Flight 

I have divided the "Treatise on Birds" into four boohj; of which the first treats of their flight by beating their wings; the second of flight without beating their wings and with the help of the wind; 
the third of flight in general, such as that of birds, bats, fishes, animals and insects; the last of the mechanism of this movement.' 

Those feathers which are farthest away from their points of attachment will be most flexible. 

The tips of the feathers of the wings therefore will always be higher than their roots, wherefore we may with reason say that the bones of the wings will always be lower when the wing is lowered than any part of the wing; and when it is raised these bones of the wing will be higher than any part of this wing. Because the heavier part will always be the guide of the movement. I ask in what part of the under surface of the breadth of the wing does this wing press the air more than in any part of the length of the wings. 

Every body that does not bend, although these are each in itself of different size and weight, will throw equal weights upon all the supports which are equidistant from their centre of gravity, this centre
being in the middle of the breadth of this body. 

But if the said body is flexible with varying thicknesses and weights, although the centre of gravity may be in the centre of its magnitude, this will not prevent the support that is nearest the centre of its
gravity, or of other inequality of gravity, from being more charged with weight than that which is above the lighter parts. 

Sul Volo 4 v. 

The man in a flying machine [has] to be free from the waist upward in order to be able to balance himself as he does in a boat, so 403 

that his centre of gravity and that of his machine may oscillate and change where necessity requires through a change in the centre of its resistance. 

When the bird desires to turn to the right or left side by beating its wings, it will beat lower with the wing on the side on which it wishes to turn, and thus the bird will twist its movement behind the impetus of the wing which moves most, Sul Volo 6 [5] r. 

and makes the reflex movement under the wind from the opposite side. 

When the bird desires to rise by beating its wings it raises its shoulders and beats the tips of the wings towards itself, and comes to condense the air which is interposed between the points of the wings
and the breast of the bird, and the pressure from this air raises up the bird. 

The kite and the other birds which beat their wings only a little, go in search of the current of the wind; and when the wind is blowing at a height they may be seen at a great elevation, but if it is blowing low down then they remain low. 

When there is no wind stirring in the air then the kite beats its wings more rapidly in its flight, in such a way that it rises to a height and acquires an impetus; with which impetus, dropping then very
gradually, it can travel for a great distance without moving its wings. 

And when it has descended it does the same over again, and so continues for many times in succession. 

This method of descending without moving the wings serves it as a means of resting in the air after the fatigue of the above-mentioned beating of the wings. 

All the birds- which fly in spurts rise to a height by beating their wings; and during their descent they proceed to rest themselves, for while descending they do not beat their wings. Sul Volo 6 [5] v. 

OF THE FOUR REFLEX AND FALLING MOVEMENTS MADE BY
BIRDS UNDER DIFFERENT CONDITIONS OF THE WIND 

The slanting descent of birds made against the wind will always be made beneath the wind, and their reflex movement will be made upon the wind. 

But if this falling movement is made to the cast when the wind is blowing from the north then the north wing will remain under the wind and it will do the same in the reflex movement, wherefore at
the end of this reflex movement the bird will find itself with its front to the north. 

And if the bird descends to the south while the wind is blowing from the north it will make this descent upon the wind, and its reflex movement will be below the wind; but this is a vexed question which shall be discussed in its proper place for here it would seem that it could not make the reflex movement. 

When the bird makes its reflex movement facing and upon the wind it will rise much more than its natural impetus requires, seeing that it is also helped by the wind which enters underneath it and plays the part of a wedge. But when it is at the end of its ascent it will have used up its impetus and therefore will depend upon the help of the wind, which as it strikes it on the breast would throw it over if it
were not that it lowers the right or left wing> for this will cause it to turn to the right or left dropping down in a half circle. 

Sui Volo 7 [6] r. 

[Of a flying machine] 

The movement of the bird ought always to be above the clouds so that the wing may not be wetted, and in order to survey more country and to escape the danger caused by the revolutions of the winds among the mountain defiles which are always full of gusts and eddies of winds. And if moreover the bird should be overturned you will have plenty of time to turn it back again following the instructions I have given, before it falls down again to the ground. 

If the point of the wing is struck by the wind and the wind enters underneath the point the bird will then find itself liable to be overturned unless it employs one of two remedies; that is either it suddenly
enters with this point under the wind or lowers the opposite wing from the middle forward. 

(Figure) abed are the four cords above for raising the wing, and they are as powerful in action as the cords below, e f g h, because of the bird being overturned so that they may offer as much resistance
above as they do below, although a single strip of hide dressed with alum thick and large may chance to suffice: but finally however we must put it to the test. Sul Volo 7 [6] v. 

The bird I have described ought to be able by the help of the wind to rise to a great height, and this will prove to be its safety; since even if all the above-mentioned revolutions were to befall it, it would still have time to regain a condition of equilibrium; provided that its various parts have a great power of resistance, so that they can safely withstand the fury and violence of the descent, by the aid of the defences which I have mentioned; and its joints should be made of strong tanned hide, and sewn with cords of very strong raw silk. And let no one encumber himself with iron bands, for these are very soon broken at the joints or else they become worn out, and consequently it is well not to encumber one's self with them. 

