m

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286

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house, as q ; and move the sliders n and O, till the intersectionof the threads at P, is directly between the eye and the pointq ; then put down the arch flat upon the paper on the hoard,as s t, and the intersection of the threads will he at w. Markthe point w on the paper with the dot of a blacklead pencil,and set the arch upright again as before ; then look throughthe hole r, and move the sliders N and o, till the intersectionof the threads comes between the eye and any other point ofthe house, as w ; this being done, put down the arch againto the paper, and make a pencil-mark thereon at the inter-section of the thread as before; obtain the point p in thesame manner, and draw a line from that mark to the one atw. The line p w, thus obtained, will be a representation intrue perspective, of the corner pq of the house.

By thus bringing the intersection of the threads success-ively between the eye and other points of the outlines ofthe house, as r s, &c., and putting down the arch to markthe corresponding points, on the paper, at the intersectionof the threads, then connecting these points by straight lines,the entire perspective outline of the house will be obtained.In like manner, find points for the corners of the doors, win-dows, &c., and draw the finishing lines from point to point.The perspective drawing thus produced, may then be com-pleted, by shading it according to the manner in which thelight is observed to fall on the original.

Great care must be taken, during the whole of the time,that the position of the machine be not shifted on the table ;and to prevent such an accident, the table or support em-ployed should be perfectly steady, and the machine fixeddown upon it by screws or clamps.

It is obvious that a landscape, or any number of objectswithin the field of view through the arch, may be delineated,by finding a sufficient number of points, and connectingthem by straight or curved lines, as they appear in the ori-ginal objects.

The arch ought to be not less than a foot wide at the bot-tom, that the eye at z may have a large field of view throughit ; and the eye should be then at least ten inches and a halffrom the intersection of the threads at p, when the arch isset upright. If the eye be nearer, the boundaries of the viewat the sides near the foot of the arch, will subtend an angleat z of more than sixty degrees, which will not only strainthe eye, but will cause the outermost parts of the drawingto have a disagreeable appearance. To avoid this, it will heproper to draw back the sliding bar i till z be fourteen inchesand a half distant from p ; then the whole field of viewthrough the foot-wide arch, will not subtend an angle to theeye at z of more than forty-five degrees : which will give amore easy and pleasant view not only of the objects them-selves, but of their representations upon the paper on whichthey are delineated. Hence, whatever may be the width ofthe arch, the distance of the eye from it should be in this pro-portion : as twelve is to the width of the arch, so is fourteenand a half to the distance of the eye (at z) from it.

If a pane of glass, previously coated with thin gum-water,and dried, be fixed in the arch, a person who looks throughthe hole at r, may delineate upon the glass the objects whichhe sees at a distance, and the delineation may be afterwardstransferred to paper. By this means will be saved the trou-ble of putting down the arch to take the position of everypoint, but it will not be so easy to obtain a correct repre-sentation.

Perspective op Shadows.— The shadow of an object isno more than the projection of its contour upon one or moreplanes, from a given luminous point, and is therefore the darkspace upon these planes, occasioned by the intervention of theobject, which hinders the rays of light from proceeding in

w liet |ief

straight lines. To avoid difficulties, the luminary! j th sthe sun or artificial light, is considered as a pointi ‘sun’s rays are considered as parallel.

Problem. — Given the vanishing line of a plane, ' rl t ,of a line insisting upon that plane, and its vanish” a h^o 111also the vanishing point of the sun’s vans ; to find 1of the line. 0 f

Elate I. Figure 1.— Let a b he the vanishing h|' t a pd ®plane, a b the image of the line, v its vanishing P°J nthe vanishing point of the sun’s rays ; join V S, an P f jp c, iit to meet A b in s : join b s and a s, cutting each 0 ■

then b c is the shadow of the line required. siU 1 ’ ■

For the vanishing point of the line, and that otrays, are in the vanishing line of the plane of sha dffore V s s is the vanishing line of the plane of sba e ’ j. gposhadow is occasioned by the intersection of the pb 111 ®, fiief 6with the original plane, whose vanishing line is g 1 0 ffore the point s, the intersection of the vanishing/ jjne 0 , |plane on which the line insists, with the vanisbing^.^jfothe plane of shade occasioned by the line, is the ,;

point of the shadow. , [

Example .— To find the shadow of a cube. j. t j, e f^ } j jFigures 2 and 3.— A b being the vanishing lin e 0 t | )g 1

of its base, and of the surface on which it rests »g d, b a, mn, being supposed to be perpendicular*i_ ;r _ _ j-<lie Ol'lS 1

the

inol i &

jin e ’

t e

then, if the picture be perpendicular to the ong“- -the vanishing line of a plane of shade occasioned by 11 Atical arrises, will be perpendicular to the vanishing Jia g |, 9 itherefore let ss be the vanishing line of the P> an ®.l po<"‘occasioned by the vertical edges, s being the vanish'^ Vof the suns rays, and « the intersection of the van* bor the plane of shade with that of the plane on *shadow is to be thrown.

Join bs and a 9, cutting each other in c; then * *

shadow occasioned by the edge b a; join cs and db

each other in e, or, if necessary, produce them to co (0

c e is the shadow occasioned by the edge, a P al ‘!

plane of its base; also join ca a nd 3 f, cutting

J9 in

i

ara -,^' 1

1 it

k/l no uactt j aiou jum c. a auu uyj — Jl©!* U* " ’

1 , or, if necessary, produce them to cut each o ^ ne i will be the shadow of the edge df; lastly? . . c .

will complete the shadow of the cube, as re ? ul ^ e f 0 reFigure 2 shows the shadow when the sun 13 n jg b e ^ture : Figure 3, shows the shadow when the is ,pthe picture ; and Figure 4, the shadow when tplane of the picture. vied 3 ^A ^

Many more examples of the shadows of 0 ^ n< jerst°°given, but if the principles here shown are ^student will not be at a loss to find the shado'- ^ aI) y » S)lined object whatever. To find the shad o\ ^ tb e 0 jil/

lined object, is no more than to find the sha 0 ^ tl)° s tM

or arrises, formed by the meeting of the si eS ’ gi v ® ’ iii 1 'of the lines forming the contour; if a c \ r ® eg j n to P a ' fb 1 "’circumference may be divided by parallel 1m ^ uI jJthe shadows of the points of division may ^.^ying , g gb 9ing the shadows of the intercepted parts, then ^ p in d p]»nround the extremities. If it were require _ ; n t . „Ao

°n which thTTi^ p,anes > first, find the shadow in " j,a u«“eets the n ' ® DE 6Ct . r f StS ; observe where the t ,ssecond plane oho " e ’ t ,en having the vanishing . pis

shade cuts’t£ rPe , W],ere tile vanishing'line

Point of iZtT mhh, S fi’-e of the second

this second nln lon 18 the vanishing point of the ,-tiCPzojzct" o/X S f e ®^ows nnder 'tt fC

a* to ShSS,*® Prij . ,ci > !es W 1 / aS ^ , *

PERUZ7I R A r T, ? projection. _ s liof"

Accajano in t) * ^P^SSARE, in biography* ‘ „iiJJ ti,e ^nitory of Sienna, in 1481, in P°° r

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