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.