The cord a set for the purpose of extending the wing ought to be of thick dressed hide, so that if the bird should be turned upside down it may be able to subdue the fury of the wind which strikes it on the wing and seeks to close it, for this would be the cause of the destruction of the bird. But to make it more safe you should make exactly the same system of cords outside as within, and you will then
avoid all suspicion of danger. 

a b c are the terminating points of the cords from the three joints of the fingers of the wings; d marks the position of the mover of the lever a d which moves the wing. Sul Volo 8 [7] r. 

When the edge of the point of the wing meets the edge of the wind for a brief moment this wing sets it either below or above this edge of the wind, and the same happens with the point and sides of the tail and in like manner with the helms of the shoulders of the wings. 

The descent of the bird will always be by that extremity which is nearest to its centre of gravity. 

The heaviest part of the bird which descends will always be in front of the centre of its bulk. 

3rd. When without the help of the wind the bird is stationary in the air without beating its wings in a position of equilibrium, this shows that its centre of gravity is identical with the centre of its bulk. 

4th. The heaviest part of the bird which descends head foremost will never remain above or level with the height of its lightest part. 

If the bird falls with its tail downwards by throwing its tail backwards it will regain a position of equilibrium, and if it throws it forwards it will come to turn right over. 

1st. When the bird being in a state of equilibrium sends the centre of resistance of its wings behind its centre of gravity it will descend with its head below. 

2nd. And this bird which is in a state of equilibrium will have the centre of resistance of its wings in front of its centre of gravity; this bird will then drop with the tail turned to the ground. 1 

Sul Volo 8 [7] v. 

If the wing and the tail are too far above the wind lower half the opposite wing and so get the impact of the wind there within it, and this will cause it to right itself. 

If the wing and the tail should be beneath the wind raise the opposite wing and it will right itself as you desire, provided that this wing which rises slants less than the one opposite to it. 

And if the wing and the breast are above the wind it should lower the half of the opposite wing, and this will be struck by the wind and thrown back upwards, and this will cause the bird to right itself. 

But if the wing and the spine are below the wind it ought then to raise the opposite wing and expand it in the wind, and the bird will immediately right itself. 

And if the bird is situated with the hinder part above the wind the tail ought then to be placed beneath the wind, and thus there will be brought about an equilibrium of forces. 

But if the bird should have its hinder parts below the wind {raising its tail 2 ) it should enter with its tail above the wind and it will right itself. Sul Volo 9 ■ [8] r. 

When the bird is above the wind, turning its bill with its trunk to the wind the bird would be liable to be overturned unless it lowered its tail and received in it a great volume of wind; and if it acts thus it is
impossible for it to be overturned. This is proved by the first section 1 The odd order of the numbered paragraphs here and elsewhere in the MSS. suggests that the numbers may have been added with the intention of amending the order when the work should take its final form. 

' Words crossed out in MS. 

of the Elements of Mechanics, which shows how things in equilibrium which are struck outside their centre of gravity send down the opposite sides which are situated on this side of the aforesaid centre. . . . 

(Example) 

And if the bird is situated with its length under the wind it is liable to be thrown upside down by the wind unless it instantly raises up its tail. . . . 

How the expanse of the wing is not all used in compressing the air; and for the truth of this see how the openings between the chief feathers are much wider spaces than the actual breadth of the feathers. 

You therefore who make research into winged creatures do not take into your reckoning the whole expanse of the wing, and note the different characteristics of the wings of all winged creatures. 

Sul Volo 9 [8] v. 

When the wind strikes the bird under its course from its centre of gravity towards this wind then the bird will turn with its spine towards the wind; and if the wind was more powerful below than above
the bird would be turned upside down if it were not instantly alert to draw to itself the lower and stretch out the upper wing; and by this means it rights itself and returns to the position of equilibrium. 

This is proved thus: — let a c be the wing folded up beneath the bird, and a b the wing extended; I say that the forces of the wind which strike the two wings will have the same proportion as that of their
extension, that is a b as against a c. It is true that c is wider than b, but it is so near the bird's centre of gravity that it offers small resistance in comparison with b. 

But when the bird is struck under the wind, beneath one of its wings, it would be possible for the wind to overturn it if it were not that so soon as ever it is turned with its breast to the wind it extended
the opposite wing towards the ground, and drew up the wing which was first struck by the wind which remains uppermost, and thus it will come to return to a position of equilibrium. This is proved by the fourth of the third according to which that object is more mastered which is opposed by a greater force; also by the fifth of the third which is that this support resists less and is situated farther away from its fixed point; also by the fourth of the third: among winds of equal force that will be of greater force which is of greater volume, and that will strike with a greater volume which finds a greater object; wherefore m f being longer than m n, m f will obey the wind. 

Sul Volo 10 [9] r. 

If the bird should wish to turn itself rapidly on one of its sides and to follow its circular movement it will beat its wings twice on that side, moving the wing back like an oar and keeping the other wing
steady or making only one beat with this as against two of the opposite wing. 

