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VOLUME I: SECTION VIII. BOTANY FOR PAINTERS, AND ELEMENTS OF LANDSCAPE PAINTING
The chapters composing this portion of the work consist of
observations on Form, Light and Shade in Plants, and particularly in
Trees summed up in certain general rules by which the author intends
to guide the artist in the pictorial representation of landscape._
With these the first principles of a_ Theory of Landscape painting
_are laid down--a theory as profoundly thought out in its main
lines as it is lucidly worked out in its details. In reading these
chapters the conviction is irresistible that such a_ Botany for
painters _is or ought to be of similar importance in the practice of
painting as the principles of the Proportions and Movements of the
human figure_ i. e. Anatomy for painters.
There can be no doubt that Leonardo, in laying down these rules,
did not intend to write on Botany in the proper scientific
sense--his own researches on that subject have no place here; it
need only be observed that they are easily distinguished by their
character and contents from those which are here collected and
arranged under the title 'Botany for painters'. In some cases where
this division might appear doubtful,--as for instance in No._
402--_the Painter is directly addressed and enjoined to take the
rule to heart as of special importance in his art._
The original materials are principally derived from MS._ G, _in
which we often find this subject treated on several pages in
succession without any of that intermixture of other matters, which
is so frequent in Leonardo's writings. This MS., too, is one of the
latest; when it was written, the great painter was already more than
sixty years of age, so we can scarcely doubt that he regarded all he
wrote as his final views on the subject. And the same remark applies
to the chapters from MSS._ E _and_ M _which were also written
between_ 1513--15.
_For the sake of clearness, however, it has been desirable to
sacrifice--with few exceptions--the original order of the passages
as written, though it was with much reluctance and only after long
hesitation that I resigned myself to this necessity. Nor do I mean
to impugn the logical connection of the author's ideas in his MS.;
but it will be easily understood that the sequence of disconnected
notes, as they occurred to Leonardo and were written down from time
to time, might be hardly satisfactory as a systematic arrangement of
his principles. The reader will find in the Appendix an exact
account of the order of the chapters in the original MS. and from
the data there given can restore them at will. As the materials are
here arranged, the structure of the tree as regards the growth of
the branches comes first_ (394-411) _and then the insertion of the
leaves on the stems_ (412-419). _Then follow the laws of Light and
Shade as applied, first, to the leaves (420-434), and, secondly, to
the whole tree and to groups of trees_ (435-457). _After the remarks
on the Light and Shade in landscapes generally_ (458-464), _we find
special observations on that of views of towns and buildings_
(465-469). _To the theory of Landscape Painting belong also the
passages on the effect of Wind on Trees_ (470-473) _and on the Light
and Shade of Clouds_ (474-477), _since we find in these certain
comparisons with the effect of Light and Shade on Trees_ (e. g.: _in
No._ 476, 4. 5; _and No._ 477, 9. 12). _The chapters given in the
Appendix Nos._ 478 _and_ 481 _have hardly any connection with the
subjects previously treated._
Classification of trees (393)
393.
TREES.
Small, lofty, straggling, thick, that is as to foliage, dark, light,
russet, branched at the top; some directed towards the eye, some
downwards; with white stems; this transparent in the air, that not;
some standing close together, some scattered.
The relative thickness of the branches to the trunk (394-396)
394.
All the branches of a tree at every stage of its height when put
together are equal in thickness to the trunk [below them].
All the branches of a water [course] at every stage of its course,
if they are of equal rapidity, are equal to the body of the main
stream.
395.
Every year when the boughs of a plant [or tree] have made an end of
maturing their growth, they will have made, when put together, a
thickness equal to that of the main stem; and at every stage of its
ramification you will find the thickness of the said main stem; as:
_i k_, _g h_, _e f_, _c d_, _a b_, will always be equal to each
other; unless the tree is pollard--if so the rule does not hold
good.
All the branches have a direction which tends to the centre of the
tree _m_.
[Footnote: The two sketches of leafless trees one above another on
the left hand side of Pl. XXVII, No. 1, belong to this passage.]
396.
If the plant n grows to the thickness shown at m, its branches will
correspond [in thickness] to the junction a b in consequence of the
growth inside as well as outside.
The branches of trees or plants have a twist wherever a minor branch
is given off; and this giving off the branch forms a fork; this said
fork occurs between two angles of which the largest will be that
which is on the side of the larger branch, and in proportion, unless
accident has spoilt it.
[Footnote: The sketches illustrating this are on the right hand side
of PI. XXVII, No. I, and the text is also given there in facsimile.]
The law of proportion in the growth of the branches (397-402)
397.
There is no boss on branches which has not been produced by some
branch which has failed.
The lower shoots on the branches of trees grow more than the upper
ones and this occurs only because the sap that nourishes them, being
heavy, tends downwards more than upwards; and again, because those
[branches] which grow downwards turn away from the shade which
exists towards the centre of the plant. The older the branches are,
the greater is the difference between their upper and their lower
shoots and in those dating from the same year or epoch.
[Footnote: The sketch accompanying this in the MS. is so effaced
that an exact reproduction was impossible.]
398.
OF THE SCARS ON TREES.
The scars on trees grow to a greater thickness than is required by
the sap of the limb which nourishes them.
399.
The plant which gives out the smallest ramifications will preserve
the straightest line in the course of its growth.
[Footnote: This passage is illustrated by two partly effaced
sketches. One of these closely resembles the lower one given under
No. 408, the other also represents short closely set boughs on an
upright trunk.]
400.
OF THE RAMIFICATION.
The beginning of the ramification [the shoot] always has the central
line [axis] of its thickness directed to the central line [axis] of
the plant itself.
401.
In starting from the main stem the branches always form a base with
a prominence as is shown at _a b c d_.
402.
WHY, VERY FREQUENTLY, TIMBER HAS VEINS THAT ARE NOT STRAIGHT.
When the branches which grow the second year above the branch of the
preceding year, are not of equal thickness above the antecedent
branches, but are on one side, then the vigour of the lower branch
is diverted to nourish the one above it, although it may be somewhat
on one side.
But if the ramifications are equal in their growth, the veins of the
main stem will be straight [parallel] and equidistant at every
degree of the height of the plant.
Wherefore, O Painter! you, who do not know these laws! in order to
escape the blame of those who understand them, it will be well that
you should represent every thing from nature, and not despise such
study as those do who work [only] for money.
The direction of growth (403-407)
403.
