different distances, when the thickness of the air and the distance
are in the same inverse proportion. It is proved thus: let A be the
eye, and H any colour whatever, placed at one degree of distance
from the eye, in a quality of air of four degrees of thickness; but
because the second degree above, A M N L, contains a thinner air by
one half, which air conveys this colour, it follows that this colour
will appear as if removed double the distance it was at before, viz.
at two degrees of distance, A F and F G, from the eye; and it will be
placed in G. If that is raised to the second degree of air A M N L, and
to the degree O M, P N, it will necessarily be placed at E, and will
be removed from the eye the whole length of the line A E, which will
be proved in this manner to be equal in thickness to the distance A G.
If in the same quality of air the distance A G interposed between the
eye and the colour occupies two degrees, and A E occupies two degrees
and a half, it is sufficient to preserve the colour G, when raised to
E, from any change, because the degree A C and the degree A F being
the same in thickness, are equal and alike, and the degree C D, though
equal in length to the degree F G, is not alike in point of thickness
of air; because half of it is situated in a degree of air of double the
thickness of the air above: this half degree of distance occupies as
much of the colour as one whole degree of the air above would, which
air above is twice as thin as the air below, with which it terminates;
so that by calculating the thickness of the air, and the distances,
you will find that the colours have changed places without undergoing
any alteration in their beauty. And we shall prove it thus: reckoning
first the thickness of air, the colour H is placed in four degrees of
thickness, the colour G in two degrees, and E at one degree. Now let
us see whether the distances are in an equal inverse proportion; the
colour E is at two degrees and a half of distance, G at two degrees,
and H at one degree. But as this distance has not an exact proportion
with the thickness of air, it is necessary to make a third calculation
in this manner: A C is perfectly like and equal to A F; the half
degree, C B, is like but not equal to A F, because it is only half a
degree in length, which is equal to a whole degree of the quality of
the air above; so that by this calculation we shall solve the question.
For A C is equal to two degrees of thickness of the air above, and the
half degree C B is equal to a whole degree of the same air above; and
one degree more is to be taken in, viz. B E, which makes the fourth.
A H has four degrees of thickness of air, A G also four, viz. A F two
in value, and F G also two, which taken together make four. A E has
also four, because A C contains two, and C D one, which is the half
of A C, and in the same quality of air; and there is a whole degree
above in the thin air, which all together make four. So that if A E is
not double the distance A G, nor four times the distance A H, it is
made equivalent by the half degree C B of thick air, which is equal
to a whole degree of thin air above. This proves the truth of the
proposition, that the colour H G E does not undergo any alteration by
these different distances.
/Chap. CCXCIX./--_Contrary Opinions in regard to Objects seen afar off._
/Many/ painters will represent the objects darker, in proportion as
they are removed from the eye; but this cannot be true, unless the
objects seen be white; as shall be examined in the next chapter.
/Chap. CCC./--_Of the Colour of Objects remote from the Eye._
/The/ air tinges objects with its own colour more or less in proportion
to the quantity of intervening air between it and the eye, so that a
dark object at the distance of two miles (or a density of air equal to
such distance), will be more tinged with its colour than if only one
mile distant.
It is said, that, in a landscape, trees of the same species appear
darker in the distance than near; this cannot be true, if they be of
equal size, and divided by equal spaces. But it will be so if the
first trees are scattered, and the light of the fields is seen through
and between them, while the others which are farther off, are thick
together, as is often the case near some river or other piece of water:
in this case no space of light fields can be perceived, but the trees
appear thick together, accumulating the shadow on each other. It also
happens, that as the shady parts of plants are much broader than the
light ones, the colour of the plants becoming darker by the multiplied
shadows, is preserved, and conveyed to the eye more strongly than that
of the other parts; these masses, therefore, will carry the strongest
parts of their colour to a greater distance.