Since the wings are swifter to press the air than the air is to escape from beneath the wings the air becomes condensed and resists the movement of the wings; and the motive power of these wings by subduing the resistance of the air raises itself in a contrary movement to the movement of the wings. 

That bird will descend with the swifter movement when its descent is at a less angle. 

The descent of a bird will be at a less angle when the tips of the wings and their shoulders are nearer together. 

The lines of the movements made by birds as they rise are of two kinds, of which one is always spiral in the manner of a screw, and the other is rectilinear and curved. 

That bird will rise up to a height which by means of a circular movement in the shape of a screw makes its reflex movement against the coming of the wind and against the flight of this wind, turning
always upon its right or left side. 

Thus if the north wind should be blowing, and you coming above in reflex movement, should glide against the said wind, until, in this straight process of rising, the wind was in such a condition that it
might turn you over, you are then at liberty to bend with the right or left wing, and holding the inner wing low you will pursue a curving movement, with the help of the tail, curving in the direction of the
lower wing, and continually descending and pivoting round the wing that is held low, until you again make the reflex movement anew above the wind, behind the course of the wind; and when you are on the point of being turned over this same lower wing will curve your line of movement, and you will return against the wind, underneath it, until you have acquired the impetus, and then raise yourself above the wind, facing its approach, and by means of the already acquired impetus, you will make the reflex movement greater than the falling movement. 

A bird as it rises always sets its wings above the wind and without beating them, and it always moves in a circular movement. And if you wish to go to the west without beating your wings, when
the north wind is blowing, make the falling movement straight and beneath the wind to the west, and the reflex movement above the wind to the north. Sul Volo (f.m.) ii [io] r. 

A bird makes the same use of wings and tail in the air as a swimmer does of his arms and legs in the water. 

If a man is swimming with his arms equally towards the east, and his body exactly faces the east, the swimmer's movement will be towards the east. But if the northern arm is making a longer stroke than
the southern arm then the movement of his body will be to the northeast. And if the right arm is making a longer movement than the left the man's movement will be to the south-east. 

The impetus of one of the wings extended edgewise towards the tail will occasion the bird a sudden circling movement following on the impetus of the above-mentioned wing. 

When the bird raises itself in circles to a height above the wind, without beating its wings, by the force of the wind, it will be transported by this wind out of the region where it desires to return, still
without beating its wings; then it turns so that it faces the approach of the wind, entering slantwise underneath this wind, and comes to descend slightly until it finds itself above the spot where it desires
to return. 

The edge a of the helm of the wing or the thumb (dito grosso) of the hand of the bird b a is that which sets the shoulder of the wing immediately below or above the wind. And if this shoulder did not
have the power of cutting with a keen and strong edge, the wing would not be able suddenly to enter below or above the wind when it happened to be necessary for the bird, seeing that if this shoulder were round, and the wind / e were to strike the wing below and it should immediately befall the wing to be . . . 

Sul Volo (f.m.) 11 [10] v. 

. . . struck from above, the power of the wind which strikes it from above is not at its full strength, seeing that the wedge of the wind which is separated from the middle of the shoulder downwards raises
the wing up almost with the same power as that exerted by the wind above to send the wing downwards. 

But if the wind strikes the bird on the right or left wing, it is necessary for it to enter below or above this wind, with the point of the wing struck by this wind, and this change occupies as much space as
the thickness of the points of these wings. As this change is beneath the wind the bird turns with its bill to the wind, and if it is above the wind the bird will turn with its tail as it pleases; and here arises
the danger of the bird being turned upside down, if nature had not provided for this by placing the weight of the body of this bird lower than the position of the extension of the wings, as will be shown here. 

Sul Volo 10 [9] v. 

When the bird flies by beating its wings it does not extend its wings wholly, because the points of the wings would be too far removed from the lever and cords which move them. If as the bird descends it moves its wings back as though they were oars the bird will make swift movement; and this comes about because the wings are striking in the air which is continually flowing in the
wake of the bird to fill up the void from whence it has departed. 

Sul Volo 12 [11] r. 

TO ESCAPE THE DANGER OF DESTRUCTION 

The destruction of these machines may come about in two ways, the first of which is when the machine breaks, the second is when it turns edgewise or almost on its edge because it ought always to descend with a long slant and almost in a level line. 

As regards the preventing of the machine from being broken one may guard against this by making it as strong as possible in whatever 

4 i2 FLIGHT 

line it may turn, that is either edgewise falling with head or tail in front, or with the point of the right or left wing, or along lines that bisect or are the quarterings of these lines as the sketch shows [figure] 
against this by turning almost edgewise one ought at the outset to guard. 

As regards constructing the machine in such a way that in descending whatever may be the direction that it takes it finds the remedy prepared; and this you will do by causing its centre of gravity to be
above that of the weight which it carries, always in a vertical line, and the one always at a sufficient distance from the other, that is that if the machine is thirty braccia in width the centres are four braccia
apart, and as has been said one is beneath the other, and the heavier is below because as it descends the heavier part always constitutes itself in part the guide of the movement. In addition to this if the bird wishes to fall with its head downwards with a fraction of the slant that would cause it to turn over this will not be able to happen, because the lighter part would be beneath the heavier and the light would be descending before the heavy, which is impossible in a descent of any length, as is proved in the fourth of the Elements of Mechanics. 

