In Fig. 425, A is the plan and B is the elevation of a shelf attached to a wall. From a and c draw a b and c d, according to the angle previously directed; from b erect a perpendicular intersecting c d at d; from d draw de parallel to the shelf; then the lines cd and de will define the shadow cast by the shelf. There is another method of finding the shadow, without the plan A. Extend the lower line of the shelf to f, and make cf equal to the projection of the shelf from the wall; from f draw fg at the customary angle, and from c drop the vertical line cg intersecting fg at g; from g draw ge parallel to the shelf, and from c draw cd at the usual angle; then the lines cd and de will determine the extent of the shadow as before.

Fig. 421.

Fig. 422.

Fig. 423.

Fig. 424.

.566. - To Find the Shadow Cast by a Shelf which is Wider at one End than at the Other. - In Fig. 426, A is the plan, and B the elevation. Find the point d, as in the previous example, and from any other point in the front of the shelf, as a, erect the perpendicular a e; from a and e draw a b and e c, at the proper angle, and from b erect the perpendicular bc, intersecting ec in c; from d, through c, draw do; then the lines id and do will give the limit of the shadow cast by the shelf.

Fig. 425.

Fig. 426.

## 567. - To Find The Shadow Of A Shelf Having One End Acute Or Obtuse Angled

Fig. 427 shows the plan and elevation of an acute-angled shelf. Find the line eg as before; from a erect the perpendicular ab; join b and e; then be and eg will define the boundary of shadow.

Fig. 427.

## 568. - To Find The Shadow Cast By An Inclined Shelf

In Fig. 428 the plan and elevation of such a shelf are shown, having also one end wider than the other. Proceed as directed for finding the shadows of Fig. 426, and find the points d and c; then ad and dc will be the shadow required. If the shelf had been parallel in width on the plan, then the line dc would have been parallel with the shelf ab.

Fig 428.

## 569. - To Find The Shadow Cast By A Shelf Inclined In Its Vertical Section Either Upward Or Downward

From a (Figs. 429 and 430) draw a b at the usual angle, and from b draw bc parallel with the shelf; obtain the point e by drawing a line from d at the usual angle. In Fig. 429 join e and i;. then ic and cc will define the shadow. In Fig. 430, from o draw oi parallel with the shelf; join i and e; then ie and c c will be the shadow required.

Fig. 429.

Fig. 43c

The projections in these several examples are bounded by straight lines; but the shadows of curved lines may be found in the same manner, by projecting shadows from several points in the curved line, and tracing the curve of shadow through these points. (Figs. 431 and 432.)

Fig. 431.

Fig. 432

570. - To Find the Shadow of a Shelf having its Front Edge, or End, Curved on the Plan, - In Figs. 431 and 432 A and A show an example of each kind. From several points, as a, a, in the plan, and from the corresponding points o, o in the elevation, draw rays and perpendiculars intersecting at e, e, etc.; through these points of intersection trace the curve, and it will define the shadow.

Fig. 433.