The science of shadows TO SIR MARQUIS DE BEUVR ON, Mejlre ~ de-Camp du Régiment dé Harcourt Y Cavalry. Gentleman,, I work that sat the honor of your presmter, ri may not have it for you Im a ii) approval of the novelty > fi s principles you have amufe in the tenderest age } their study stated your inclination & your ta- % lens for Mathematics y Science fi for the perfonnes of your rank, & who seems to give to this treaty? sais hommage3 some right to parody fools your aufpices. What support does not take place to expect from a born Lord} for ainfidirey with a taste for geometry ? This taste, ass- tamed by a beautiful Education, began by throwing germs into your mind penfésy that reflection has hatched with fuccès, & who will not fail to rappor- a hundredfold increase in this hope more certain what efl probed as the noble defiance of returning one day to the state of fervices sgnalés; defir puissant fur un Coeur au / JZ gé- only yours. It is in this view that you work^ to make you samilier all what modern geometry has produced from discoveries; this Science, between your hands s will have fans doubt usefulness too great i that Fefi end extended in VArt Military, plans & profiles places 3 sor» * their attacks & defenses , army encampments, orders of battles marches of the troops, the disserent forms quon know how to take them; all these Opera- the knowledge of an infinity of au* very, make the resfort of a military Lord & Surveyor. You have convinced us in the camp of Regenne (a) , abbreviated exact & ingenious of that, of Compiegne ( b ) ; in practice, you have reduced the rules to a minimum.- blies by the Great Masters, for the attack & the defenfe of the places, for the camp & the March of the troops; you ave there^saii see that the Art Of War has rules jures, & a theory founded on principles follies of Mathematics. Such efila car- you have set out to (a) two leagues from Auxerre, on the River Yonne » The Marquis de narcourt & De Beuvron 1741, drew a sortification at the entrance of a pres» that Issus had her lifted up, and led her in the chains. In 1739. * - a iv vii) running; she announces a warrior deflinê a cover yourself one day with all the glory of [es ancestors, although one of their qualities is fussifi to make all their imitators immortal* I run away with a prosond refpeB s GENTLEMAN, tTotre very-humble & very* obeyed siant servîeur. Pupil The Elder. - PREFACE. When considering the difficulties that those that apply to the drawing have to overcome, when it comes to expressing, by means of Shadows, differens mor- civil & military Architecture, of which the various parts are not equal- exposed to light, are more or less less light than each other; we feel how useful it would be to have principles on S to know the place , species, shape & strength of om- bre, depending on the difserent wants to express. The purpose of this book 9 is to give some rules & fa- ciles to follow 5 by means of which one puisTe learn geometrically, what which is usually acquired only by induction & copying long-tems& by therefore without ever being within reach of@ % PREFACE. make reason of the motives on which we stand determine. To achieve this more surely, we -- went into great detail; we have done rehearsals, in favor of those to whom it is necessary to say the same things more than once ; we also have choir! the most stmple figures, which we explained as a surveyor & as drawn on, in order to be more airy- of all those to whom this Book can be useful; & we have divided this treatise into eight chapters. In the first we taught the way of laying the different species shadow, so as not to screw anything to destroy to those who start. In the second, after making vorr the need to assume the fixed Sun , we examine the diseren degrees of light that flat sursaces receive , more or less inclined to horison; Se also the vertical surfaces, likewise* PREFACE. x) pece, more or less inclined, by rap- port in The Sun. . In the third, it is observed that what way the sun's rays illuminate- bent convex curved surfaces, for coming to the connotation of the place, the kind of shadows they wear. In the fourth we make the the same applies to threats concave curves. In the fifth, we examine the esfets of the day on various excavations. In the sixth, we point out- see which side should be Pombre pro- of objects differently placed on the horison: The Shape of these shadows by report to their cause, & what happens when an obstacle prevents the shadow from spread out on the horison. In the seventh, we give general rules for determining the lar- geur & the length of shadows caused on a horisontals map or on a map xij preface. inclined, to-deius or to-desibus of the ho- risort. In the eighth finally we exami- in what ways do the spokes of the Sun illuminate mixed bodies. Those we have chosen, are soft dissertations- lures of Architecture; we have exa- mined each in particular, for know the place & the species of shadow that suitable for them, starting with those that make up the base of a column, & finishes- of the entablature. Following several of these chapters, we apply the observations which were made. By supplemenr, one gives a work title: The Dejjinateur at the Cabinet & at army., in which people who- military & field architecture- ters, will find the way to express by the wash } what belongs to Tune & k the other one. a. j*. jh*. I*. I*. r& "^i 3^*" ^" ^* &. & & & ® ® . & ® $ -4g £ # & & ^ ^ % ^ ^ ^ T A B L Of the chapters & sessions of the Science Of Shadows. HAPITRE FIRST. Where Fon ignites the way to pofer