OF THE RAMIFICATIONS OF PLANTS.
The plants which spread very much have the angles of the spaces
which divide their branches more obtuse in proportion as their point
of origin is lower down; that is nearer to the thickest and oldest
portion of the tree. Therefore in the youngest portions of the tree
the angles of ramification are more acute. [Footnote: Compare the
sketches on the lower portion of Pl. XXVII, No. 2.]
404.
The tips of the boughs of plants [and trees], unless they are borne
down by the weight of their fruits, turn towards the sky as much as
possible.
The upper side of their leaves is turned towards the sky that it may
receive the nourishment of the dew which falls at night.
The sun gives spirit and life to plants and the earth nourishes them
with moisture. [9] With regard to this I made the experiment of
leaving only one small root on a gourd and this I kept nourished
with water, and the gourd brought to perfection all the fruits it
could produce, which were about 60 gourds of the long kind, andi set
my mind diligently [to consider] this vitality and perceived that
the dews of night were what supplied it abundantly with moisture
through the insertion of its large leaves and gave nourishment to
the plant and its offspring--or the seeds which its offspring had
to produce--[21].
The rule of the leaves produced on the last shoot of the year will
be that they will grow in a contrary direction on the twin branches;
that is, that the insertion of the leaves turns round each branch in
such a way, as that the sixth leaf above is produced over the sixth
leaf below, and the way they turn is that if one turns towards its
companion to the right, the other turns to the left, the leaf
serving as the nourishing breast for the shoot or fruit which grows
the following year.
[Footnote: A French translation of lines 9-12 was given by M.
RAVAISSON in the _Gazette des Beaux Arts_, Oct. 1877; his paper also
contains some valuable information as to botanical science in the
ancient classical writers and at the time of the Renaissance.]
405.
The lowest branches of those trees which have large leaves and heavy
fruits, such as nut-trees, fig-trees and the like, always droop
towards the ground.
The branches always originate above [in the axis of] the leaves.
406.
The upper shoots of the lateral branches of plants lie closer to the
parent branch than the lower ones.
407.
The lowest branches, after they have formed the angle of their
separation from the parent stem, always bend downwards so as not to
crowd against the other branches which follow them on the same stem
and to be better able to take the air which nourishes them. As is
shown by the angle _b a c_; the branch _a c_ after it has made the
corner of the angle _a c_ bends downwards to _c d_ and the lesser
shoot _c_ dries up, being too thin.
The main branch always goes below, as is shown by the branch _f n
m_, which does not go to _f n o_.
The forms of trees (408-411)
408.
The elm always gives a greater length to the last branches of the
year's growth than to the lower ones; and Nature does this because
the highest branches are those which have to add to the size of the
tree; and those at the bottom must get dry because they grow in the
shade and their growth would be an impediment to the entrance of the
solar rays and the air among the main branches of the tree.
The main branches of the lower part bend down more than those above,
so as to be more oblique than those upper ones, and also because
they are larger and older.
409.
In general almost all the upright portions of trees curve somewhat
turning the convexity towards the South; and their branches are
longer and thicker and more abundant towards the South than towards
the North. And this occurs because the sun draws the sap towards
that surface of the tree which is nearest to it.
And this may be observed if the sun is not screened off by other
plants.
410.
The cherry-tree is of the character of the fir tree as regards its
ramification placed in stages round its main stem; and its branches
spring, 4 or five or 6 [together] opposite each other; and the tips
of the topmost shoots form a pyramid from the middle upwards; and
the walnut and oak form a hemisphere from the middle upwards.
411.
The bough of the walnut which is only hit and beaten when it has
brought to perfection...
[Footnote: The end of the text and the sketch in red chalk belonging
to it, are entirely effaced.]
The insertion of the leaves (412-419)
412.
OF THE INSERTION OF THE BRANCHES ON PLANTS.
Such as the growth of the ramification of plants is on their
principal branches, so is that of the leaves on the shoots of the
same plant. These leaves have [Footnote 6: _Quattro modi_ (four
modes). Only three are described in the text, the fourth is only
suggested by a sketch.
This passage occurs in MANZI'S edition of the Trattato, p. 399, but
without the sketches and the text is mutilated in an important part.
The whole passage has been commented on, from MANZI'S version, in
Part I of the _Nuovo Giornale Botanico Italiano_, by Prof. G.
UZIELLI (Florence 1869, Vol. I). He remarks as to the 'four modes':
"_Leonardo, come si vede nelle linie sententi da solo tre esempli.
Questa ed altre inessattezze fanno desiderare, sia esaminato di
nuovo il manoscritto Vaticano_". This has since been done by D.
KNAPP of Tubingen, and his accurate copy has been published by H.
LUDWIG, the painter. The passage in question occurs in his edition
as No. 833; and there also the drawings are wanting. The space for
them has been left vacant, but in the Vatican copy '_niente_' has
been written on the margin; and in it, as well as in LUDWIG'S and
MANZI'S edition, the text is mutilated.] four modes of growing one
above another. The first, which is the most general, is that the
sixth always originates over the sixth below [Footnote 8: _la sesta
di sotto. "Disposizione 2/5 o 1/5. Leonardo osservo probabilmente
soltanto la prima"_ (UZIELLl).]; the second is that two third ones
above are over the two third ones below [Footnote 10: _terze di
sotto: "Intende qui senza dubbio parlare di foglie decussate, in cui
il terzo verticello e nel piano del primo"_ (UZIELLI).]; and the
third way is that the third above is over the third below [Footnote
11: 3a _di sotto: "Disposizione 1/2"_ (UZIELLI).].
[Footnote: See the four sketches on the upper portion of the page
reproduced as fig. 2 on P1. XXVII.]
413.
A DESCRIPTION OF THE ELM.
The ramification of the elm has the largest branch at the top. The
first and the last but one are smaller, when the main trunk is
straight.
The space between the insertion of one leaf to the rest is half the
extreme length of the leaf or somewhat less, for the leaves are at
an interval which is about the 3rd of the width of the leaf.
The elm has more leaves near the top of the boughs than at the base;
and the broad [surface] of the leaves varies little as to [angle
and] aspect.
[Footnote: See Pl. XXVII, No. 3. Above the sketch and close under
the number of the page is the word '_olmo_' (elm).]
414.