And if the bird should fall head downwards with the body partly slanting towards the ground the underneath sides of the wings ought to turn flat against the earth, and the tail to rise towards the back, and the head or the underpart of the jaw is also turned towards the ground, and from this there will immediately originate in this bird its reflex movement which will cast it up again towards the sky; for which reason the bird at the close of its reflex movement will come to fall back unless it should while rising lower one of its wings slightly, which would curve such movement and cause it to turn into a half circle; then this bird will find itself at the close of this movement with its bill turned to the spot at which this reflex movement started. And if this is done against the course of the wind the end of the reflex movement will be much higher than was the commencement of the falling movement. And this is the way in which the bird rises up to a height without beating its wings and circling. And the remainder of the circle of which I have spoken is completed by the help of the wind, by a falling movement, with one of the wings always kept low and similarly one side of the tail. And it subsequently makes a reflex movement towards the direction of the wind and is left at the end with its bill turned in the direction of the wind, and then makes again the falling and reflex movements against the wind always going in circles. 

When the bird wishes suddenly to turn on one of its sides it pushes out swiftly towards its tail, the point of the wing on that side, and since every movement tends to maintain itself, or rather every body that is moved continues to move so long as the impression of the force of its mover is retained in it, therefore the movement of this wing with violence, in the direction of the tail, keeping still at its termination a portion of the said impression, not being able of itself to follow the movement which has already been commenced, will come to move the whole bird with it until the impetus of the moved air has been consumed. 

When the tail is thrust forward with its face and the wind strikes upon it it makes the bird move suddenly in an opposite direction. 

Sul Volo 13 [12] r. and v. 

[With drawing of bird with wings outstretched} 

Here the big fingers of the wings are those which keep the bird motionless in the air against the movement of the wind; that is the wind moves, and it maintains itself upon it without beating its wings, 
and the bird does not change its position. 

The reason is that the bird arranges its wings so as to slant so much that the wind which strikes it below does not form itself into a wedge of such a kind as tends to raise it, raising it however just so much as its weight wishes to lower it, that is to say if the bird's impulse to fall be expressed by two units of power the wind's impulse to rise will be expressed by two units also, and because things which are equal can- not overcome one another the bird remains in its position without either rising or falling. It remains for us to speak of the motion which does not impel it either forward or backward; and that is if the wind should wish to accompany it or drive it out of its position with a power expressed by four units and the bird with the same power is slanting at the same angle against the wind. Here also as the powers are equal the bird will not move forward nor will it be driven back when the wind is equal. But inasmuch as the movements and powers of the winds are variable the angle of the wings ought not to change, because if the wind grows and it should alter the angle in order not to be driven upward by this wind. . . . 

In the aforesaid instances the wind does not enter like a wedge underneath the slanting wings, but only meets the wing along the edge which wishes to descend against the wind; and there strikes it on
the edge of the shoulder which serves as a shield for all the rest of the wing; and there would be here no protection against the descent of the wing if it were not for the big finger a which then comes to the front and receives the whole force of the wind full upon it, or less than full according to the greater or less power of the wind. 

Sul Volo 14 [13] r. 

[With drawing of wing] 

The big finger n of the hand m n is that which when the hand is
lowered comes to lower itself more than the hand, in such a way as to
close and prevent the exit of the stream of air compressed by the lower- 
ing of the hand, in such a way that in this place the air becomes
condensed and offers resistance to the oarage of the wing. And for this
reason nature has formed in this big finger a bone of such great
strength, to which are united very strong sinews with the feathers
short and of greater strength than the feathers which are on birds' 
wings, because the bird leans upon it, upon the air which is already
compressed, with all the power of the wing and of its strength, be- 
cause it is this by means of which the bird moves forward. 

And this finger here performs for the wings the function which its
claws do for a cat when it climbs up trees. 

But when the wing regains fresh force with its return upward and
forward, the big finger of the wing then puts itself in a straight line
with the other fingers, and thus with its sharp edge it strikes the
air and performs the office of a helm or rudder, which strikes the air
continually in some movement high or low when the bird wishes to
rise. 

The second helm or rudder is placed on the opposite side beyond
the bird's centre of gravity, and this is its tail, which if it is struck by
the wind below, through being beyond the aforesaid centre will come
to lower the bird in its front part. 

But if the tail is struck above, the bird is raised in its front part. 
And if the tail is somewhat twisted, and shows its front slanting under
the right wing, the front part of the bird will be turned towards the
right side. And if the slant of the lower side of the tail is turned to the
left wing, it will turn with its front part to the left side; and in each
of the two conditions the bird will descend. But if the tail in a slant- 
ing position is struck by the wind in its upper part the bird will turn
revolving slowly on that side on which the upper surface of the tail
shows its slant. Sul Volo 14 [13] v. 

The axis of the shoulder of birds is that which is turned by the
muscles of the breast and back; and it is here that the discretion of
lowering or raising the tail originates according to the will or necessity
of the animal that moves. 