/Chap. CCCI./--_Of the Colour of Mountains._
/The/ darker the mountain is in itself, the bluer it will appear at a
great distance. The highest part will be the darkest, as being more
woody; because woods cover a great many shrubs, and other plants,
which never receive any light. The wild plants of those woods are also
naturally of a darker hue than cultivated plants; for oak, beech, fir,
cypress, and pine trees are much darker than olive and other domestic
plants. Near the top of these mountains, where the air is thinner and
purer, the darkness of the woods will make it appear of a deeper azure,
than at the bottom, where the air is thicker. A plant will detach very
little from the ground it stands upon, if that ground be of a colour
something similar to its own; and, _vice versâ_, that part of any white
object which is nearest to a dark one, will appear the whitest, and
the less so as it is removed from it; and any dark object will appear
darker, the nearer it is to a white one; and less so, if removed from
it.
/Chap. CCCII./--_Why the Colour and Shape of Objects are lost in some
Situations apparently dark, though not so in Reality._
/There/ are some situations which, though light, appear dark, and in
which objects are deprived both of form and colour. This is caused by
the great light which pervades the intervening air; as is observable by
looking in through a window at some distance from the eye, when nothing
is seen but an uniform darkish shade; but if we enter the house, we
shall find that room to be full of light, and soon distinguish every
small object contained within that window. This difference of effect
is produced by the great brightness of the air, which contracts
considerably the pupil of the eye, and by so doing diminishes its
power. But in dark places the pupil is enlarged, and acquires as much
in strength, as it increases in size. This is proved in my second
proposition of perspective[73].
/Chap. CCCIII./--_Various Precepts in Painting._
/The/ termination and shape of the parts in general are very little
seen, either in great masses of light, or of shadows; but those which
are situated between the extremes of light and shade are the most
distinct.
Perspective, as far as it extends in regard to painting, is divided
into three principal parts; the first consists in the diminution of
size, according to distance; the second concerns the diminution of
colours in such objects; and the third treats of the diminution of the
perception altogether of those objects, and of the degree of precision
they ought to exhibit at various distances.
The azure of the sky is produced by a mixture composed of light and
darkness[74]; I say of light, because of the moist particles floating
in the air, which reflect the light. By darkness, I mean the pure air,
which has none of these extraneous particles to stop and reflect the
rays. Of this we see an example in the air interposed between the eye
and some dark mountains, rendered so by the shadows of an innumerable
quantity of trees; or else shaded on one side by the natural privation
of the rays of the sun; this air becomes azure, but not so on the side
of the mountain which is light, particularly when it is covered with
snow.
Among objects of equal darkness and equal distance, those will appear
darker that terminate upon a lighter ground, and _vice versâ_[75].
That object which is painted with the most white and the most black,
will shew greater relief than any other; for that reason I would
recommend to painters to colour and dress their figures with the
brightest and most lively colours; for if they are painted of a dull
or obscure colour, they will detach but little, and not be much seen,
when the picture is placed at some distance; because the colour of
every object is obscured in the shades; and if it be represented as
originally so all over, there will be but little difference between
the lights and the shades, while lively colours will shew a striking
difference.
AERIAL PERSPECTIVE.
/Chap. CCCIV./--_Aerial Perspective._
/There/ is another kind of perspective called aerial, because by the
difference of the air it is easy to determine the distance of different
objects, though seen on the same line; such, for instance, as buildings
behind a wall, and appearing all of the same height above it. If in
your picture you want to have one appear more distant than another, you
must first suppose the air somewhat thick, because, as we have said
before, in such a kind of air the objects seen at a great distance,
as mountains are, appear blueish like the air, by means of the great
quantity of air that interposes between the eye and such mountains.
You will then paint the first building behind that wall of its proper
colour; the next in point of distance, less distinct in the outline,
and participating, in a greater degree, of the blueish colour of the
air; another which you wish to send off as much farther, should be
painted as much bluer; and if you wish one of them to appear five times
farther removed beyond the wall, it must have five times more of the
azure. By this rule these buildings which appeared all of the same
size, and upon the same line, will be distinctly perceived to be of
different dimensions, and at different distances.
/Chap. CCCV./--_The Parts of the Smallest Objects will first disappear
in Painting._
/Of/ objects receding from the eye the smallest will be the first lost
to the sight; from which it follows, that the largest will be the last
to disappear. The painter, therefore, ought not to finish the parts of
those objects which are very far off, but follow the rule given in the
sixth book[76].
