections will be followed:

H = horizontal co-ordinate plane. V = vertical co-ordinate plane. a - point in space.

av = vertical projection (or elevation) of the point. ah = horizontal projection (or plan) of the point. avS = shadow on V of the point a. ahs = shadow on II of the point a. R, = ray. of light in space.

Rv = vertical projection (or elevation) of ray of light. Rh = horizontal projection (or plan) of ray of light. GL= ground line, refers to a plane on which a shadow is to be cast, and is that projection of the plane which is a line.

14. In orthographic projection a given point is determined by "projecting"'it upon a vertical and upon a horizontal plane. In representing these planes upon a sheet of drawing paper it is evident, since they are at right angles to each other, that when the plane of the paper represents V (the vertical "co-ordinate" plane), the horizontal "co-ordinate" plane H, would be seen and represented as a horizontal line, Fig. 2. Vice versa, when the plane of the paper represents H(the horizontal coordinate plane), the vertical co-ordinate plane V, would be seen and represented by a horizontal line, Fig. 2.

15. In architectural drawings having the elevation and plans upon the same sheet, it is customary to place the "elevation," or vertical projection, above the plan, as in Fig. 2.

It is evident that the distance between the two ground lines can be that which best suits convenience.

16. As the problems of finding the shades and shadows of objects are problems dealing with points, lines, surfaces, and solids, they are dealt with as problems in Descriptive Geometry. It is assumed that the student is familiar with the principles of orthographic projection. In the following problems, the objects are referred to the usual co-ordinate planes, but as it is unusual in architectural drawings to have the plan and elevation on the same sheet, two ground lines are used instead of one.

17. Ray of Light. The assumed direction of the conventional ray of light R, is that of the diagonal of a cube, sloping downward, forward and to the right; the cube being placed so that its faces are either parallel or perpendicular to II and V. Fig, 3 shows the elevation and plan of such a cube and its diagonal. It will be seen from this that the II anil V projections of the ray of light make angles of 45° with the ground lines. The true angle which the actual ray in space makes with the co-ordinate planes is So9 15' 52' This true angle can be determined as shown in Fig. 4. Revolve the ray parallel to either of the co-ordinate planes. In Fig. 4, it has been revolved parallel to V, hence T is its true angle.

FIG-3.

FIG.4.

18. It is important in the following explanations to realize the difference in the terms "ray of light," and "projections of the ray of light."