all Jones from Om- bres , Page i From the choice of brushes, & beyond way to preserve them; 2 Section one. In the way of pofer a flat shade, & cut shadows or flat, 3 Averiifjement, 5 Note/, 7 Note II, ibid. Note III, S Section H. how shadows are softened, on one side feulement ^ ibid. Section II. How shadows are softened on both sides, 1 o Chapter II where the need is shown to fix the Sun 5 jsi* or fon .examine xiv TABLE. next in what way the farsaces receive the rays of the Soleili z Section one. Or we examine the dis- SERE ns degrees of day that receive the^ furfaces more or less inclined on rhorifon, ibid. Note I \6 Note II\ 17 Note III, ibid. Note IV, ibid. Note V, iS Average ^ 19 Settion II, or Von obferve of which ma<- niere the sun's rays come ren- counter fur vertical faces, more or less less declined s ibid. Seftion III. Or your application- of what we have just seen, 2j Chapter III. Where Ion examines the nature shadows that the day produces as the convex fursaces, 3 1 Second, ibid. Se£lion II. Or Von makes applications of previous remarks, 37 Chapter IV. Where Von examines how the rays of The Sun meet the furs- concave curved faces, & or Von thimble- covers the nature of the shadows that their belong, 3 9 Se£Hon premiere. From vefpace of shadows that 1 TABLE. xy wear the curved furjaces toncaves, 3 9 Se£tion II. Where applications of previous remarks, 44 Chapter V way The Sun's rays illuminate disserent excavations, 47 Se£lion first. Places where ex- cavities bounded by flat furfaces m receive shadows & days, ibid. Warning, 49 Seftion II. From the place of shadows that received- wind the excavations enclosed by curved surfaces, 50 Chapter VI. Shadows produced as a result of Vhorifon, or fur plans, by objects placed there, 5 2 Se & ion first, ILO rating I made V Shadow quun object produced % ibid Seftion II. Or we discover the SORM of shadows caufed by dissèrens objects, 57 Sestion III. Or Von examines what happens when an obflacle prevents Vomber from s extend fur Vhorifon, 65 CHAPTER VII. Which contains the rules it leaking jump to determine the width & shadow length, 70 Se & ion first. Or Von gives a rule to determine the width of the shadows, ibid, xvj T B L Ë. Seclion II. Where Von gives a general rule- to determine the length of the shadows, 73 Seclion III. Or we break a rule of thumb. to determine the length of the shadows in inclined planes 77 Note, 78 Chapter VIII. Where Von examines t esset du day Jur mixed bodies, 80 First time. From place & nature shadows make fur the bafe of a co- lonne , 81 Se&ion II. The place & nature of the om- Bres fur the capital of a column, 82 Se&ion III. The place & nature of the om- Bres, what do the moldings that corn- pofent an entablature, 8| Section IV. Application of observations previous years, 89 End of the shadow Table. 1 THERE SCIENCE SHADOW^ To COMPARED TO DRAWING, CHAPTER I; Ozi/'o / z enjèigne pojet way strong tomes of Shadows, I-shadows are used to make Parofcre Utmtem on paper a drawing as it should be °mhrts° in execution; distancing the parties round plates; those that are full , of those who are seen ; ensin those who are more or less sharp, some of them the others. There are three species; sa-ComtUn see, equal shadows in all their D^pebce\ To % science extended, so-called flat shadows ; uneven & fading shadows- substantially, either on one side only, or two sides, what you call shadows softened with a feul side, & softened shadows on both sides. We'll teach the way to wash these different kinds of Shadows, after making some observations on the choice of brushes, & the way of them keep. The choice of brushes, & the way to preserve them. We only 2 * a brush, to be good, must be well trimmed; it is necessary that the hairs that are IZtxà?~ - ^years*e pipe > Be ^U Less As long Worm. than those who are outside, & related to way that if the pipe comes to split 9 the paintbrush cannot come out of it: it is plus, let the tip Be Sharp & well trimmed; for there is where the tip is faith- ble, that it is not possible to use it , without crossing the lines. This comes from what those who make them, pousfent the hair of the pine- CEAU in-dehorsy in order to make her do the tip, the hairs go away as we use it, & whatever precaution we take take, you can't cleanly wash with these kinds of brushes j there are none shadow.1 % no better than the ones we find at Bonnaire ** 3. To keep the brushes well, 'f0 ° te'. never let them dry without the v%kTpia* have washed several times in water"a" *4 net, until it appears that the one that comes out of it, is not dyed at all from the color of which the brush was char- it is also not necessary to leave them soakingf long-tems in the water, because the tip y pren- right a wrong fold., & the brush is not worth* right plus nothing* The use is to have two adjustable brushes- ends of the same stick, that one is called ente : one serves for the neck- their t & each other for the water it takes pouif soften* SECTION I, In the way depofer a flat tint$ 6 cut or flat shadows, N puts flat shades between two PnmUn lines, to mark the thickness of a JF^im wall or parapet, or finally leten- * the house is on Rue du Roule, at the corner of rue d"s Fossés Saint-Germain l'auxerrois; A 4 Science due of something this sok. Plan. ï. To put a flat shade between two Flê - * * parallel to C, B D, the brush being full enough, we start with^ put them along part of the line higher A C, as From A to E, & on leads the brush from left to right, in parallel with A E, in- cendant up to line B D, & la Part A E, B F is covered by the shade. We return promptly to put hue, from E to G, while driving the brush parallel to E G, going always from left to right, until that having arrived downstairs, he filled the es- pace E G F H; then we come back again put From G to l, then we go down juice- in HL, & we continue the same, juice- that the Parallel Space is integer^ filled mept. Fig. 2. 