How many, in the representation of towns, and other objects remote
from the eye, express every part of the buildings in the same manner
as if they were very near. It is not so in nature, because there is no
sight so powerful as to perceive distinctly at any great distance the
precise form of parts or extremities of objects. The painter therefore
who pronounces the outlines, and the minute distinction of parts, as
several have done, will not give the representation of distant objects,
but by this error will make them appear exceedingly near. Again, the
angles of buildings in distant towns are not to be expressed (for they
cannot be seen), considering that angles are formed by the concurrence
of two lines into one point, and that a point has no parts; it is
therefore invisible.
/Chap. CCCVI./--_Small Figures ought not to be too much finished._
/Objects/ appear smaller than they really are when they are distant
from the eye, and because there is a great deal of air interposed,
which weakens the appearance of forms, and, by a natural consequence,
prevents our seeing distinctly the minute parts of such objects. It
behoves the painter therefore to touch those parts slightly, in an
unfinished manner; otherwise it would be against the effect of Nature,
whom he has chosen for his guide. For, as we said before, objects
appear small on account of their great distance from the eye; that
distance includes a great quantity of air, which, forming a dense body,
obstructs the light, and prevents our seeing the minute parts of the
objects.
/Chap. CCCVII./--_Why the Air is to appear whiter as it approaches
nearer to the Earth._
/As/ the air is thicker nearer the earth, and becomes thinner as it
rises, look, when the sun is in the east, towards the west, between the
north and south, and you will perceive that the thickest and lowest air
will receive more light from the sun than the thinner air, because its
beams meet with more resistance.
If the sky terminate low, at the end of a plain, that part of it
nearest to the horizon, being seen only through the thick air, will
alter and break its natural colour, and will appear whiter than over
your head, where the visual ray does not pass through so much of that
gross air, corrupted by earthy vapours. But if you turn towards the
east, the air will be darker the nearer it approaches the earth; for
the air being thicker, does not admit the light of the sun to pass so
freely.
/Chap. CCCVIII./--_How to paint the distant Part of a Landscape._
/It/ is evident that the air is in some parts thicker and grosser than
in others, particularly that nearest to the earth; and as it rises
higher, it becomes thinner and more transparent. The objects which
are high and large, from which you are at some distance, will be less
apparent in the lower parts; because the visual ray which perceives
them, passes through a long space of dense air; and it is easy to prove
that the upper parts are seen by a line, which, though on the side of
the eye it originates in a thick air, nevertheless, as it ascends to
the highest summit of its object, terminates in an air much thinner
than that of the lower parts; and for that reason the more that line
or visual ray advances from the eye, it becomes, in its progress
from one point to another, thinner and thinner, passing from a pure
air into another which is purer; so that a painter who has mountains
to represent in a landscape, ought to observe, that from one hill
to another, the tops will appear always clearer than the bases. In
proportion as the distance from one to another is greater, the top will
be clearer; and the higher they are, the more they will shew their
variety of form and colour.
/Chap. CCCIX./--_Of precise and confused Objects._
/The/ parts that are near in the fore-ground should be finished in a
bold determined manner; but those in the distance must be unfinished,
and confused in their outlines.
/Chap. CCCX./--_Of distant Objects._
/That/ part of any object which is nearest to the luminary from which
it receives the light, will be the lightest.
The representation of an object in every degree of distance, loses
degrees of its strength; that is, in proportion as the object is more
remote from the eye it will be less perceivable through the air in its
representation.
/Chap. CCCXI./--_Of Buildings seen in a thick Air._
[Illustration]
/That/ part of a building seen through a thick air, will appear less
distinct than another part seen through a thinner air. Therefore the
eye, N, looking at the tower A D, will see it more confusedly in the
lower degrees, but at the same time lighter; and as it ascends to the
other degrees it will appear more distinct, but somewhat darker.
