# Shadows of Solids 42

## shadow, line, shade, prism, plane and plinth

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(2) These determine the shade lines.

(3) Cast the shadows of these shade lines by the method fol lowed in Problem II. .

47. Problem VI. To find the shade and shadow of one object on another..

In Fig. 22 is shown in plan and elevation a prism B, resting on H and against V. Upon this prism rests a plinth A: To find the shadow of the plinth on the prism and the shadow of both or. the co-ordinate planes. Since these dbjects have their faces either perpendicular to, or parallel to, the co-ordinate planes, we can deter mine immediately the light and shade faces and from them the 'shade lines.

48. Considering first the plinth A, it is evident that its top, left-hand and front faces will receive the light, that the lower and right-hand faces will be in shade. The back face resting against the V plane will be its own shadow on V. (§ 39) The shade lines of A will be, therefore, ef,fy, ye and ed.

Cast the shadows of these lines. A rests against V and part of its shadow will fall on V; also, since it rests on B the remainder will fall on B. Begin with the point e, one end of the shade line; this point, lying. in V, is its own shadow on V. (§ 39).

The line of being perpendicular to its shadow, or as much of its shadov as falls on V, will be, therefore, a 45° line drawn, from ev. The point th, in plan, shows the amount of the line of which falls on V, the rest If falls on the side face of the prism;and this shadow, is not visible in elevation or plan..

The shadow of 'the point f evidently falls on the edge of the prism at f, see plan. This point f is one end of the shade line fy, there fore f is one point in the shadow of fy on the front face of the prism B.

The line fig being parallel to this front face, its shadow will be parallel to the -line, therefore from the point fs we draw the horizontal linetr,..

If from the point we draw the projection of a ray of light back to the shade line fvyv we the amount of the line casting a shadow on the front face of B, that is to say, the distancetrv. The shadow of the remainder, rvyv, falls beyond the prism on the V plane, and is evidently tha line rvsgvs. Thus

the shadow of the shade line from e to y has been determined.

The next portion of the shade line, ye, is a vertical line and we have already obtained the shadow of the end g. Since it is a vertical line its shadow on V will be vertical and equal in length. Therefore draw gvsevs.

There remains now only the edge, ed, of which to cast the shadow. The end d being in the V plane must be its own shadow on that plane. (§ 39). We have already found the shadow of the other end c, at cvs. Therefore dyes is the shadow of de and completes the outline of the shadow of the plinth.

It will be noted that dvevs.is a 45° line, which would be expected since the edge do is perpendicular to V.

49. Considering next the prism B, we find by applying the projections of the rays of light to the plan, that the front and left-hand faces are in light, and that the right-hand face is in shade. Therefore the only shade line in this case is the edge 972n. The upper part of this, ner,s is in the shade of the plinth and therefore cannot cast any shadow.

It is to be noted that thq ray of light from the point ry in the plinth A passes through the point r,s in the shade line of the prism B. In finding the shadow of this point at rvs we therefore have found the shadow also of one end of the shade line nr. Since air is vertical, its shadow will be vertical on V. There fore draw rvswvs. This line completes the shadow of the two objects upon the V plane.

From the point of shadow woo draw the V projection of the ray back to the line ns'r,o. This shows how much of the total line nr falls upon V, and how much upon IL .

The shadow on 11 of the portion nw will be a 45° line since ftw is perpendicular to II. The point n being in the Ii plane is its own shadow on that plane.

It to be noted that the point who is on the perpendicular directly below wvo. .

50. Problem Vll. To find the shade and shadow of a pedestal.

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