I conclude that the rising of birds without beating their wings is
not produced by anything other than their circular movement amid
the movement of the wind, which movement when it ceases to have
the support of the wind continues to descend as far as the place at
which the reflex movement starts, after which, and having thus re- 
volving described a semicircle it finds itself again with its face turned
to the wind, and follows the reflex movement, above the wind, con- 
tinually revolving until with the help of the wind it makes its highest
ascent between its lowest descent and the arrival of the wind, and re- 
mains with its left wing to the wind; and from this maximum eleva- 
tion circling anew it drops again to the last falling movement, re- 
maining with its right wing to the wind. 

The equal power of resistance of a bird's wings is always due to the
fact of their being equally remote in their extremities from the bird's
centre of gravity. 

But when one of the extremities of the wings is nearer the bird's
centre of gravity than the other the bird will then descend on the
side on which the extremity of the wing is nearer to the centre of
gravity. Sul Volo 15 [14] r. 

The hand of the wing is the part that causes the impetus; and the
elbow is then held edgewise in order not to check the movement which
creates the impetus; and when this impetus is afterwards created the 

elbow is lowered and set slantwise and in slanting it makes the air
upon which it rests almost into the form of a wedge, upon which the
wing comes to raise itself, and if it did not do thus the movement of
the bird during the time that the wing returns forward would cause
the bird to fall as the impetus gradually becomes consumed; but it is
not able to fall because as the impetus fails so in proportion does the
pressure exerted by the elbow resist the descent and again raise the
bird up. 

The elbows of the creature are not lowered quite at the commence- 
ment, because in the chief flight of the impetus the bird will bound
upwards, but they are lowered by as much as may be necessary to
check the descent, according to the desire and discretion of the bird. 

When the bird wishes to soar upwards suddenly it immediately
lowers its elbows, after it has produced the impetus. 

But if it wishes to descend it keeps its elbows rigid and raised up
after the creation of the impetus. Sul Volo 15 [14] v. 

Remember that your bird should have no other model than the bat, 
because its membranes serve as an armour or rather as a means of
binding together the pieces of its armour, that is the framework of
the wings. 

And if you take as your pattern the wings of feathered birds, these
are more powerful in structure of bone and sinew because they are
penetrable, that is to say the feathers are separated from one another
and the air passes through them. But the bat is aided by its mem- 
brane, which binds the whole together and is not penetrated by the
air. 

OF THE METHOD OF BALANCING ONESELF 

It will always be the heaviest part of bodies which constitutes itself
the guide of their movement. 

The bird which has to raise itself without beating its wings sets
itself so that it slants against the wind, presenting its wings to it with
the elbows in front, with its centre of gravity more towards the wind
than the centre of the wings. Whence it comes about that if the power
which impels the bird when slanting to descend is represented by two 

HUMAN PROPORTIONS
Accademia, Venice 

FLIGHT 417 

and the force with which the wind strikes it by three the movement
obeys the three and not the two. Sul Volo 16 [15] r. 

[With drawing of pulley with bird suspended with wings outstretched] 

This is made in order to find the bird's centre of gravity, and with- 
out this instrument this machine would have little value. 

When the bird drops down its centre of gravity is outside the centre
of its resistance. 

And if the bird wishes to raise itself its centre of gravity remains
behind the centre of its resistance. 

The bird can stay poised in the air without keeping its wings in a
position of equality because owing to its not having the centre of
gravity in the middle of its axis as balances have, it is not necessarily
obliged to keep its wings at an equal height like the said balances. 
But if these wings are outside this position of equality the bird will
descend by the line of the slant of the wings. And if the slant is com- 
plex, that is double, as if we say that the slant of the wings points to
the south, and the slant of the head and tail points to the east, then
the bird will descend slanting towards the south-east. And if the slant
of the bird is double the slant of its wings the bird will descend by a
line midway between the south-east and the east, and the slant of its
movement will be between the two positions that have been men- 
tioned. Sul Volo 16 [15] v. 

AN ARGUMENT TO DISPOSE OF THE OBJECTIONS
TO THE ATTEMPT 

You will perhaps say that the sinews and muscles of a bird are
incomparably more powerful than those of man, because all the girth
of so many muscles and of the fleshy parts of the breast goes to aid and
increase the movement of the wings, while the bone in the breast is all
in one piece and consequently affords the bird very great power, the
wings also being all covered with a network of thick sinews and other
very strong ligaments of gristle, and the skin being very thick with
various muscles. 

But the reply to this is that such great strength gives it a reserve of
power beyond what it ordinarily uses to support itself on its wings, 

418 FLIGHT 

since it is necessary for it whenever it may so desire either to double
or treble its rate of speed in order to escape from its pursuer or to fol- 
low its prey. Consequently in such a case it becomes necessary for it
to put forth double or treble the amount of efTort, and in addition to
this to carry through the air in its talons a weight corresponding to
its own weight. So one sees a falcon carrying a duck and an eagle
carrying a hare; which circumstance shows clearly enough where the
excess of strength is spent; for they need but little force in order to
sustain themselves, and to balance themselves on their wings, and flap
them in the pathway of the wind and so direct the course of their
journeyings; and a slight movement of the wings is sufficient for
this, and the movement will be slower in proportion as the bird is
greater in size. 

