SHADOW, 



vanilhingline of the plane of (hade ; and becaufe the plane 

 of (hade is fuppofed to cut the original plane, the interfec- 

 tion, which is the (hadow, will be a line in the original plane, 

 and therefore the vanifhing point of the Ihadow will be in 

 the vanifhing line of the original plane ; and as it has been 

 fliewn that it is alfo in the plane of (hade, it will therefore 

 be in the interfcftion of the plane of ftiade, and the vaniiTi- 

 ing line of the plane on which the fhadow is thrown. 



This problem is general for planes and lines in all fitua- 

 tions, but in the following examples the centre and dijlance 

 of the pifture are fuppofed to be given, and the pofition of 

 the pidure is that of being perpendicular to the primary 

 plane or firft original plane : the objeas themfelves are 

 folids, whofe edges or planes are fuppofed to be perpen- 

 dicular to the plane on which they Hand. As oblique pofi- 

 lions very feldom occur in praftice, we fhall fuppofe the 

 vanifhing line of the original plane, on which the objeft is 

 placed, to be given. 



To find the fhadow of a prifm placed on the primary 

 plane. 



Let AB (fgs. 3, 4, and 5.) be the vanifhing line of the 

 plane of the bafe, and fince the pifture is fuppofed to be per- 

 pendicular to the primary plane, the vanifhing line of the plane 

 of fhade, occafioned by the vertical lines which form the 

 concourfe of the fides of the objeft, will be perpendicular 

 to the vanifhing line A B. Let S J, therefore, be the va- 

 nifhing line of a plane of fhade, occafioned by any line of 

 concourfe, S being the vanifhing point of the fun's rays, 

 and s the interfedion of the vanifhing line of the plane of 

 fhade, with that of the plane on which the fhadow is to be 

 thrown. 



'Let g d, b a, mn, be the edges of the folid ; join bs and 

 a S, cutting each other in c ; and I c i?. the fhadow, occa- 

 fioned by the edge or line of concourfe b a. Draw c B and 

 d?>, cutting each other in e; or, if iiecefTary, produce them 

 to cut in c, and c e\i the fhadow, occafioned by the edge a d, 

 parallel to the plane of the original plane ; alfo draw ; A 

 and S/, cutting each other in i ; or, if neceflary, produce 

 them to cut each other in », then el will be the fhadow of 

 the edge df. L:iflly, draw i s, which will complete the 

 (hadow of the prifm, as required. 



Fig. 3. fhewi the fhadows of the objeft when the fun 

 is before the pifture ; Jig. 4. inews the fliadow when the fun 

 is behind the pidurc ; and Jig. 5. when the fun is in the 

 plane of the pifture. 



To find the fhadow of a building with a break. Let V L 

 (Jig. 6.) be the vanifhing line of the horizon, V the vanifliing 

 point of the horizontal lines, reprefented by a c and b d, 

 that form the end of the building, alfo of ef, g h, which 

 reprcfent the horizontal lines forming the fides of the break. 

 Let the fun be fuppofed to be in the plane of the piflure, 

 or its rays parallel thereto, and let the planes abdczwA 

 eghfhe in fliade, and the plane e g /j f v:\\\ throw a 

 ftiadow upon the plane ablk, and the plane abde upon 

 the horizon. As the fun's rays are parallel to the pifture, 

 they will have no vanifhing point, but ftill the rule will hold 

 in this cafe alfo. Through the vanifhing point L, draw 

 L M perpendicular to V L, then L M is the vanifhing line 

 of the plane abl h, on which the fhadow is to be thrown ; 

 through V draw V M parallel to the fun's rays, or make 

 the angle L V M equal to the angle which the fun's rays 

 make with the plane of the horizon. Thus M is the va- 

 nifhing point of the fhadow of all lines vanifhing in V, 

 upon the plane abli: therefore, to find the fhadow of the 

 line hg, join M h, and produce it to m ; and draw g m paral- 

 lel to M V, then m will be the fhadow of the point g, and 

 h m of hg. Draw m n parallel to g e, and m n will be the 



fhadow of ge: therefore hmnf will be the whole fhadow of 

 the plane hgef, upon the plane ablk. 



