788

THEORY AND PRACTICE OF ENGINEERING.

Book II.

Fig. 900

Fig. 901.

And the ring LB, which has its face in shade, casts a cir-cular shadow on the ground, which is darker than the ob-ject that has defined it : the globe MC receives its lightin front.

In a polygonal or circular ring, the boundaries of light andshade may be accurately defined, by having its ichnographyand elevation properly drawn out. If the seat of the sun’sravs be drawn on any plane, on which a cylinder is laid, withits axis perpendicular to the seat and parallel to the plane,the lightest line on the cylinder will be nearer to the planein this position than in any other ; but if the axis of thecylinder make oblique angles, then the line of light will behigher on the cylinder. And, should the axis of the cylinderbe parallel to the seat of the sun, the lightest line on thecylinder will be at its greatest distance from the plane : theserules cannot be so well understood as by a reference to themodel of a polygonal ring laid in a position to receive thesun’s rays, and then its several planes may be traced geome-trically, and the principles of light and shadow rendered clear.

In shading the globe , we must first consider the point uponwhich the rays of light directly fall, and then graduallydiminish its effects until the shade commences. But wemust not forget that the outer edges receive a reflected light,and that no part of the surface which bounds the figure isblack. When the sun’s rays fall upon a reflecting plane, theangles made by them will produce reflected light, which isreceived by every part of the object within its influence: theglobe standing over a sheet of white paper would conse-quently have all its under side illuminated and renderedbrighter. To project its shadow it is necessary to draw outthe several planes, and pursue the course adopted in descrip-tive geometry.

As the light of the sun falls perpendicularly or from above,the top edges and the interior of a hollow body will re-ceive a portion of it, and the sides N, O. P will be of differentshades as they are more or less removed from the position toreceive the direct rays of light.

E, F, D, will show the ordinary manner of shading solidbodies, the light being presumed ordinarily to proceed fromthe left hand, and where two objects are shown, as II, I, theirseveral planes which are on the same parallels must be shadedin the same manner. As the rays of light proceed instraight lines, every opaque object on which they fall throwsa shadow on the side opposite the luminous body ; and thisshadow is darker in proportion as the illumination is stronger.

Shadows are either right or versed , according to the positionof the planes which receive them: that which is thrown byan upright body, as the prism whi'*h is projected on theplane of the horizon, is a right shadow ; that on a verticalplane, as a beam fixed perpendicular to the face of a wall,is a versed shadow. In both instances the length of theshadow is to the height of the opaque body, as the cosine tothe sine of the angle which the luminous ray makes with theplane. The altitudes of objects may be thus taken bymeasuring the shadows they produce, and which was fre-quently done by the ancients.

Sciography , or the science which teaches the projection ofshadows, has been very successfully studied by many artists,and it will only be necessary to allude to a few more simplearchitectural forms to make the subject perfectly clear.

A cylinder, having an abacus or square tile laid upon it,would, when the sun is at an angle of 45°, form a shadowin depth equal to its projection. A line drawn from the F ‘S-

centre to the angle of the abacus is the seat or plane of a ray of light; perpendicularlines represent the surface of the cylinder, and when parallel lines to the rays of light areprojected and made to intersect with those that are perpendicular, the points of intersec-tion express the extent of the shadow, and a line drawn through them indicates it.

l-jg. 902.