5. If the parallel space makes some- turn, we will turn the paper; ensorte que Tone can always walk the brush parallel to self, & wash like we just said it. Fig. 3; 6. If the disiance of a parallel A B to the other C D in: extremely wide, it is certain that the hue that your corn- menceroit to put at the top of A En E, would be dry before we had arrived from C shadow. $ in F at the lower parallel C D; that if next to it we again put a se- conde, this last recovery will not be able to ^therefore unite perfectly with the first, what eft absolutely needed- saire. To avoid this inconvenience, it is necessary put the hue right away from A to B ; then after go down to CD, going from left to right, as we have already said. When the brush arrived in the year- gle d % - cende nothing more, because this place is find out stronger than the refte, if he is dead loaded with a larger amount of neck- their. To avoid this, the brush on the edge of the shell, &c y forms its tip, after which we come extend, with this tip, what was remained in angle D ; in this way, the tint lies laid by-everything equally. WARNING. There are two things to observe, when we want to cleanse a desiin. There the first is that- white rights above the brush, without need, because to repafîer it, this forces to leave the hue, which must be; A iij 6 Science setting without interruption, as far as it is pos- {ible; & û after the hue is set, we want to repasfer the brush on what we will have left white, it often happens that the hue that surrounds these places, - in?" dry ; so that the one we talk about again, not being able to unite intimately with her s makes a strong bad esfet. The seconde, which is no less stupid- sequence, it is that we must not lose view the tip of his brush, so as not to not speak the lines, 7. If instead of a tint put between two lines, or in a quelcon figure- that, it is a question of placing a shadow cut, like the one we see at the Figure Four, we'll put some first 4" on a small length, as of A in B, & we will go down the brush until that the shadow has the width A C, that we judge about giving it; then after we still put as many, as B in D, along the line, that tone of- cend like this-front, c $ always of even. Fig, j, if the shadow makes a few detours, we will return the paper; for it always takes walk the brush parallel to yourself, from left to right, & never from top to low» shadow. 7 RE m ARQUE I. 8. It is good to observe here that, when vnous let's say we have to go left h right, Ion must design that pin- ceau having reached the right, where he brought the color, we do not turn right left, but as before, we just put it to the left for the OAR- to the right again; otherwise, one color from the right to the right. left,& this last part will be douoit- fully charged. NOTE IT 9. It almost always happens that Pine- water that can not hold enough neck- their to fully wash the part of a drawing that requires the same shade, we get is forced to take another : but we must ensure that this new- tint blends so well with the first that we can not perceive from their junction; for this, it is not necessary wait for the brush to be quite dry, that is, without color, so that the hue that is on the paper, being a little tems to dry, gives ease Âiv science to pick up another, which will mingle easily.* with the previous one. NOTE III. \ ? ïo. Every time we have to re- take a new color, you need to be good stir it with the brush, so that it has the same degree of strength; & as the pin- ceau gets too loaded, gets his tip- too grosTe, we do it again, we unload it by testing, & turning it on the edge shell. SECTION II. How to soften the shadows, side feulement% o n softens shadows on one side , shade for a * re by°to be a talud, a glaze 9 or a concave curved surface; then one uses two brushes fitted into the the same ente s of which one esk for water &c the other for color. Fi* 5&6. Suppose one wants to soften a shadow, in order to express the slope of a gla- or a talud , it is necessary to put the tint on the skin. shadow. 9 h along Line A B, over a width of- equal to half or about of the talud. This shade should be moist enough to that we can have the tems to turn the to water, to soften; what one the third party or the Me- of the shadow we have just cast, the along Line A B, & walking it alternately from left to right & from right to left, pulling down ; L'ombre y deseend En s'éclairant insen- Sibly, & sits perfectly smooth.- cie. We must not lose sight of the brush, I repeat again, on-all when it approaches lines that border what we wash. Concave surfaces are expressed in- core by a shadow softened from a single side 3 & this as we come in- seigner. 