/Chap. CCCXII./--_Of Towns and other Objects seen through a thick Air._
[Illustration]
/Buildings/ or towns seen through a fog, or the air made thick by
smoke or other vapours, will appear less distinct the lower they
are; and, _vice versâ_, they will be sharper and more visible in
proportion as they are higher. We have said, in Chapter cccxxi. that
the air is thicker the lower it is, and thinner as it is higher. It is
demonstrated also by the cut, where the tower, A F, is seen by the eye
N, in a thick air, from B to F, which is divided into four degrees,
growing thicker as they are nearer the bottom. The less the quantity of
air interposed between the eye and its object is, the less also will
the colour of the object participate of the colour of that air. It
follows, that the greater the quantity of the air interposed between
the eye and the object seen, is, the more this object will participate
of the colour of the air. It is demonstrated thus: N being the eye
looking at the five parts of the tower A F, viz. A B C D E, I say,
that if the air were of the same thickness, there would be the same
proportion between the colour of the air at the bottom of the tower and
the colour of the air that the same tower has at the place B, as there
is in length between the line M and F. As, however, we have supposed
that the air is not of equal thickness, but, on the contrary, thicker
as it is lower, it follows, that the proportion by which the air tinges
the different elevations of the tower B C F, exceeds the proportion
of the lines; because the line M F, besides its being longer than the
line S B, passes by unequal degrees through a quality of air which is
unequal in thickness.
/Chap. CCCXIII./--_Of the inferior Extremities of distant Objects._
/The/ inferior or lower extremities of distant objects are not so
apparent as the upper extremities. This is observable in mountains
and hills, the tops of which detach from the sides of other mountains
behind. We see the tops of these more determined and distinctly than
their bases; because the upper extremities are darker, being less
encompassed by thick air, which always remains in the lower regions,
and makes them appear dim and confused. It is the same with trees,
buildings, and other objects high up. From this effect it often happens
that a high tower, seen at a great distance, will appear broad at top,
and narrow at bottom; because the thin air towards the top does not
prevent the angles on the sides and other different parts of the tower
from being seen, as the thick air does at bottom. This is demonstrated
by the seventh proposition[77], which says, that the thick air
interposed between the eye and the sun, is lighter below than above,
and where the air is whiteish, it confuses the dark objects more than if
such air were blueish or thinner, as it is higher up. The battlements
of a fortress have the spaces between equal to the breadth of the
battlement, and yet the space will appear wider; at a great distance
the battlements will appear very much diminished, and being removed
still farther, will disappear entirely, and the fort shew only the
straight wall, as if there were no battlements.
/Chap. CCCXIV./--_Which Parts of Objects disappear first by being
removed farther from the Eye, and which preserve their Appearance._
/The/ smallest parts are those which, by being removed, lose their
appearance first; this may be observed in the gloss upon spherical
bodies, or columns, and the slender parts of animals; as in a stag,
the first sight of which does not discover its legs and horns so soon
as its body, which, being broader, will be perceived from a greater
distance. But the parts which disappear the very first, are the lines
which describe the members, and terminate the surface and shape of
bodies.
/Chap. CCCXV./--_Why Objects are less distinguished in proportion as
they are farther removed from the Eye._
/This/ happens because the smallest parts are lost first; the second,
in point of size, are also lost at a somewhat greater distance, and so
on successively; the parts by degrees melting away, the perception of
the object is diminished; and at last all the parts, and the whole, are
entirely lost to the sight[78]. Colours also disappear on account of
the density of the air interposed between the eye and the object.
/Chap. CCCXVI./--_Why Faces appear dark at a Distance._
/It/ is evident that the similitude of all objects placed before us,
large as well as small, is perceptible to our senses through the iris
of the eye. If through so small an entrance the immensity of the sky
and of the earth is admitted, the faces of men (which are scarcely any
thing in comparison of such large objects), being still diminished by
the distance, will occupy so little of the eye, that they become almost
imperceptible. Besides, having to pass through a dark medium from the
surface to the _Retina_ in the inside, where the impression is made,
the colour of faces (not being very strong, and rendered still more
obscure by the darkness of the tube) when arrived at the focus appears
dark. No other reason can be given on that point, except that the speck
in the middle of the apple of the eye is black, and, being full of a
transparent fluid like air, performs the same office as a hole in a
board, which on looking into it appears black; and that those things
which are seen through both a light and dark air, become confused and
obscure.
/Chap. CCCXVII./--_Of Towns and other Buildings seen through a Fog in
the Morning or Evening._
/Buildings/ seen afar off in the morning or in the evening, when there
is a fog, or thick air, shew only those parts distinctly which are
enlightened by the sun towards the horizon; and the parts of those
buildings which are not turned towards the sun remain confused and
almost of the colour of the fog.