Man is also possessed of a greater amount of strength in his legs
than is required by his weight. And in order to show the truth of this, 
place a man to stand upon the sea-shore, and observe how far the
marks of his feet sink in; and then set another man on his back, and
you will see how much deeper the marks of his feet will be. Then
take away the man from his back, and set him to jump straight up
as high as he can; you will then find that the marks of his feet make
a deeper impression where he has jumped than where he has had the
other man on his back. This affords us a double proof that man is
possessed of more than twice the amount of strength that is required
to enable him to support himself. [With drawing] Leather bags with
which a man falling from a height of six braccia will not do himself
any harm, whether he falls into water or on land; and these leather
bags tied after the fashion of the beads of a rosary are wrapped round
by others. Sul Volo 17 [16] r. 

If you should fall with the double chain of leather bags which you
have tied underneath you so manage that these are what first strike
the ground. 

[With drawing of part of mechanism of flying machine] 

Since the wings have to row downwards and backwards, in order to
keep the machine up and so that it may progress forward, it moves by
the lever c d with a slanting track, guided by the strap a b. 

I might so make it that the foot which presses the stirrup g was that 

FLIGHT 419 

which in addition to its ordinary i unction pulled down the lever /. 
But this would not serve our purpose, because it is necessary that the
lever / should first rise or descend before the stirrup g moves from its
place, in order that the wing — as it throws itself forward and raises
itself up at the time at which the already acquired impetus of itself
drives the bird forward without it beating its wings — can present it- 
self edgewise to the air, because if it did not do this the surface of the
wings would clash upon the air, would hinder its movement, and
would not allow the impetus to carry the bird forward. 

Sul Volo 17 [16] v. 

If the bird drops to the east with its right wing extended above the
south wind then undoubtedly it will be turned over unless it suddenly
turns its bill to the north; and then the wind will strike the palms of
its hands beyond the centre of its gravity and will raise up again the
part of the bird which is in front. 

When the bird has great breadth of wings and a small tail and wishes
to raise itself up it will raise its wings vigorously and will in turning
receive the wind under its wings; this wind forming itself into a wedge
will drive it up to a height with swiftness as is the case with the
cortone, a bird of prey which I saw going to Fiesole above the place o£ 
the Barbiga in 5 (the year 1505) on the fourteenth day of March. 

Movements of the tail: how sometimes it is flat and the bird as it
moves has it in a level position; sometimes it has the extremities
equally low and it is then that the bird rises; sometimes it has the ex- 
tremities equally high and this occurs when it descends. But when
the tail is low and the left side is lower than the right the bird will
then rise with a circling movement towards the right side; this may- 
be proved but not here. And if when the tail is low the right extremity
is lower than the left the bird will turn towards the left side. And if
when the tail is high the left side of its extremities is higher than the
right the bird will then turn with its head towards the right side; but
if when the tail is high the right side of its extremities is higher than
the left then the bird will circle towards the left side. 

Sul Volo (f.m.) 18 [17] v. 
[With drawings of birds' wings] 

Always in raising the hand the elbow is lowered and presses the air, 

4 2o FLIGHT 

and as this hand is lowered the elbow rises and remains edgewise, in
order not to check the movement by means of the air which would
strike into it. 

The lowering of the tail at the time that the bird sends its wings
forward again edgewise a little above the wind, guided by the impetus
already acquired, is the reason why the wind strikes under this elbow
and forms itself into a wedge, upon which the bird proceeds to rise
with the aforesaid impetus without beating its wings. 

And if the bird be three pounds and the breast a third the width of
the wings the wings will only bear two thirds of the bird's weight. 

The hand feels great fatigue towards the thumb or rather the helm
of the wing because this is the part that strikes the air. 

The palm of the hand goes from a to b always between almost equal
angles, dropping and pressing the air, and at b it turns immediately
edgewise and goes backwards, rising by the line c d, and having arrived
at d it turns suddenly opposite and goes dropping by the line a b, and
as it turns it always turns round the centre of its breadth. 

The turning of the hand backwards edgewise will be done with great
rapidity, and the pressing of it backwards open will be done with such
rapidity as the final urge of the motive power requires. 

The course of the point of the fingers is not the same in going as in
coming back but it follows a higher line in returning; and beneath this
is the figure made by the higher and lower line, and it is oval with a
long and regular curve. Sul Volo 18 r. 

The great bird will take its first flight upon the back of the great
swan, filling the whole world with amazement and filling all records
with its fame; and it will bring eternal glory to the nest where it
was born. Sul Volo, cover, 2 r. 

1505 on the evening of Tuesday the fourteenth day of April Lorenzo
came to live with me : he said that he was seventeen years of age. 

And on the fifteenth day of this April I had twenty-five gold florins
from the treasurer of Santa Maria Nuova. 

From the mountain which takes its name from the great bird, the 

FLIGHT 421 

famous bird will take its flight, which will fill the world with its great
renown. 1 Sul Volo 18 v. 