12. If the extent that one wants to soften ISL Fig. too long to undertake it from one end 7 & 's- to the other, then we do it to several re- taken, in this way: we put on the neck- line B D, over a length of one inch or so, like from B to C, & on a width proportional to that of from the surface, observing, as we have seen,- let's not say , let the color be asTeZr wet to have the tems soften, science without fear that it will be cut ; then from C to E on the same width, that one softens like the previous one, & similarly from E to F, that we soften the same- the same goes on, until the end of the year. finally the B D scope is finished. We don't always have to come in if before on the color, in order to soften it; when space is. narrow, just pass only the tip of the brush with water on the edge of the color, to prevent let her not Parish cut off. 13. When one of / sins where one places softened shadows, deserves attention , we warn the place that should receive the color, that is, we begin with wash it with water, so that the color does not take not so fast on paper, let's the freedom to soften it before it softens. drier. SECTION III. How to soften the shadows of two sides. Vroisitme 14, L E s softened shadows of both 'Dark. C ^ S J fervent in parostering surfaces shadow. rt convex curves; they are placed on the right, & up and down, when the bodies are laid vertically, or at the lower, when they are laid horison- \ atment > observing to let a little es- pace between shadow & ending line the body on that side, to be able to- doucir. If it is en1, for example, a cylin- dre, a cone or a column we want wash, it is necessary to begin with prevention with water the whole figure, or at least its part where one has to lay the color, to prevent it from drying too fast , then lay the shade from A to B, & adou- cir on both sides, as can be re- mark in figures jo, il, 12 & 14. 15. If the body or surface has too much to be able to put the om- bre all of a sudden from one end to the other, it will be put on several occasions, in com- leading by one end, & finisTant by the other, & one will soften it as each- what side ; we will see in the following Why we place the shadow right on the bodies vertical, & why we put it down on those who are horisontal. 16. To express the roundness of a list - Fig. 13. be, we put the shadow inside t & little by little distance of the circular line A B C D , which finishes its size 5 6c always on ii Science the right 3 is turned from the bottom in crescent shape; then it is softened from each side. These shadows, to be well softened , must be pale, cV ironed to plusieurs times: this is the advice we give to those who want / aver cleanly. CHAPTER II Or did you see the birth of fixcr?- The Sun, 6 where one examines- leak in what way fur faces receive the sun's Rays. SECTION ONE. Or Von reviews disserens degrees of day that fursaces receive more or less respondents fur Vhorison* o u r fill in the object that we ourselves let's propose here, who eft to teach the rules that must be followed to shade at about all differens body, in order to parody them on paper as they (have , or they must be embossed y shadow dice s. is let's examine what happens when they are exposed to the day, in order to show that it is not by chance that one places Jes_ shadows, & that it must necessarily follow certain rules; otherwise one shading or what needs to be illuminated, & au otherwise, we would clarify what must be shade» We shall not examine here the- Bres nor the days that the objects receive enclosed, in places illuminated by artificial lights ; we will assume all these objects on the horison exposed to sun rays; & as long as one pay attention to the remarks we let's do, we hope we'll be in state of well placing the shadows, Se de bien observe the days, assuming the light p^AN ^ & the objects placed where we want. Fi m- 17. The sun being at The Point S of level RJ^ * / BJ£ with the horison M N, if he is presented with a UU rencon- vertical surface ABCD, it will receive the greatest light y^diflfi possible. 'O, PlusJfLflr ex t ' s r • rii 3 Jolt II). When the sun is at Point T, possàu. high above the horison MN3 its FJti 'les ray . coming obliquely meet ™ y ° nsdUfo- •1 c-r 1 • * 1 rencon- this iurrace, will not produce a lu-kentobuqm- /y . * F 1 * ment la. on- miere auiii Long Live that sus met her saCe, euee / i perpendicularly. ' ¥air ? science Pig. %?i 19. When the sun will be at point V, When US djrest; ement above the suriace verti- poi * y Rays ^ "perfect * - wedge a B c D, then the spokes do not make- fursace % iu sant that shave this surface, 1 will illuminate totTsTcUi-even less than if they met her k-obliquely* Fig. 18. 2G > * finally, the sun having reached the point X, to the right of point V, the surface vertical no longer receiving, on the left side %Tduz Y, The Sun's Rays, will be in- rte. When, the spokes do meet receives more teperly in the shade. clarity* On d P ' fer l at 4s degrees rfV height. We see that he would arrive from gran* annoyances, if, to shade, it fal* must conform to the movement of the so- leil. Fig. 19. ii. To avoid these variations, we sup* lejbz'i P°fe Ie sun left, & fixed at 45 of- R elevation ridges, that is, at point S , between the horisontal line & the Meridian* It is not, however, that we cannot assume the sun higher or lower, at left or right , it depends on the taste or the reasons artists have for it; it is: why we will establish principles which will also serve to place the shadows in these different cases* The sun being assumed at 45 degrees let's see the effect it produces on the different bodies, which we divide into four species \ sa see, I°. those who are t> e s, Shadows. t j finished with flat surfaces; 2°. that which are terminated by a convex surface ; 30. those that (ended with a surface concave ; 40. those that are terminated by piusieurs surfaces, que nous ap- mixed body pelions, it. Let's imagine that an ABCD surface Fig. 19: rotates freely on axle EF, as / U^°tls4i a balance, it is indisputable that Jf & fy dc r r n r 1 R height, a. 11 this situation is per-M / ace, ^ i " 1 • i / * i m 11 ja.it the mems pendicular to the rays of the loleil, she angu with will receive the greatest light it is ^^ / çïiTùT DOssible (I7). "worm Rays- 21. If this surface moves to pren-im* r, 1 any other re a vertical position, rig, 20, or situati0 * %tLu horisontale, Fig, 21, in these two cases % JdJÏS**. it was less illuminated than when it was cevqit perpendicularly the rays of the 2U Sun (i8). 