SHADOW

, Shade, in Optics, a certain space deprived of light, or where the light is weakened by the interposition of some opaque body before the luminary.

The doctrine of Shadows makes a considerable article in optics, astronomy, and geography; and is the general foundation of dialling.

As nothing is seen but by light, a mere shadow is invisible; and therefore when we say we see a shadow, we mean, partly that we see bodies placed in the Shadow, and illuminated by light reflected from collateral bo- i es, and partly that we see the confines of the light.

When the opaque body, that projects the Shadow, is perpendicular to the horizon, and the plane it is projected on is horizontal, the Shadow is called a right one: such as the Shadows of men, trees, buildings, mountains, &c. But when the body is placed parallel to the horizon, it is called a versed Shadow; as the arms of a man when stretched out, &c.

1. Every opaque body projects a Shadow in the same direction with the rays of light; that is, towards the part opposite to the light. Hence, as either the luminary or the body changes place, the Shadow likewise changes its place.

2. Every opaque body projects as many Shadows as there are luminaries to enlighten it.

3. As the light of the luminary is more intense, the shadow is the deeper. Hence, the intensity of the Shadow is measured by the degrees of light that space is deprived of In reality, the Shadow itself is not deeper; but it appears so, because the surrounding bodies are more intensely illuminated.

4. When the luminous body and opaque one are equal, the Shadow is always of the same breadth with the opaque body. But when the luminous body is the larger, the Shadow grows always less and less, the farther from the body. And when the luminous body is the smaller of the two, the Shadow increases always the wider, the farther from the body. Hence, the Shadow of an opaque globe is, in the first case a cylinder, in the second case it is a cone verging to a point, and in the third case a truncated cone that enlarges still the more the farther from the body Also, in all these cases, a transverse Section of the Shadow, by a plane, is a circle, respectively, in the three cases, equal, less, or greater than a great circle of the globe.

5. To find the length of the Shadow, or the axis of the shady cone, projected by a sphere, when it is illuminated by a larger one; the diameters and distance of the two spheres being known. Let C and D be the centres of the two spheres, CA the semidiameter of the larger, and DB that of the smaller, both perpendicular to the side of the conical Shadow BEF, whose axis is DE, continued to C; and draw BG parallel to the same axis. Then, the two triangles AGB and BDE being similar, it will be AG : GB or CD :: BD : DE, that is, as the difference of the semidiameters is to the distance of the centres, so is the semidiameter of the opaque sphere to the axis of the Shadow, or the distance of its vertex from the said opaque sphere.

Ex. gr. If BD = 1 be the semidiameter of the earth, and AC = 101 the mean semidiameter of the sun, also their distance CD or GB = 24000; then as 100 : 24000 :: 1 : 240 = DE, which is the mean height of the earth's Shadow, in semidiameters of the base.

6. To find the length of the shadow AC projected by an opaque body AB; having given the altitude of the luminary, for ex. of the sun, above the horizon, viz, the angle C, and the height of the object AB. Here the proportion is, as tang. [angle] C : radius :: AB : AC.

Or, if the length of the Shadow AC be given, to find the height AB, it will be, as radius : tang. [angle] C :: AC : AB. |

Or, if the length of the Shadow AC, and of the object AB, be given, to find the sun's altitude above t<*> horizon, or the angle at C. It will be, as AC : AB :: radius : tang. [angle] C sought.

7. To measure the height of any object, ex. gv. a tower AB, by means of its shadow projected on an horizontal plane.—At the extremity of the shadow, at C, erect a stick or pole CD, and measure the length of its shadow CE; also measure the length of the Shadow AC of the tower. Then, by similar triangles, it will be, as EC : CD :: CA : AB. So if EC = 10 feet, CD = 6 feet, and CA = 95 feet; then as 10 : 6 :: 95 : 57 feet = AB, the height of the tower sought.

, in Geography. The inhabitants of the earth are divided, with respect to their shadows, into Ascii, Amrhiscii, Heteroscii, and Periscii. See these terms in their places.

, in Perspective, is of great use in this art. —Having given the appearance of an opaque body, and a luminous one, whose rays diverge, as a candle, or lamp, &c; to find the just appearance of the Shadow, according to the laws of perspective. The method is this: From the luminous body, which is here considered as a point, let fall a perpendicular to the perspective plane or table; and from the several angles, or raised points of the body, let fall perpendiculars to the same plane; then connect the points on which these latter perpendiculars fall, by right lines, with the point on which the first falls; continuing these lines beyond the side opposite to the luminary, till they meet with as many other lines drawn from the centre of the luminary through the said angles or raised points; so shall the points of intersection of these lines be the extremes on bounds of the Shadow.

For Example, to project the appearance of the Shadow of a prism ABCDEF, scenographically drli- neated. Here M is the place of the perpendicular of the light L, and D, E, F those of the raised points A, B, C, of the prism; therefore, draw MEH, MDG, &c, and LBH, LAG, &c, which will give DEGH &c for the appearance of the Shadow.

As for those Shadows that are intercepted by other objects, it may be observed, that when the Shadow of a line falls upon any object, it must necessarily take the form of that object. If it fall upon another plane, it will be a right line; if upon a globe, it will be circular; and if upon a cylinder or cone, it will be circular, or oval, &c. If the body intercepting it be a plane, whatever be the situation of it, the shadow falling upon it might be found by producing that plane till it intercepted the perpendicular let fall upon it from the luminous body; for then a line drawn from that point would determine the Shadow, just as if no other plane had been concerned. But the appearance of all these Shadows may be drawn with less trouble, by first drawing it through these intercepted objects, as if they had not been in the way, and then making the Shadow to ascend perpendicularly up every perpendicular plane, and obliquely on those that are situated obliquely, in the manner described by Dr. Priestley, in his Perspective, pa. 73 &c.

Here we may observe in general, that since the Shadows of all objects which are cast upon the ground, will vanish into the horizontal line; so, for the same reason, the vanishing points of all Shadows, which are cast upon any inclined or other plane, will be somewhere in the vanishing line of that plane.

When objects are not supposed to be viewed by the light of the sun, or of a candle, &c, but only in the light of a cloudy day, or in a room into which the sun does not shine, there is no sensible Shadow of the upper part of the object, and the lower part only makes the neighbouring parts of the ground, on which it stands, a little darker than the vest. This imperfect obscure kind of Shadow is easily made, being nothing more than a shade on the ground, opposite to the side on which the light comes; and it may be continued to a greater or less distance, according to the supposed brightness of the light by which it is made. It is in this manner (in order to save trouble, and sometimes to prevent consusion) that the Shadows in most drawings are made. On this subject, see Priestley's Perspect. above quoted; also Kirby's Persp. book 2, ch. 4.

SHAFT of a Column, in Building, is the body of it; thus called from its straightness: but by architects more commonly the Fust.

Shaft is also used for the spire of a church steeple; and for the shank or tunnel of a chimney.