To find the fliadow of the end abed upon the plane of 

 the horizon : draw a o parallel to L V, and b parallel to 

 M V ; then a is the fhadow of the vertical line A B : join 

 V, and draw dp parallel to M V, and op is the fhadow of 

 bd: join^L, and draw r q parallel to M V, and /> 5 will be 

 the fhadow of the line dr, not feen : join s q, or draw it pa- 

 rallel to L V, then aopqs will be the fhadow of the build- 

 ing upon the plane of the horizon. 



Many more examples of fhadows might be givi^n, but if 

 the principles here fliewn are underflood, the artiil will not 

 be at a lofs to find the (hadow of any right-lined objeCl 

 whatever: for to find the fhadow of an objeft contlituted by 

 planes, and confequently terminated by ftraight lines, is no 

 more than to find the fhadow of thefe lines. If a circle be 

 given, the circumference may be divided by parallel lines 

 into parts, and the fhadows of the points of divillon may 

 be found by finding the fhadows of the intercepted hues, 

 and drawing a curve round the extremities. 



If it were required to find the fliado%vs upon feveral planes, 

 firft find the fliadow in the plane on which the objcdl Hands, 

 and obfcrve where the fhadow meets the next plane ; then 

 having the vanifhing line of this fccond plane, oblerve where 

 the vanifhing line of the plane of fliade cuts the vanifhing line 

 of thi'; fccond plane, then the point of interfedion is the 

 vanifhing point of the fliadow on the fecond plane. 



The principles fliewn under the article Pkojectios, will 

 apply equally to the reprefentation of objeds in perfpeflive, 

 particularly where the planes which throw the (hadow inter- 

 ItSl the plane on which the fliadow is to be throv/n ; for by 

 continuing the line that throws the fhadow, and the inter- 

 fedion of the plane to meet each other, you have the point 

 where the fliadow terminates ; and therefore, it a point be 

 given in the fhadow, the diredion of the fhadow will be 

 known. Thus in the lafl: example, fuppofe the line ao ob- 

 tained ; and fince the point is the beginning of the fliadow 

 of the line b (•/„ produce ac and b d to meet in V : join V, 

 and draw the ray of the fun dp, then op is the fhadow of 

 id: produce f/r and f J to meet in L, and ]oin p I ; draw 

 the ray rq from r, then pq n the fhadow of dr, not feen. 



To find the vanifhn^g hue of a pole upon feveral planes. 



Let A B C D E F G H I K, {Plate II. Shado-jus, fg. i.) 

 be the outline of a building, with a lean-to or pent-houfe 

 D E N P Q : V is the vanifhing point of all horizontal lines, 

 in the g^atsle ABL IK of the main houfe, and alfo of the 

 gable D MQ C of the pent-houfe ; L' is the vanifliing point 

 of all the horizontal lines in the parallel fronts BFGLand 

 DENM; and as all vertical planes have vertical vanifliinrj 

 lines, V Ris the vanifhing line of the parallel gables ABLI K 

 and C D M Q ; LU the vanifliing line of the fronts B F G L 

 and D EN M ; I L G H is the reprefentation of the roof of 

 the main building, and OMN P that of the pent-houfe. 



Produce L I to m.eet V R, its va^iifhing point, in S : draw 

 S L', which will be the vanifhinj line of the inclined plane 

 L G H I, for S and L are the vanilTiing points of two lines 

 in that plane : produce M Q to meet V R in T, and draw 

 T L ; then T L is the vanifhing line of the uicjined plane 

 M N P Q of the roof of the pent-houfe, becaufe T and L 

 are the vanifliing points of two lines in that plane. 



Let W X be a pole, relling upon the end of the houfe in 

 the fame plane with the gable A B L I K ; and let be the 

 vanifhing point of the fun's rays : produce the pole X W 

 t") meet V R in R, then R is the vanifhing poist of the pole, 

 or of the line tliat throws the fliadow : therefore by drawing 

 R, R will he the vanifhing line of the plane of fhade, 

 which let cut V I, the vanifhing line of the horizon, in Y; and 



LU, 