24. If this ABCD surface tilts Fig. arii opposite the day, so that B C becomes the lower part, in the tems that AD will become the superior, she re- it will be even less day than when she horisontal disease, since the silkit will meet her more obliquely (17, 18). % < J. If this ABCD surface is % *$* alignment with the spokes, in this case, she gets the least light she gets \6 The Sctencë can receive, since the Rays do not there meet more, & that they are alone- (19). fcig. 24. 26. Finally, if this surface tilts da~ vantage^the rays of light will pass by-delsus its upper part has D, & s'eloi- of the lower B C ; hence it is easy to conclude that the strength of the shadow will always increase, going towards the lower Part B C ; What would be sen- sible , if the surface had a lot of loiv- gueur (20). Oneoh 27. One can, without erreuri look at the itlttu length D C of a surface, as very- i7 / urjkcfu- tance that there is Earth in the sun but if one had regard to the length of the sur- face, then there are several remarks to make* NOTE L F;g. ao & 28. The surface being vertical, it is 25-certain that the S-Rays G, the more pro- ches de la partie supérieure BC, rencon- this surface less obliquely that the following Rays S H > & these even less than the lower ones though; hence it is understood that the shadow must SAG inscnsibly, coming from the in part- lower A D higher B C. NOTE IT Shadows. ty NOTE IT 2,9. Than this on fa this had: also Fig. 19 8c illuminated, that when the Rays S K, SI, H- who meet her, make with her years of- equal rules SKI, S I K ; What Happens when she makes , with the horison, an angle 45 degree CD N, because qualors eile perpendicular to the radii of the Sun. NOTE I1L 30. When this surface APO d made Fig. aj; with the DN horison, an odn angle, less open than that of 45 degrees; then the Rays meet her more and more obliquely, coming towards part IIII- PO, since the sqd angle is more open than the following S R Q, & ce last more open than next STQ ; this surface is therefore less illuminated towards its upper PTO, that towards its less than a D. RE M ARQUE IK 31, the opposite happens,, when this Sur-Fîg, 22 & face AB C D tilts to-deisous of the hon-26> B î8 Science sound; for it is wing to see that the Rays Fig. 22 & closest to bottom B C, I6-do with this on fa this ABCD, angles more acute than the angles formed by the same surface & radii SE, s F, which approach most of its upper part?- D A; so it is more enlightened to this part only to its bottom. RE m ARQUE V. « Fig. 248c if the spokes can no longer rencon- 6-trer, the upper part DA, by-desTus which pass the Rays, will always be F less obscure than its lower CB. This 25' is therefore, as we have just seen in the third remark, as far as the APOD surface is inclined beyond the horison DN, & she does it with him one angle ODN, less than 45 degree, she gets at her top a shade that decreases when coming towards the in- & if it is customary to put it so at all on inclined faces, we let us see no other reason, if this is that we want to show that the upper part is farther than the lower one, & that we see it less distinct- tement. shadows; WARNING. We will be careful that it was not pos- to keep between the figures & the place from where the rays of light, a cîistance which had some proportion to the- away from The Sun to the Earth. SECTION M. Where one obfervates in what way the sun rays come rencon- vertical faces, more or less declined. Now consider the effect that the pLAN. m day produced on vertical surfaees, 27> in their different versions. For this, let's imagine that the ABCD subsace turns, like a weather vane, around its side A B; ii this surface cit direct- exposed to The Sun's rays, it is strongly illuminated , but not as much as li she receive the rays of the sun perpcn* dicularly. Its clarity will decrease to me- sure that it will turn away ; so that the Rays will only shave it, golds -< & B ij %o Science Fig. 28. that she will present herself to them from the side, this is- to say, when the body, which it is a surface, will present its direct thickness- lie in the sun, as can be seen by figure 28. Fig. 19. If this surface still turns away, the s b f Rays will no longer be able to- or even shave it ; they will pass alone- side AB, & will do with this surface BCDA, a CBF angle; this which shows that the Remote Part C D of the surface ( 11- B C) must be more obscure than the part Ba, which is closer to the rays of light. Fig. 3 © . Than two contiguous surfaces A & B are arranged as shown in the figure 30, The Sun being assumed at 45 degrees of height, we will see that the surface a receives light, because it is exposed to the Sun, & that the other surface B, which is him opposite, is in the shadows. Fig. 31. If these two surfaces A & B, instead of . present a Convex angle 5 present a concave angle, The Sun, on the contrary from what we have just pointed out, strike on surface B, & the other a se find it in the shadows. Fig. 32 & when raining surfaces A, B, C se 3i ' meet, 6k that they present s e s Shadows. ii convex angles & concave