/Chap. CCCXVIII./--_Of the Height of Buildings seen in a Fog._
/Of/ a building near the eye the top parts will appear more confused
than the bottom, because there is more fog between the eye and the top
than at the base. And a square tower, seen at a great distance through
a fog, will appear narrower at the base than at the summit. This is
accounted for in Chapter cccxiii. which says, that the fog will appear
whiter and thicker as it approaches the ground; and as it is said
before[79], that a dark object will appear smaller in proportion as it
is placed on a whiter ground. Therefore the fog being whiter at bottom
than at top, it follows that the tower (being darkish) will appear
narrower at the base than at the summit.
/Chap. CCCXIX./--_Why Objects which are high, appear darker at a
Distance than those which are low, though the Fog be uniform, and of
equal Thickness._
/Amongst/ objects situated in a fog, thick air, vapour, smoke, or at
a distance, the highest will be the most distinctly seen: and amongst
objects equal in height, that placed in the darkest fog, will be most
confused and dark. As it happens to the eye H, looking at A B C, three
towers of equal height; it sees the top C as low as R, in two degrees
of thickness; and the top B, in one degree only; therefore the top C
will appear darker than the top of the tower B.
[Illustration]
/Chap. CCCXX./--_Of Objects seen in a Fog._
/Objects/ seen through a fog will appear larger than they are in
reality, because the aerial perspective does not agree with the linear,
viz. the colour does not agree with the magnitude of the object[80];
such a fog being similar to the thickness of air interposed between the
eye and the horizon in fine weather. But in this case the fog is near
the eye, and though the object be also near, it makes it appear as if
it were as far off as the horizon; where a great tower would appear no
bigger than a man placed near the eye.
/Chap. CCCXXI./--_Of those Objects which the Eyes perceive through a
Mist or thick Air._
/The/ nearer the air is to water, or to the ground, the thicker it
becomes. It is proved by the nineteenth proposition of the second
book[81], that bodies rise in proportion to their weight; and it
follows, that a light body will rise higher than another which is heavy.
/Chap. CCCXXII./--_Miscellaneous Observations._
/Of/ different objects equal in magnitude, form, shade, and distance
from the eye, those will appear the smaller that are placed on the
lighter ground. This is exemplified by observing the sun when seen
behind a tree without leaves; all the ramifications seen against that
great light are so diminished that they remain almost invisible. The
same may be observed of a pole placed between the sun and the eye.
Parallel bodies placed upright, and seen through a fog, will
appear larger at top than at bottom. This is proved by the ninth
proposition[82], which says, that a fog, or thick air, penetrated by
the rays of the sun, will appear whiter the lower they are.
Things seen afar off will appear out of proportion, because the parts
which are the lightest will send their image with stronger rays than
the parts which are darkest. I have seen a woman dressed in black,
with a white veil over her head, which appeared twice as large as her
shoulders covered with black.
MISCELLANEOUS OBSERVATIONS.
LANDSCAPE.
/Chap. CCCXXIII./--_Of Objects seen at a Distance._
/Any/ dark object will appear lighter when removed to some distance
from the eye. It follows, by the contrary reason, that a dark object
will appear still darker when brought nearer to the eye. Therefore the
inferior parts of any object whatever, placed in thick air, will appear
farther from the eye at the bottom than at the top; for that reason the
lower parts of a mountain appear farther off than its top, which is in
reality the farthest.
/Chap. CCCXXIV./--_Of a Town seen through a thick Air._
/The/ eye which, looking downwards, sees a town immersed in very thick
air, will perceive the top of the buildings darker, but more distinct
than the bottom. The tops detach against a light ground, because they
are seen against the low and thick air which is beyond them. This is a
consequence of what has been explained in the preceding chapter.
/Chap. CCCXXV./--_How to draw a Landscape._
/Contrive/ that the trees in your landscape be half in shadow and half
in the light. It is better to represent them as when the sun is veiled
with thin clouds, because in that case the trees receive a general
light from the sky, and are darkest in those parts which are nearest to
the earth.
/Chap. CCCXXVI./--_Of the Green of the Country._
/Of/ the greens seen in the country, that of trees and other plants
will appear darker than that of fields and meadows, though they may
happen to be of the same quality.