In the walnut tree the leaves which are distributed on the shoots of
this year are further apart from each other and more numerous in
proportion as the branch from which this shoot springs is a young
one. And they are inserted more closely and less in number when the
shoot that bears them springs from an old branch. Its fruits are
borne at the ends of the shoots. And its largest boughs are the
lowest on the boughs they spring from. And this arises from the
weight of its sap which is more apt to descend than to rise, and
consequently the branches which spring from them and rise towards
the sky are small and slender [20]; and when the shoot turns towards
the sky its leaves spread out from it [at an angle] with an equal
distribution of their tips; and if the shoot turns to the horizon
the leaves lie flat; and this arises from the fact that leaves
without exception, turn their underside to the earth [29].
The shoots are smaller in proportion as they spring nearer to the
base of the bough they spring from.
[Footnote: See the two sketches on Pl XXVII, No. 4. The second
refers to the passage lines 20-30.]
415.
OF THE INSERTION OF THE LEAVES ON THE BRANCHES.
The thickness of a branch never diminishes within the space between
one leaf and the next excepting by so much as the thickness of the
bud which is above the leaf and this thickness is taken off from the
branch above [the node] as far as the next leaf.
Nature has so placed the leaves of the latest shoots of many plants
that the sixth leaf is always above the first, and so on in
succession, if the rule is not [accidentally] interfered with; and
this occurs for two useful ends in the plant: First that as the
shoot and the fruit of the following year spring from the bud or eye
which lies above and in close contact with the insertion of the leaf
[in the axil], the water which falls upon the shoot can run down to
nourish the bud, by the drop being caught in the hollow [axil] at
the insertion of the leaf. And the second advantage is, that as
these shoots develop in the following year one will not cover the
next below, since the 5 come forth on five different sides; and the
sixth which is above the first is at some distance.
416.
OF THE RAMIFICATIONS OF TREES AND THEIR FOLIAGE.
The ramifications of any tree, such as the elm, are wide and slender
after the manner of a hand with spread fingers, foreshortened. And
these are seen in the distribution [thus]: the lower portions are
seen from above; and those that are above are seen from below; and
those in the middle, some from below and some from above. The upper
part is the extreme [top] of this ramification and the middle
portion is more foreshortened than any other of those which are
turned with their tips towards you. And of those parts of the middle
of the height of the tree, the longest will be towards the top of
the tree and will produce a ramification like the foliage of the
common willow, which grows on the banks of rivers.
Other ramifications are spherical, as those of such trees as put
forth their shoots and leaves in the order of the sixth being placed
above the first. Others are thin and light like the willow and
others.
417.
You will see in the lower branches of the elder, which puts forth
leaves two and two placed crosswise [at right angles] one above
another, that if the stem rises straight up towards the sky this
order never fails; and its largest leaves are on the thickest part
of the stem and the smallest on the slenderest part, that is towards
the top. But, to return to the lower branches, I say that the leaves
on these are placed on them crosswise like [those on] the upper
branches; and as, by the law of all leaves, they are compelled to
turn their upper surface towards the sky to catch the dew at night,
it is necessary that those so placed should twist round and no
longer form a cross.
[Footnote: See Pl. XXVII, No. 5.]
418.
A leaf always turns its upper side towards the sky so that it may
the better receive, on all its surface, the dew which drops gently
from the atmosphere. And these leaves are so distributed on the
plant as that one shall cover the other as little as possible, but
shall lie alternately one above another as may be seen in the ivy
which covers the walls. And this alternation serves two ends; that
is, to leave intervals by which the air and sun may penetrate
between them. The 2nd reason is that the drops which fall from the
first leaf may fall onto the fourth or--in other trees--onto the
sixth.
419.
Every shoot and every fruit is produced above the insertion [in the
axil] of its leaf which serves it as a mother, giving it water from
the rain and moisture from the dew which falls at night from above,
and often it protects them against the too great heat of the rays of
the sun.
Light on branches and leaves (420-422)
420.
That part of the body will be most illuminated which is hit by the
luminous ray coming between right angles.
[Footnote: See Pl. XXVIII, No. 1.]
421.
Young plants have more transparent leaves and a more lustrous bark
than old ones; and particularly the walnut is lighter coloured in
May than in September.
422.
OF THE ACCIDENTS OF COLOURING IN TREES.
The accidents of colour in the foliage of trees are 4. That is:
shadow, light, lustre [reflected light] and transparency.
OF THE VISIBILITY OF THESE ACCIDENTS.
These accidents of colour in the foliage of trees become confused at
a great distance and that which has most breadth [whether light or
shade, &c.] will be most conspicuous.
The proportions of light and shade in a leaf (423-426)
423.
OF THE SHADOWS OF A LEAF.
Sometimes a leaf has three accidents [of light] that is: shade,
lustre [reflected light] and transparency [transmitted light]. Thus,
if the light were at _n_ as regards the leaf _s_, and the eye at
_m_, it would see _a_ in full light, _b_ in shadow and _c_
transparent.
424.
A leaf with a concave surface seen from the under side and
up-side-down will sometimes show itself as half in shade, and half
transparent. Thus, if _o p_ is the leaf and the light _m_ and the
eye _n_, this will see _o_ in shadow because the light does not fall
upon it between equal angles, neither on the upper nor the under
side, and _p_ is lighted on the upper side and the light is
transmitted to its under side. [Footnote: See Pl. XXVIII, No. 2, the
upper sketch on the page. In the original they are drawn in red
chalk.]
425.
Although those leaves which have a polished surface are to a great
extent of the same colour on the right side and on the reverse, it
may happen that the side which is turned towards the atmosphere will
have something of the colour of the atmosphere; and it will seem to
have more of this colour of the atmosphere in proportion as the eye
is nearer to it and sees it more foreshortened. And, without
exception the shadows show as darker on the upper side than on the
lower, from the contrast offered by the high lights which limit the
shadows.
The under side of the leaf, although its colour may be in itself the
same as that of the upper side, shows a still finer colour--a colour
that is green verging on yellow--and this happens when the leaf is
placed between
426.
the eye and the light which falls upon it from the opposite side.
And its shadows are in the same positions as those were of the
opposite side. Therefore, O Painter! when you do trees close at
hand, remember that if the eye is almost under the tree you will see
its leaves [some] on the upper and [some] on the under side, and the
upper side will be bluer in proportion as they are seen more
foreshortened, and the same leaf sometimes shows part of the right
side and part of the under side, whence you must make it of two
colours.
Of the transparency of leaves (427-429)
427.