angles , we see that the surfaces A, the most expo- are more illuminated than conventional other surfaces B s to which the radii are parallel, & that the surfaces C of- die in 1 Shadow. If we assume these surfaces horison-Fîg. ^4; pillowcases has instead ofvertical meter, the day pro-35 & SE- will produce the same effects, as it is easy esh to be convinced, if we reread what comes to be said in the three preceding articles a looking at one after another the three figures 34,35 & 36. If we examine the effect that Fig. 37J produces day on a roof, we will appercevront that 38&3* & B surfaces are those that are illuminated : the first A , more than the secondes B, & other C & D demeu- will be in a less strong shadow to the surfaces C than surfaces D. Just look at figures 37, 38 , 39, 40 & 41, to understand without pain (li we heard what we just pointed out ) that the surfaces E, F are illuminated; the first E plus that the seconds F, & the other G are in the shadows, because of their different situation. If it is a body enclosed by more than one plan iv flat surfaces?as is a cube, or Fig, B iij 22 Science sees that the top surface is also illuminated, as the rays pass parallel- B, & that the other G does not receives light point. Kg, 43. If the body is a prism, or a tower in pans, we see that the plan F & la on- face a are totally exposed on Day 5 & than others on fa these B, C " D, E , are all the less illuminated what are further from iurrace A on the left, & R s closer to the surface E to the right, that is, the surface E is more obscure than its previous D; that the surface D is more than the surface C> Finally, the surfaces closer to the left of the body are more illuminated than the ones to his right. Although we let us point out here that the upper plane AF, Fig. 41 & 43, is also illuminated in all its extent, we will see in the applications the necefficient to make him wear shadow. Fig. 44. If the prism, or hexagon Tower, is laid horisontally, it is certain that the a & b surfaces of its left are still lighted, as well as the upper surface of the- C, not the threat of the lower ones; that the surfaces to the left, who receive the most direct- the rays of light, are the most shadow. 23 on the contrary, those of the farthest from it, are the shaded ones. When the body is in a situation fîs-45* horisontaie, ensorte Qu'au lieu de voir en facing the plan G that ends it, we see the surfaces A, B, C, D, E, which ren- it is still visible that the- E > D faces, which are closer to the lower part, are more obscure than the surfaces that precede them immediate- lie. One can make the same reasoning for the following eight figures, including the first six represent pyrami- whole, & the other two pyra- truncated sides, one & the other laid vertically & horisontally. It is seen that the surfaces A, of the three pre-p; g> 4g ; mieres, are illuminated, since they are ex-47 &4&. s rays , than the others on the- B faces are not, & that plane C , • of figure 48 is less illuminated than the top surface has, because the latter is encountered by Rays, & that plan C their is only pa- rallele. The base E of the Inverted Pyramid, Fig. 49, Fig, 49, is illuminated, since the Rays meet her; & surfaces has more ex- B w 1 24 Science by day, are more illuminated than the other B, C, D, which do not lose their clarity, that as much as they receive more obliquely the rays of light, or let them get away from it. F: g. 5a & the same applies to pyra- 53-Mide truncated,, the surfaces of the Lefta who are most directly exposed to the day, are the most illuminated ; as well as the ones on the right ,which have the most far away, are the most shaded. Fig. 50. Figure 50 shows a pyramid, 1 so laid on Thorison, that we see that there is only its base E that can be illuminated, & that all surfaces that- vironate , are shaded ; the lower ones more than the superiors, because these closer to the shelves who pass by-Delius the pyramid. Fig* 5> if the pyramid is in a htuation contrary, we see that its base does not receive day point, & that surfaces A, B, C surrounding it, are always shaded towards the lower part, & illuminated towards the upper part. Fie 54, if a pyramidal roof covers a tower 55 & 56-at sides B, Fig. 5 4, or a prism B silk supported by a cul-de-lamp inverted pyramid, Fig. 5 5, or finally that these bodies be joined together ? O M E R E S. 2? as shown in figure 56. The on- faces furthest from the left3 when these bodies will be Vertical s or higher away from the top, when they will be horisomal, will always be the more shaded, as we just did point out. If " sursaces were arranged from my- instead of representing the former- inside prisms, or side towers, whole pyramids & tron pyramids- they represent us all.