Fig. 63.

Fig. 64.

The same principles are observed in the end elevation of the hollow cylinder, shown in [Fig. 63]. The extreme rays meet the circumference in the points a and b; consequently the surface a c b is in light, and the surface a d b is in shade. The middle ray meets the surface perpendicularly at the point c, which will be the lightest part of that surface; similarly, d will be the darkest part. To show this, the shade line must be gradually increased in thickness towards the point d. The shading of the inner circle will be the converse of the outer. [Fig. 64] shows a plan of the same object.

Fig. 65.

Cylindrical Surfaces.

—Let a b c d, [Fig. 65], be a plan, and k l n m an elevation of a cylinder. The portion a c b is in light, and the portion a d b is in shade, of which latter portion a and b are the edges. From the points a and c draw vertical lines e f, g h. Then will e f be that part of the cylinder upon which the light falls perpendicularly, or the lightest part, and g h the edge of the surface in shade, or that portion of the surface of the cylinder that would cast a shadow upon the plane of projection. Hence this will be the darkest part, and consequently it is obviously improper to make the line k l a shade line. This demonstration, which is given by Binns, shows that shade lines must never be applied to cylindrical surfaces. If this principle be observed, cylindrical may be readily distinguished from flat surfaces.

Fig. 66.