The shadows in transparent leaves seen from the under side are the
same shadows as there are on the right side of this leaf, they will
show through to the underside together with lights, but the lustre
[reflected light] can never show through.
428.
When one green has another [green] behind it, the lustre on the
leaves and their transparent [lights] show more strongly than in
those which are [seen] against the brightness of the atmosphere.
And if the sun illuminates the leaves without their coming between
it and the eye and without the eye facing the sun, then the
reflected lights and the transparent lights are very strong.
It is very effective to show some branches which are low down and
dark and so set off the illuminated greens which are at some
distance from the dark greens seen below. That part is darkest which
is nearest to the eye or which is farthest from the luminous
atmosphere.
429.
Never paint leaves transparent to the sun, because they are
confused; and this is because on the transparency of one leaf will
be seen the shadow of another leaf which is above it. This shadow
has a distinct outline and a certain depth of shade and sometimes is
[as much as] half or a third of the leaf which is shaded; and
consequently such an arrangement is very confused and the imitation
of it should be avoided.
The light shines least through a leaf when it falls upon it at an
acute angle.
The gradations of shade and colour in leaves (430-434)
430.
The shadows of plants are never black, for where the atmosphere
penetrates there can never be utter darkness.
431.
If the light comes from _m_ and the eye is at _n_ the eye will see
the colour of the leaves _a b_ all affected by the colour of _m_
--that is of the atmosphere; and _b c_ will be seen from the under
side as transparent, with a beautiful green colour verging on
yellow.
If _m_ is the luminous body lighting up the leaf _s_ all the eyes
that see the under side of this leaf will see it of a beautiful
light green, being transparent.
In very many cases the positions of the leaves will be without
shadow [or in full light], and their under side will be transparent
and the right side lustrous [reflecting light].
432.
The willow and other similar trees, which have their boughs lopped
every 3 or 4 years, put forth very straight branches, and their
shadow is about the middle where these boughs spring; and towards
the extreme ends they cast but little shade from having small leaves
and few and slender branches. Hence the boughs which rise towards
the sky will have but little shade and little relief; and the
branches which are at an angle from the horizon, downwards, spring
from the dark part of the shadow and grow thinner by degrees up to
their ends, and these will be in strong relief, being in gradations
of light against a background of shadow.
That tree will have the least shadow which has the fewest branches
and few leaves.
433.
OF DARK LEAVES IN FRONT OF TRANSPARENT ONES.
When the leaves are interposed between the light and the eye, then
that which is nearest to the eye will be the darkest, and the most
distant will be the lightest, not being seen against the atmosphere;
and this is seen in the leaves which are away from the centre of the
tree, that is towards the light.
[Footnote: See Pl. XXVIII, No. 2, the lower sketch.]
434.
OF THE LIGHTS ON DARK LEAVES.
The lights on such leaves which are darkest, will be most near to
the colour of the atmosphere that is reflected in them. And the
cause of this is that the light on the illuminated portion mingles
with the dark hue to compose a blue colour; and this light is
produced by the blueness of the atmosphere which is reflected in the
smooth surface of these leaves and adds to the blue hue which this
light usually produces when it falls on dark objects.
OF THE LIGHTS ON LEAVES OF A YELLOWISH GREEN.
But leaves of a green verging on yellow when they reflect the
atmosphere do not produce a reflection verging on blue, inasmuch as
every thing which appears in a mirror takes some colour from that
mirror, hence the blue of the atmosphere being reflected in the
yellow of the leaf appears green, because blue and yellow mixed
together make a very fine green colour, therefore the lustre of
light leaves verging on yellow will be greenish yellow.
A classification of trees according to their colours (435)
435.
The trees in a landscape are of various kinds of green, inasmuch as
some verge towards blackness, as firs, pines, cypresses, laurels,
box and the like. Some tend to yellow such as walnuts, and pears,
vines and verdure. Some are both yellowish and dark as chesnuts,
holm-oak. Some turn red in autumn as the service-tree, pomegranate,
vine, and cherry; and some are whitish as the willow, olive, reeds
and the like. Trees are of various forms ...
The proportions of light and shade in trees (436-440)
436.
OF A GENERALLY DISTRIBUTED LIGHT AS LIGHTING UP TREES.
That part of the trees will be seen to lie in the least dark shadow
which is farthest from the earth.
To prove it let _a p_ be the tree, _n b c_ the illuminated
hemisphere [the sky], the under portion of the tree faces the earth
_p c_, that is on the side _o_, and it faces a small part of the
hemisphere at _c d_. But the highest part of the convexity a faces
the greatest part of the hemisphere, that is _b c_. For this
reason--and because it does not face the darkness of the earth--it
is in fuller light. But if the tree has dense foliage, as the
laurel, arbutus, box or holm oak, it will be different; because,
although _a_ does not face the earth, it faces the dark [green] of
the leaves cut up by many shadows, and this darkness is reflected
onto the under sides of the leaves immediately above. Thus these
trees have their darkest shadows nearest to the middle of the tree.
437.
OF THE SHADOWS OF VERDURE.
The shadows of verdure are always somewhat blue, and so is every
shadow of every object; and they assume this hue more in proportion
as they are remote from the eye, and less in proportion as they are
nearer. The leaves which reflect the blue of the atmosphere always
present themselves to the eye edgewise.
OF THE ILLUMINATED PART OF VERDURE AND OF MOUNTAINS.
The illuminated portion, at a great distance, will appear most
nearly of its natural colour where the strongest light falls upon
it.
438.
OF TREES THAT ARE LIGHTED BY THE SUN AND BY THE ATMOSPHERE.
In trees that are illuminated [both] by the sun and the atmosphere
and that have leaves of a dark colour, one side will be illuminated
by the atmosphere [only] and in consequence of this light will tend
to blueness, while on the other side they will be illuminated by the
atmosphere and the sun; and the side which the eye sees illuminated
by the sun will reflect light.
439.
OF DEPICTING A FOREST SCENE.
The trees and plants which are most thickly branched with slender
branches ought to have less dark shadow than those trees and plants
which, having broader leaves, will cast more shadow.
440.
ON PAINTING.
In the position of the eye which sees that portion of a tree
illuminated which turns towards the light, one tree will never be
seen to be illuminated equally with the other. To prove this, let
the eye be _c_ which sees the two trees _b d_ which are illuminated
by the sun _a_; I say that this eye _c_ will not see the light in
the same proportion to the shade, in one tree as in the other.