- for example, the three figu-planes.V. res 57, 58, 59, let us see tinted-53 & 5^ of the prism, or hexagonal lathe, vertical & horisontal, & the eight figures sui van tes the inside of the whole pyramids & tron- in all situations where we just seen them; we understand, without doubt, that to the vertical figures 57, 60, 62, 63 & 66 3 These are no longer the on -. faces to, B of the inner left, which day; but those E, D, C of the inner right, which are all the more shaded as they approach the left, Similarly to figures 58 , 59 , 61 , 64, 6 s & 67 j these are no longer the surfaces k, I, H, nor the insides of the left, which receives the light of day; but the 26 Science lower F, G, & cellesE of the right; & as they turn around from the body, they receive more directly the rays of light , so they are fully illuminated on the right side 5 & completely obscure to the left. RE M ARQUES. When it comes to showing the in front of a building, it is assumed that The Sun always at 45 degrees of height, is a little turned in front of this face, because what if we assume the day come aside, or behind the face of which it is ques- we will have to cover it all- of a shadow, instead of must have as much as it is necessary to distinguish the different by- protruding & retracting ties that compo- feel. The Sun assumes at the Point S, ensorte that its rays come to meet oblique- the front of an object, such as #IG."68& would be a true door or window or it is certain that the rays of the Sun, palsing through openings A, B, make an angle C A D with the left part A C of the opening, meet the remote surface C E, that in shadow. 27 starting at point D, going to^S E, it is visible that it makes it a shadow CD, to the left of the opening, I see by figures 68 & 6y. The Sun, albeit in front of objects, Kg. 70 & is always assumed at 45 degrees hau-7U it is still visible, that the rays passing through-all the part higher A C ? make with it an angle DAC, & therefore cannot illuminate- rer the pressed surface only by starting at point D, which produces a shadow at- deisous of the upper part. SECTION III. Where F is made to make applications from this qiion just saw. Application. The use to be made of what we have just noticed in this Cha- Piter, is that we have conti-plane surfaces m gues, which have a Convex angle 3 f. g. 30 & Fig. 30 & 34 , or a concave angle, Fig. 34 ,31 & 31 Se 3 5, shade the surface B of the one, 3 5* Se the surface has the other, i.e., 1 science that we will not make a shadow on each jj because they receive no day like the others. Fîg. 32, if they are several vertical surfaces ss^ & 36-or horisontales, which have alternati- vement of convex angles & angles concave, Fig. 32 , 33 & 36on leave clear the sursaces to, because they are the most exposed to the day: we will go through- desfuses surfaces B, less exposed than the previous A, a very light shade ; Se on other surfaces C, which does not receive- wind point at all by day, a shadow much stronger. Plan. iv. If it is a prism, or hexagon turn, Fig. 44%44% 43 ' 44 & 45 > or a pyramid, Fig. 49 » 53. '51 & 5 3 5 leave blank on- A-sides, more exposed to daylight than others; but on the following B, we will put a shade , or a very light shade, on those after C, D, E, F of the shades all- stronger days, in proportion will move away from the day. To have no trouble making seven at eight different shades, it is necessary first make a suitable one to put it on the second surface B, & pass it in same tems on all other surfaces C , D , E, F ; then after the repasTer a (econde be on the four surfaces C ? Of% shadow. i$ E , F, & not on the surface B , the re- \ pasîer une troisieme fois sur les surfaces D , E, F, & not on the previous two- dentes B, C, la Iron a fourth Times on surfaces È, F, & always from even if there were more of surfaces ; so that the- B-side will only have one tint , the third-the third.- C will have two, the fourth D in will have three, the fifth E will have four, that is, one more than the previous ones.- toothed. Observing in what way the Rays meet surfaces that contain a prism, or a stepped tower, or a pyramid, Fig, 42, 43 , 49, 52, 55, we Fîg. 4*2 have pointed out that the upper plane gc 5 " 5a was also illuminated in all its expanse- due; but as we see less dis- part X of this upper plane the furthest away, it will be necessary to lay a shadow that will be brightened by coming towards the nearest pane. The same reason , & observation as we made, that part of one on- the more distant the face of the spokes, the more dark than the one who approaches it.- vantage, concludes that after or before than to have put flat shadow on the on- face, it will be necessary to ask a seconde, & 30 Science soften it by coming to the most illuminated from the surface. We have seen that if surfaces arranged in such a way that they see inside prisms, or towers at pans, whole & truncated pyramids, than the surfaces that are to the left are shaded, & only those that are the right are illuminated ; therefore it will be necessary wash them, or shade them the same way.- we have just shown that it Pian v kUoit shade the previous ones. The DIF- Fig. 57 '^, 63 & grancl number of colours on surfaces from the left; thus the surface E, which is the most enlightened, will not have; the next - vante D will have one , that we will pass , as above, on the other C, B, A ; the third C will have a second, that we p a siera on the following surfaces (B , A ; fourth surface B will have a third, that we will palsera at the same tems on that A who follows her, & she has one fourth. We have observed that in- mens doors, windows, or anything other subject, Fig. 68, 69, 70 & 71, there internally to the left upper part, a space as the spokes can not meet ; what makes see shadow. 31 than after putting on a light shade, for mark the Depression of the openings , Fig. 72, it is necessary mertre in the interior of Pp; AN "J1' these openings to the left, & by- tie higher a shade B stronger, which one will end right in shape when the openings are closed in the middle of the belt, as seen in the places C, Fig. 72, plate VI. CHAPTER III. Or we examine the nature of the shadows what the day produces as the Jurfaces convex. SECTION ONE. e have just examined, in the- previous pitre, the shadows that The Sun product on flat surfaces: let's see now the ones he's causing on the sur- convex faces. For this, suppose A pLAS surface yr flat & vertical A B CD is ssexible, from Fig. 75. so that being able to bend it at will, we make it represent the convex surface science At EF, it is certain, that by bending it « the right side will be moved further and further away Eghf rays of light; what makes see that the strength of the shadow will increase always going to the most distant F H. gig, 74. 