Chap. VIII.

GEOMETRY.

785

All Opaque Bodies which are lighted up on one side cast a shadow on the opposite; andthose which receive their light from bodies larger than themselves cast a shadow as at A :

B

Fig. 890.

those that are of equal magnitude as those at 13, and those that receive their rays from asmaller light, as that of a candle or lamp, as shown at C.

All luminaries, as the sun, emit a stream of light by which objects are rendered visible,and those bodies which cannot be penetrated by it are called opaque bodies: the part whichis deprived of light, or which does not receive it, is said to be in shade, and that part ofany surface on which a shade is projected is called the shadow.

The side of the body, as that of a prism, which is not opposite the light, isthat which is in shade, as A K. Should the top of the prism receive the directlight, then the side K ought to have a teint, to distinguish it from the facewhich is so strongly illuminated : but if the rays fall at an angle of 45 degrees,the horizontal and vertical faces which receive them may be supposed equallybright.

Sciagraphy, or the principles upon which shadows are projected, will be thebetter understood as we advance in our knowledge of descriptive geometry,which explains as well as removes all the difficulty of understanding theposition of the several planes, or their relation to each other : as the rays ofthe sun are reflected in all directions, the projecture of the prism prevents apart of the reflected rays from proceeding to the plane behind the prism, andconsequently that plane would be a little darker than the face of the prismwhich is parallel to it; but as the side of the prism adjoining to the plane will throw areflection, it is difficult to distinguish any difference between them. The difference oflight between the side of the prism which is perpendicular to the plane and the planedepends on the position of the luminary ; if its plane be equally inclined to both, there willbe the same light on each ; but when it is more inclined to one than the other, then thatwhich is the most oblique will be the darkest.

In a cube that is doubly inclined, as in thefigure, its projection upon a horizontal plane is aregular hexagon, and upon a vertical plane a rect-angle ; thus showing the variety of shadows sucha solid may cast. By dropping perpendicularsfrom the solid angles of the cube, we may, upon thehorizontal plane, where the hexagon is shown, setout the seat of every portion of the cube which isobliquely placed above : by parallel lines we de-scribe upon the vertical plane the quadrangularfigure which the cube exhibits, and which is similarto a section seen diagonally. In stone cutting, aswe shall hereafter find, it is highly important thatwe understand the form of a cube in every position,and this is only to be exhibited by imagining avariety of planes, upon which the figure may bedrawn : the cube may be made to contain the sphereor portions of it, the planes of which can be foundin every direction, and afford the student an opportunity of study and practice in drawing.

Fig. 892.

A

r\

Fig.891.