Because, the tree which is nearest to the sun will display so much
the stronger shadow than the more distant one, in proportion as one
tree is nearer to the rays of the sun that converge to the eye than
the other; &c.
You see that the eye _c_ sees nothing of the tree _d_ but shadow,
while the same eye _c_ sees the tree _b_ half in light and half in
shade.
When a tree is seen from below, the eye sees the top of it as placed
within the circle made by its boughs[23].
Remember, O Painter! that the variety of depth of shade in any one
particular species of tree is in proportion to the rarity or density
of their branches.
[Footnote: The two lower sketches on the left of Pl XXVIII, No. 3,
refer to lines 21-23. The upper sketch has apparently been effaced
by Leonardo himself.]
The distribution of light and shade with reference to the position of the spectator (441-443)
441.
The shadows of trees placed in a landscape do not display themselves
in the same position in the trees on the right hand and those on the
left; still more so if the sun is to the right or left. As is proved
by the 4th which says: Opaque bodies placed between the light and
the eye display themselves entirely in shadow; and by the 5th: The
eye when placed between the opaque body and the light sees the
opaque body entirely illuminated. And by the 6th: When the eye and
the opaque body are placed between darkness and light, it will be
seen half in shadow and half in light.
[Footnote: See the figure on the right hand side of Pl. XXVIII, No.
3. The first five lines of the text are written below the diagram
and above it are the last eight lines of the text, given as No.
461.]
442.
OF THE HERBS OF THE FIELD.
Of the plants which take a shadow from the plants which spring among
them, those which are on this side [in front] of the shadow have the
stems lighted up on a background of shadow, and the plants on which
the shadows fall have their stems dark on a light background; that
is on the background beyond the shadow.
OF TREES WHICH ARE BETWEEN THE EYE AND THE LIGHT.
Of the trees which are between the eye and the light the part in
front will be light; but this light will be broken by the
ramifications of transparent leaves--being seen from the under
side--and lustrous leaves--being seen from the upper side; and the
background below and behind will be dark green, being in shadow from
the front portion of the said tree. This occurs in trees placed
above the eye.
443.
FROM WHENCE TO DEPICT A LANDSCAPE
Landscapes should be represented so that the trees may be half in
light and half in shadow; but it is better to do them when the sun
is covered with clouds, for then the trees are lighted by the
general light of the sky, and the general darkness of the earth. And
then they are darkest in certain parts in proportion as those parts
are nearest to the middle of the tree and to the earth.
The effects of morning light (444-448)
444.
OF TREES TO THE SOUTH.
When the sun is in the east the trees to the South and to the North
have almost as much light as shadow. But a greater share of light in
proportion as they lie to the West and a greater share of shadow in
proportion as they lie to the East.
OF MEADOWS.
If the sun is in the East the verdure of the meadows and of other
small plants is of a most beautiful green from being transparent to
the sun; this does not occur in the meadows to the West, and in
those to the South and North the grass is of a moderately brilliant
green.
445.
OF THE 4 POINTS OF THE COMPASS [IN LANDSCAPES].
When the sun is in the East all the portions of plants lighted by it
are of a most lively verdure, and this happens because the leaves
lighted by the sun within the half of the horizon that is the
Eastern half, are transparent; and within the Western semicircle the
verdure is of a dull hue and the moist air is turbid and of the
colour of grey ashes, not being transparent like that in the East,
which is quite clear and all the more so in proportion as it is
moister.
The shadows of the trees to the East cover a large portion of them
and are darker in proportion as the foliage of the trees is thicker.
446.
OF TREES IN THE EAST.
When the sun is in the East the trees seen towards the East will
have the light which surrounds them all round their shadows,
excepting on the side towards the earth; unless the tree has been
pruned [below] in the past year. And the trees to the South and
North will be half in shade and half in light, and more or less in
shade or in light in proportion as they are more or less to the East
or to the West.
The [position of] the eye above or below varies the shadows and
lights in trees, inasmuch as the eye placed above sees the tree with
the little shadow, and the eye placed below with a great deal of
shadow.
The colour of the green in plants varies as much as their species.
447.
OF THE SHADOWS IN TREES.
The sun being in the East [to the right], the trees to the West [or
left] of the eye will show in small relief and almost imperceptible
gradations, because the atmosphere which lies between the eye and
those trees is very dense [Footnote 7: _per la 7a di questo_. This
possibly referred to something written on the seventh page of this
note book marked _G_. Unfortunately it has been cut out and lost.],
see the 7th of this--and they have no shade; for though a shadow
exists in every detail of the ramification, it results that the
images of the shade and light that reach the eye are confused and
mingled together and cannot be perceived on account of their
minuteness. And the principal lights are in the middle of the trees,
and the shadows to wards the edges; and their separation is shown by
the shadows of the intervals between the trees; but when the forests
are thick with trees the thin edges are but little seen.
448.
OF TREES TO THE EAST.
When the sun is in the East the trees are darker towards the middle
while their edges are light.
The effects of midday light(449)
449.
OBJECTS IN HIGH LIGHT SHOW BUT LITTLE, BUT BETWEEN LIGHT AND SHADOW
THEY STAND OUT WELL.
To represent a landscape choose that the sun shall be at noon and
look towards the West or East and then draw. And if you turn towards
the North, every object placed on that side will have no shadow,
particularly those which are nearest to the [direction of the]
shadow of your head. And if you turn towards the South every object
on that side will be wholly in shadow. All the trees which are
towards the sun and have the atmosphere for their background are
dark, and the other trees which lie against that darkness will be
black [very dark] in the middle and lighter towards the edges.
The appearance of trees in the distance (450-451)
450.
OF THE SPACES [SHOWING THE SKY] IN TREES THEMSELVES.
The spaces between the parts in the mass of trees, and the spaces
between the trees in the air, are, at great distances, invisible to
the eye; for, where it is an effort [even] to see the whole it is
most difficult to discern the parts.--But a confused mixture is the
result, partaking chiefly of the [hue] which predominates. The
spaces between the leaves consist of particles of illuminated air
which are very much smaller than the tree and are lost sight of
sooner than the tree; but it does not therefore follow that they are
not there. Hence, necessarily, a compounded [effect] is produced of
the sky and of the shadows of the tree in shade, which both together
strike the eye which sees them.
OF TREES WHICH CONCEAL THESE SPACES IN ONE ANOTHER.