11 will happen the same, if the surface ABGD is horisontal, & if folded so that it represents the convex surface B G H , the rays passing over this surface, will move further and further away from its lower part F H, which they will Bisse, as we just said, in a shadow who will become insensibly stronger in coming towards its part F H , the furthest ray, fr g. 75. If we examine the effect of the day on a cy- Lind laid vertically, we'll see from a- edge as the circle that crowns it esh left to is exposed to the day, & that his right B receives none; but as the rays of light are or can be viewed as lines inflexible straight, there are some that strike on the left of the cylinder & end- nent, & others who are tan people at the then further away from the surface in addition; which makes that the line B of the cylinder , or Round Tower, abides in shadow line that takes strength to me- sour cream shadow. 33 sure that the Rays move away from this Part B. If the cylinder is laid horisontally, Fig. 76 8t its upper part C will receive the Rays 77 ° of light , & the lower D will be in a shadow that will lighten insensitive- win the upper part C, with this difference, only if the cylinder is in a honsontal lesion, ensorte that it presents one of its bays f y as in the figure, 76, the Rays shaving the circle F, seclairera; instead only if it pre- feel its length, as in figure 77, the spokes not giving point on the circle E, it will be in the shadows, The same thing happens with respect to py- round branches or cones , both whole and truncated. Their left has, when they (have vertical, is illuminated, & their right B , is in a shadow, which loses its strength , when turning it comes insenlible- ment earn the enlightened rating. The circle E of the inverted cone, Fig, 79, as well as the circle F of the truncated cone, Fig. 80, re^ they also drink the rays of light, When the cone is lying on tuna-Fig. U.S.A.%, its, its upper part C is the one that 82 & 8.3, receives the day, & the lower one is in the shadow, which is always more sort in moving away from the Rays. The circle E of the 34 the Saw n c Cone, Fig, 82, is only shaved by the rays; which makes it less illuminated that the circle F of the truncated cone, Fig. 83, who receives them more directly. TIG. 84 & if the cone is in one of the two situa- $5 * represented by figures 84 & 85, base E of the first receives the day, & the convex surface that envelops it receives point; but the upper part has being closer to the passing Rays over the cone, is less obscure than £7g> 85. B; on the contrary, the base F of the second cone is. shaded, because it does not receive the Rays, which can- wind meet only the upper A > of the convex surface that ends the body, as we have already done re- mark. JSg. 86. If the day srappe on a globe, it is viable only a few rays of light are stopped by its left Part A, & by sa superior B, & that some others rays touch in a few points the on- the globe, then moving away from the Right C, & of the lower Part D of this globe, who ? consequently, both in the shadows, which lightens by coming to win the enlightened parties A & B, since the surface, which envelops the globe A is getting closer and closer to n E S O M B R Ë s. 3s iumiere rays coming from D & C to B & to A. To examine the esfet of the day on a Fig. 87. half sphere or dome, suppose we has cut a globe horilontally: the two half spheres being separated from each other by the other, we see that the Left has, & the deilus B of the upper half sphere , Fig, 87, are illuminated; & that the Right C eit in a shadow that weakens when coming to the illuminated parts A & B. The left A of the lower half sphere-Fig. 58. fig. 88, esl exposed to the day, sa Right C, & its lower Part D, are in a shadow, which begins where the Rays leaving the globe, & which increases in ve- Nant win the C & D games. The circle E, which comes out of base at the half- upper sphere, Fig. 87, EIL shaded; for rays can only meet it in the situation where it is : the circle F, which runs- ronne the lower half sphere, Fig, 88 , is on the contrary illuminated, since the Rays meet him. If the globe had been cut vertically-Fig. 89 & in two half spheres, we see that 9°- the left A of the first, Fig, 89, & ta upper part B of one & of the other , Fig. 89 & 90, are illuminated; that the right C of the second, & the lower D of the one C ij 1.6 Science & this the other, are in a shadow that fainting as people approach illuminated parts a 6V B, as we just to see it above. The circle E of the pre- mière ESL ombre, & the one F de la leconde is illuminated, because the latter F the pre- day, & that the other E is not present- set! re not, Fig. 91 & if a cone-shaped roof covers 93, A Round Tower, Fig. 91 . or a tower is supported by a cul-de-lamp made of inverted cone, Fig. 92, the Left has one & the other will be lighted, & the shadow who will take birth imperceptibly where the Rays will leave the surface, come- dra by increasing it to line B of one & the other, because this right, as we did feel, is the most away from the Rays } who are tan people to these on curved faces , i.e. touch each in a point.