If the bird wishes to make headway against the wind it beats its
wings and moves them as oars backwards. c.a. 37 r. h 

Unless the bird beats its wings downwards with more rapidity than
there would be in its natural descent with its wings extended in the
same position, its movement will be downwards. But if the movement
of the wings is swifter than the aforesaid natural descent then this
movement will be upwards, with so much greater velocity in propor- 
tion as the downward stroke of the wings is more rapid. 

The bird descends on that side on which the extremity of the wing is
nearer to the centre of its gravity. 

You will make an anatomy of the wings of a bird together with the
muscles of the breast which are the movers of these wings. 

And you will do the same for a man, in order to show the possibility
that there is in man who desires to sustain himself amid the air by the
beating of wings. c.a. 45 r. a 

[ With figures] 

The bird which descends above or below the wind keeps its wings
closed in order not to be held up or checked by the air; it keeps them
well above its body, so that it may not be turned upside down by the
impetus. 

When the bird keeps the shoulders of its wings closed and their
points wide it makes the air thicker than the other air where it does
not pass; and it does this in order to check its movement and not devi- 
ate from the line of this movement. 

x This passage should be regarded as a key to the one before it. In the phrase 'sopra
del dosso del suo magnio cecero', 'upon the back of the great swan', Leonardo was ap- 
parently referring to Monte Ceccri, the mountain above Fiesole immediately to the
south. It was from the summit or from a ridge of this mountain that he intended to
make a trial of his flying machine. The locality is also referred to in another page of
the same manuscript where he speaks of 'the cortone a bird of prey which I saw going
to Fiesole above the place of the Barbiga in the year 1505 on the fourteenth day of March' 
(Sul Volo, Fogli Mancanti 18 [17] v.). This points to the probability that 1505 was
the year in which the trial took place. It may have been this trial of which Cardan
chronicled the ill success. 

422 FLIGHT 

But when the bird opens the shoulders more than the points of its
wings it wishes to delay the movement more forcibly. 

When the points and the shoulders of the wings are equally near to
each other the bird wishes to descend without being checked by the air. 

When the bird uses its wings as oars, or beats the wings backwards
in their descent, it is a clear sign that it increases the speed of its
descent. 

Here by means of the attitudes of the birds one sees the results of the
effects and both of these joined together show the intention of the bird. 

The wing extended on one side and drawn up on the other show the
bird dropping with a circular movement round the wing that is drawn
up. 

Wings drawn up equally show that the bird wishes to descend in a
straight line. 

The bird above the wind at the end of the reflex movement will
never keep its wings open equally, because it would be turned upside
down by the wind. But it draws that wing in to itself round which it
desires to make the revolving movement, and descends behind it and
moves in a circle behind it, when it wishes to rise or descend. 

The opponent says that he has seen the proofs of how the bird
standing with its wings entirely open cannot descend perpendicularly
to its own hurt or the damage of any part, and that he admits the
proofs that it cannot fall backwards edgewise because he cannot deny
the proofs assigned, and also it cannot fall with its head below it; but
that he doubts whether if it should find itself with the line of the
breadth of the wings perpendicular to the ground it would not descend
edgewise along this line. Here the reply is that in this case the heaviest
part of the bodies would not be a guide of the movement, and such
movement would be contrary to the fourth of this, which was proved
to be impossible. c.a. 66 r. a 

The rudders of the wings of birds are the parts which immediately
place the bird above or below the coming of the wind, and with their
tiny movement cleave the air in whatever line along the opening of
which the bird can then penetrate with ease. 

The bird will never descend backwards because its centre of gravity
is nearer to the head than towards the tail. 

FLIGHT 423 

The descent of the bird in all or part of its movement will always be
along that line in which its centre of gravity is nearest to the extremi- 
ties of the width of the bird. 

I have said the descent will be entirely towards that part which is
nearest to the centre of gravity when one part only is near to this centre
of gravity, and the extremities of the other opposite parts remain equi- 
distant from this centre; as when the bird presses its head close in to its
body and the wings remain equally distant from the centre tail straight
and wide, the bird will then descend with its head in front, and the
body in its central line will direct itself by. this movement. 

But when in such movement one of the wings narrows itself towards
the said centre the line of the bird's descent will be between the
gathered-in wing and the head of the bird. 

And if during the movement of the wings, when opened equally, the
tail should bend towards one of the wings, the movement will then
continue between the head of the bird and the opposite wing. 

And if the head only is bent down towards one of the .wings open
equally, the slanting descent will then proceed between the head and
the wing which the head is near. 

Swimming upon water teaches men how birds do upon the air. 

c.a. 66 r. b 

HOW THE BIRD STOPS ON THE WING ABOVE THE WIND
AND DOES NOT MOVE FROM ITS POSITION 

If the wind which drives the bird forward is of the same power as
the bird, that stays above the wind and desires to drop towards this
wind, the bird will then be motionless; and the movement which it was
on the point of making will be made by the wind from the opposite
side. 

And if the wind is more powerful and the bird moves its wings
backwards as oars, the bird will be motionless. 

And if the wind comes from above and in front, and the bird resists
it below and behind, then according to the conditions of the places
whence it may fall the bird remains motionless. 