That part of a tree will show the fewest spaces, behind which a
large number of trees are standing between the tree and the air
[sky]; thus in the tree _a_ the spaces are not concealed nor in _b_,
as there is no tree behind. But in _c_ only half shows the spaces
filled up by the tree _d_, and part of the tree _d_ is filled up by
the tree _e_ and a little farther on all the spaces in the mass of
the trees are lost, and only that at the side remains.
451.
OF TREES.
What outlines are seen in trees at a distance against the sky which
serves as their background?
The outlines of the ramification of trees, where they lie against
the illuminated sky, display a form which more nearly approaches the
spherical on proportion as they are remote, and the nearer they are
the less they appear in this spherical form; as in the first tree
_a_ which, being near to the eye, displays the true form of its
ramification; but this shows less in _b_ and is altogether lost in
_c_, where not merely the branches of the tree cannot be seen but
the whole tree is distinguished with difficulty. Every object in
shadow, of whatever form it may be, at a great distance appears to
be spherical. And this occurs because, if it is a square body, at a
very short distance it loses its angles, and a little farther off it
loses still more of its smaller sides which remain. And thus before
the whole is lost [to sight] the parts are lost, being smaller than
the whole; as a man, who in such a distant position loses his legs,
arms and head before [the mass of] his body, then the outlines of
length are lost before those of breadth, and where they have become
equal it would be a square if the angles remained; but as they are
lost it is round.
[Footnote: The sketch No. 4, Pl. XXVIII, belongs to this passage.]
The cast shadow of trees (452)
452.
The image of the shadow of any object of uniform breadth can never
be [exactly] the same as that of the body which casts it.
[Footnote: See Pl. XXVIII, No. 5.]
Light and shade on groups of trees (453-457)
453.
All trees seen against the sun are dark towards the middle and this
shadow will be of the shape of the tree when apart from others.
The shadows cast by trees on which the sun shines are as dark as
those of the middle of the tree.
The shadow cast by a tree is never less than the mass of the tree
but becomes taller in proportion as the spot on which it falls,
slopes towards the centre of the world.
The shadow will be densest in the middle of the tree when the tree
has the fewest branches.
[Footnote: The three diagrams which accompany this text are placed,
in the original, before lines 7-11. At the spots marked _B_ Leonardo
wrote _Albero_ (tree). At _A_ is the word _Sole_ (sun), at _C Monte_
(mountain) at _D piano_ (plain) and at _E cima_ (summit).]
Every branch participates of the central shadow of every other
branch and consequently [of that] of the whole tree.
The form of any shadow from a branch or tree is circumscribed by the
light which falls from the side whence the light comes; and this
illumination gives the shape of the shadow, and this may be of the
distance of a mile from the side where the sun is.
If it happens that a cloud should anywhere overshadow some part of a
hill the [shadow of the] trees there will change less than in the
plains; for these trees on the hills have their branches thicker,
because they grow less high each year than in the plains. Therefore
as these branches are dark by nature and being so full of shade, the
shadow of the clouds cannot darken them any more; but the open
spaces between the trees, which have no strong shadow change very
much in tone and particularly those which vary from green; that is
ploughed lands or fallen mountains or barren lands or rocks. Where
the trees are against the atmosphere they appear all the same
colour--if indeed they are not very close together or very thickly
covered with leaves like the fir and similar trees. When you see the
trees from the side from which the sun lights them, you will see
them almost all of the same tone, and the shadows in them will be
hidden by the leaves in the light, which come between your eye and
those shadows.
TREES AT A SHORT DISTANCE.
[Footnote 29: The heading _alberi vicini_ (trees at a short
distance) is in the original manuscript written in the margin.] When
the trees are situated between the sun and the eye, beyond the
shadow which spreads from their centre, the green of their leaves
will be seen transparent; but this transparency will be broken in
many places by the leaves and boughs in shadow which will come
between you and them, or, in their upper portions, they will be
accompanied by many lights reflected from the leaves.
454.
The trees of the landscape stand out but little from each other;
because their illuminated portions come against the illuminated
portions of those beyond and differ little from them in light and
shade.
455.
Of trees seen from below and against the light, one beyond the other
and near together. The topmost part of the first will be in great
part transparent and light, and will stand out against the dark
portion of the second tree. And thus it will be with all in
succession that are placed under the same conditions.
Let _s_ be the light, and _r_ the eye, _c d n_ the first tree, _a b
c_ the second. Then I say that _r_, the eye, will see the portion _c
f_ in great part transparent and lighted by the light _s_ which
falls upon it from the opposite side, and it will see it, on a dark
ground _b c_ because that is the dark part and shadow of the tree _a
b c_.
But if the eye is placed at _t_ it will see _o p_ dark on the light
background _n g_.
Of the transparent and shadowy parts of trees, that which is nearest
to you is the darkest.
456.
That part of a tree which has shadow for background, is all of one
tone, and wherever the trees or branches are thickest they will be
darkest, because there are no little intervals of air. But where the
boughs lie against a background of other boughs, the brighter parts
are seen lightest and the leaves lustrous from the sunlight falling
on them.
457.
In the composition of leafy trees be careful not to repeat too often
the same colour of one tree against the same colour of another
[behind it]; but vary it with a lighter, or a darker, or a stronger
green.
On the treatment of light for landscapes (458-464)
458.
The landscape has a finer azure [tone] when, in fine weather the sun
is at noon than at any other time of the day, because the air is
purified of moisture; and looking at it under that aspect you will
see the trees of a beautiful green at the outside and the shadows
dark towards the middle; and in the remoter distance the atmosphere
which comes between you and them looks more beautiful when there is
something dark beyond. And still the azure is most beautiful. The
objects seen from the side on which the sun shines will not show you
their shadows. But, if you are lower than the sun, you can see what
is not seen by the sun and that will be all in shade. The leaves of
the trees, which come between you and the sun are of two principal
colours which are a splendid lustre of green, and the reflection of
the atmosphere which lights up the objects which cannot be seen by
the sun, and the shaded portions which only face the earth, and the
darkest which are surrounded by something that is not dark. The
trees in the landscape which are between you and the sun are far
more beautiful than those you see when you are between the sun and
them; and this is so because those which face the sun show their
leaves as transparent towards the ends of their branches, and those
that are not transparent--that is at the ends--reflect the light;
and the shadows are dark because they are not concealed by any
thing.
The trees, when you place yourself between them and the sun, will
only display to you their light and natural colour, which, in
itself, is not very strong, and besides this some reflected lights
which, being against a background which does not differ very much
from themselves in tone, are not conspicuous; and if you are lower
down than they are situated, they may also show those portions on
which the light of the sun does not fall and these will be dark.
In the Wind.
But, if you are on the side whence the wind blows, you will see the
trees look very much lighter than on the other sides, and this
happens because the wind turns up the under side of the leaves,
which, in all trees, is much whiter than the upper sides; and, more
especially, will they be very light indeed if the wind blows from
the quarter where the sun is, and if you have your back turned to
it.
[Footnote: At _S_, in the original is the word _Sole_ (sun) and at
_N parte di nuvolo_ (the side of the clouds).]
459.
When the sun is covered by clouds, objects are less conspicuous,
because there is little difference between the light and shade of
the trees and of the buildings being illuminated by the brightness
of the atmosphere which surrounds the objects in such a way that the
shadows are few, and these few fade away so that their outline is
lost in haze.
460.
OF TREES AND LIGHTS ON THEM.
The best method of practice in representing country scenes, or I
should say landscapes with their trees, is to choose them so that
the sun is covered with clouds so that the landscape receives an
universal light and not the direct light of the sun, which makes the
shadows sharp and too strongly different from the lights.
461.
OF PAINTING.
In landscapes which represent [a scene in] winter. The mountains
should not be shown blue, as we see in the mountains in the summer.
And this is proved [Footnote 5. 6.: _Per la_ 4_a di questo_. It is
impossible to ascertain what this quotation refers to. _Questo_
certainly does not mean the MS. in hand, nor any other now known to
us. The same remark applies to the phrase in line 15: _per la_ 2_a
di questo_.] in the 4th of this which says: Among mountains seen
from a great distance those will look of the bluest colour which are
in themselves the darkest; hence, when the trees are stripped of
their leaves, they will show a bluer tinge which will be in itself
darker; therefore, when the trees have lost their leaves they will
look of a gray colour, while, with their leaves, they are green, and
in proportion as the green is darker than the grey hue the green
will be of a bluer tinge than the gray. Also by the 2nd of this: The
shadows of trees covered with leaves are darker than the shadows of
those trees which have lost their leaves in proportion as the trees
covered with leaves are denser than those without leaves--and thus
my meaning is proved.
The definition of the blue colour of the atmosphere explains why the
landscape is bluer in the summer than in the winter.
462.
OF PAINTING IN A LANDSCAPE.
If the slope of a hill comes between the eye and the horizon,
sloping towards the eye, while the eye is opposite the middle of the
height of this slope, then that hill will increase in darkness
throughout its length. This is proved by the 7th of this which says
that a tree looks darkest when it is seen from below; the
proposition is verified, since this hill will, on its upper half
show all its trees as much from the side which is lighted by the
light of the sky, as from that which is in shade from the darkness
of the earth; whence it must result that these trees are of a medium
darkness. And from this [middle] spot towards the base of the hill,
these trees will be lighter by degrees by the converse of the 7th
and by the said 7th: For trees so placed, the nearer they are to the
summit of the hill the darker they necessarily become. But this
darkness is not in proportion to the distance, by the 8th of this
which says: That object shows darkest which is [seen] in the
clearest atmosphere; and by the 10th: That shows darkest which
stands out against a lighter background.
[Footnote: The quotation in this passage again cannot be verified.]
463.
OF LANDSCAPES.
The colours of the shadows in mountains at a great distance take a
most lovely blue, much purer than their illuminated portions. And
from this it follows that when the rock of a mountain is reddish the
illuminated portions are violet (?) and the more they are lighted
the more they display their proper colour.
464.
A place is most luminous when it is most remote from mountains.
On the treatment of light for views of towns (465-469)
465.
OF LIGHT AND SHADOW IN A TOWN.
When the sun is in the East and the eye is above the centre of a
town, the eye will see the Southern part of the town with its roofs
half in shade and half in light, and the same towards the North; the
Eastern side will be all in shadow and the Western will be all in
light.
466.
Of the houses of a town, in which the divisions between the houses
may be distinguished by the light which fall on the mist at the
bottom. If the eye is above the houses the light seen in the space
that is between one house and the next sinks by degrees into thicker
mist; and yet, being less transparent, it appears whiter; and if the
houses are some higher than the others, since the true [colour] is
always more discernible through the thinner atmosphere, the houses
will look darker in proportion as they are higher up. Let _n o p q_
represent the various density of the atmosphere thick with moisture,
_a_ being the eye, the house _b c_ will look lightest at the bottom,
because it is in a thicker atmosphere; the lines _c d f_ will appear
equally light, for although _f_ is more distant than _c_, it is
raised into a thinner atmosphere, if the houses _b e_ are of the
same height, because they cross a brightness which is varied by
mist, but this is only because the line of the eye which starts from
above ends by piercing a lower and denser atmosphere at _d_ than at
_b_. Thus the line a _f_ is lower at _f_ than at _c_; and the house
_f_ will be seen darker at _e_ from the line _e k_ as far as _m_,
than the tops of the houses standing in front of it.
467.
OF TOWNS OR OTHER BUILDINGS SEEN IN THE EVENING OR THE MORNING
THROUGH THE MIST.
Of buildings seen at a great distance in the evening or the morning,
as in mist or dense atmosphere, only those portions are seen in
brightness which are lighted up by the sun which is near the
horizon; and those portions which are not lighted up by the sun
remain almost of the same colour and medium tone as the mist.
WHY OBJECTS WHICH ARE HIGH UP AND AT A DISTANCE ARE DARKER THAN THE
LOWER ONES, EVEN IF THE MIST IS UNIFORMLY DENSE.
Of objects standing in a mist or other dense atmosphere, whether
from vapour or smoke or distance, those will be most visible which
are the highest. And among objects of equal height that will be the
darkest [strongest] which has for background the deepest mist. Thus
the eye _h_ looking at _a b c_, towers of equal height, one with
another, sees _c_ the top of the first tower at _r_, at two degrees
of depth in the mist; and sees the height of the middle tower _b_
through one single degree of mist. Therefore the top of the tower
_c_ appears stronger than the top of the tower _b_, &c.
468.
OF THE SMOKE OF A TOWN.
Smoke is seen better and more distinctly on the Eastern side than on
the Western when the sun is in the East; and this arises from two
causes; the first is that the sun, with its rays, shines through the
particles of the smoke and lights them up and makes them visible.
The second is that the roofs of the houses seen in the East at this
time are in shadow, because their obliquity does not allow of their
being illuminated by the sun. And the same thing occurs with dust;
and both one and the other look the lighter in proportion as they
are denser, and they are densest towards the middle.
469.
OF SMOKE AND DUST.
If the sun is in the East the smoke of cities will not be visible in
the West, because on that side it is not seen penetrated by the
solar rays, nor on a dark background; since the roofs of the houses
turn the same side to the eye as they turn towards the sun, and on
this light background the smoke is not very visible.
But dust, under the same aspect, will look darker than smoke being
of denser material than smoke which is moist.
The effect of wind on trees (470-473)
470.
OF REPRESENTING WIND.
In representing wind, besides the bending of the boughs and the
reversing of their leaves towards the quarter whence the wind comes,
you should also represent them amid clouds of fine dust mingled with
the troubled air.
471.
Describe landscapes with the wind, and the water, and the setting
and rising of the sun.
THE WIND.
All the leaves which hung towards the earth by the bending of the
shoots with their branches, are turned up side down by the gusts of
wind, and here their perspective is reversed; for, if the tree is
between you and the quarter of the wind, the leaves which are
towards you remain in their natural aspect, while those on the
opposite side which ought to have their points in a contrary
direction have, by being turned over, their points turned towards
you.
472.
Trees struck by the force of the wind bend to the side towards which
the wind is blowing; and the wind being past they bend in the
contrary direction, that is in reverse motion.
473.
That portion of a tree which is farthest from the force which
strikes it is the most injured by the blow because it bears most
strain; thus nature has foreseen this case by thickening them in
that part where they can be most hurt; and most in such trees as
grow to great heights, as pines and the like. [Footnote: Compare the
sketch drawn with a pen and washed with Indian ink on Pl. XL, No. 1.
In the Vatican copy we find, under a section entitled '_del fumo_',
the following remark: _Era sotto di questo capitulo un rompimento di
montagna, per dentro delle quali roture scherzaua fiame di fuoco,
disegnate di penna et ombrate d'acquarella, da uedere cosa mirabile
et uiua (Ed. MANZI, p. 235. Ed. LUDWIG, Vol. I, 460). This appears
to refer to the left hand portion of the drawing here given from the
Windsor collection, and from this it must be inferred, that the leaf
as it now exists in the library of the Queen of England, was already
separated from the original MS. at the time when the Vatican copy
was made.]
Light and shade on clouds (474-477)
474.
Describe how the clouds are formed and how they dissolve, and what
cause raises vapour.
475.
The shadows in clouds are lighter in proportion as they are nearer
to the horizon.
[Footnote: The drawing belonging to this was in black chalk and is
totally effaced.]
476.
When clouds come between the sun and the eye all the upper edges of
their round forms are light, and towards the middle they are dark,
and this happens because towards the top these edges have the sun
above them while you are below them; and the same thing happens with
the position of the branches of trees; and again the clouds, like
the trees, being somewhat transparent, are lighted up in part, and
at the edges they show thinner.
But, when the eye is between the cloud and the sun, the cloud has
the contrary effect to the former, for the edges of its mass are
dark and it is light towards the middle; and this happens because
you see the same side as faces the sun, and because the edges have
some transparency and reveal to the eye that portion which is hidden
beyond them, and which, as it does not catch the sunlight like that
portion turned towards it, is necessarily somewhat darker. Again, it
may be that you see the details of these rounded masses from the
lower side, while the sun shines on the upper side and as they are
not so situated as to reflect the light of the sun, as in the first
instance they remain dark.
The black clouds which are often seen higher up than those which are
illuminated by the sun are shaded by other clouds, lying between
them and the sun.
Again, the rounded forms of the clouds that face the sun, show their
edges dark because they lie against the light background; and to see
that this is true, you may look at the top of any cloud that is
wholly light because it lies against the blue of the atmosphere,
which is darker than the cloud.
[Footnote: A drawing in red chalk from the Windsor collection (see
Pl. XXIX), representing a landscape with storm-clouds, may serve to
illustrate this section as well as the following one.]
477.
OF CLOUDS, SMOKE AND DUST AND THE FLAMES OF A FURNACE OR OF A
BURNING KILN.
The clouds do not show their rounded forms excepting on the sides
which face the sun; on the others the roundness is imperceptible
because they are in the shade. [Footnote: The text of this chapter
is given in facsimile on Pls. XXXVI and XXXVII. The two halves of
the leaf form but one in the original. On the margin close to lines
4 and 5 is the note: _rossore d'aria inverso l'orizonte_--(of the
redness of the atmosphere near the horizon). The sketches on the
lower portion of the page will be spoken of in No. 668.]
If the sun is in the East and the clouds in the West, the eye placed
between the sun and the clouds sees the edges of the rounded forms
composing these clouds as dark, and the portions which are
surrounded by this dark [edge] are light. And this occurs because
the edges of the rounded forms of these clouds are turned towards
the upper or lateral sky, which is reflected in them.
Both the cloud and the tree display no roundness at all on their
shaded side.
On images reflected in water (478)
478.
Painters often deceive themselves, by representing water in which
they make the water reflect the objects seen by the man. But the
water reflects the object from one side and the man sees it from the
other; and it often happens that the painter sees an object from
below, and thus one and the same object is seen from hind part
before and upside down, because the water shows the image of the
object in one way, and the eye sees it in another.
Of rainbows and rain (479-480)
479.
The colours in the middle of the rainbow mingle together.
The bow in itself is not in the rain nor in the eye that sees it;
though it is generated by the rain, the sun, and the eye. The
rainbow is always seen by the eye that is between the rain and the
body of the sun; hence if the sun is in the East and the rain is in
the West it will appear on the rain in the West.
480.
When the air is condensed into rain it would produce a vacuum if the
rest of the air did not prevent this by filling its place, as it
does with a violent rush; and this is the wind which rises in the
summer time, accompanied by heavy rain.
Of flower seeds (481)
481.
All the flowers which turn towards the sun perfect their seeds; but
not the others; that is to say those which get only the reflection
of the sun. _
Read next: VOLUME I: IX. THE PRACTICE OF PAINTING
Read previous: VOLUME I: VII. ON THE PROPORTIONS AND ON THE MOVEMENTS OF THE HUMAN FIGURE
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