But when the wind comes in front and below it will be more power- 
ful than the weight of the bird; it will then be necessary for the wings 

424 FLIGHT 

to contract and occupy less of the atmosphere, and consequently they
will be smitten by a lesser quantity of wind, and for the strokes which
it takes to have rather a backward direction, and then the bird will
remain motionless. c.a. 71 r. b 

The simple power of the man will never work the wing of the crow
with such swiftness as the crow did when it was attacked. 

And the proof of this will be shown in the uproar they make, for
that of the man will never produce so great a noise as the wing of the
bird made when it was attacked. 

WHY THE BIRD SUSTAINS ITSELF UPON THE AIR 

The air which is struck with most swiftness by the movable thing is
compressed to the greatest degree in itself. 

This is proved by the fact that the less thick flexible body will never
support the thicker upon itself, as for example one sees the anvil float- 
ing upon melted bronze, and gold and silver when liquefied staying
beneath a fusion of lead; and for this reason, as the atmosphere is a
body capable of being itself compressed when it is struck by something
which is moving at a greater rate of speed than that of its flight, it is
compressed into itself and becomes like a cloud within the rest of the
air, that is it is of the same density. 

But when the bird finds itself within the wind, it can sustain itself
above it without beating its wings, because the function which the wing
performs against the air when the air is motionless is the same as that
of the air moved against the wings when these are without motion. 

c.a. 77 r. b 

WHY THE BIRD FALLS IN A PARTICULAR LINE 

On whatever side the weight of the bird is as it drops from a position
of equality, on that side its descent will be. 

And at whatever angle the bird sets itself, in the same angle its
descent will be. 

And if a part is bent forward and the wings spread out at an equal
slant, the movement of the bird will be in the centre of the two inclined
parts. 

FLIGHT 425 

And this movement will slope more towards the part which bends
more. 
[Drawing] 

That circle will be of less size in which the bird sets itself on a less
slanting line. 

The slant of the wings always tends to be equal to the slant of the
body of the bird. 
[ Drawing a b\ 

If the wings are held slanting and the bust in a position of equality, 
without doubt the bird will descend along the line of the slant of the
wings; but this slant will be varied to the right or left as is in the
movement a b. c.a. 77 v. b 

HOW MANY ARE THE WAYS IN WHICH A BIRD TURNS ITS
STRAIGHT MOVEMENT INTO A CURVING MOVEMENT? 

The bird that wishes to turn its straight course into a curved one
without raising or lowering its height, moves the wing on the convex
side of its curving movement more frequently than it does that on the
concave side of this movement. 

The wing of the bird as it beats its wings has the shoulder raised
more in front than behind; and this it does in order to acquire move- 
ment, because if the wings were to move equally up and down the
bird would not move from its first position. 

The bird bends its straight course towards that side on which the
wing is most lowered. And it is as though this wing were more smit- 
ten by the wind than the other. 

OF THE BIRD AS IT FLIES WITH BOUNDS (BALZI) 

The bird which flies with a bound acquires impetus in its descent, 
because in the course of this by closing its wings it acquires weight, 
and consequently velocity; it follows therefore that the reflex move- 
ment is more powerful, and adding to this the fact of it beating its
wings, it creates double the power which is produced by the simple
reflex movement, and by the fact of this duplication the reflex move- 
ment becomes longer than it would have been without the addition 

426 FLIGHT 

made by the beating of its wings. And this is the real cause why the
reflex movement is equal to its falling movement and why at the end of
the flight there is equality in the extent of its descent and of its ascent. 

When the bird descends with a great slant without beating its wings
all the extremities of the wings and tail bend upwards, and this move- 
ment is slow, for the bird is not only supported by the air beneath it
but by the lateral air towards which the convex surface of the bent
feathers spreads itself at equal angles. 

When the bird rises from the ground to a height and leaps and closes
its open wings with impetus, and makes a wave of the air which is
compressed and strikes upwards at its breast from below, the impetus
of this tending to continue, the movement drives the bird to a height, 
and it flaps its wings many times quite regularly in the course of this
movement until it has risen up sufficiently. 

The bird which rises with a circular movement stays in a slanting
position with the breadth of its wings, and the circle in which it
revolves will be so much greater in proportion as its position is more
slanting; and this circle will be so much smaller as its position is less
slanting. 

The bird which makes a greater movement with one wing than the
other will describe a circular movement, and the movement will also
be circular when the wing is beaten on one side and held motionless on
the other; and the circle will be so much greater or less according as
this wing is moved more slowly or more rapidly. 

Movement of the bird driven by the wind: 

The bird which is driven by the wind, when it raises itself without
beating its wings lengthens the turning process more in the falling
movement than in the reflex movement; but in the reflex movement it
rises and in the falling movement it lowers itself. 

The bird in descending against the wind lowers its feet as the wind
strikes them, and this it does in order not to disarrange the tail from
the direction of the whole body when it wishes to lower itself. 

c.a. 97 v. a 

The bird which makes the shortest revolving movement prepares the
extreme extension of its wings with less slant, and for this reason the 

FLIGHT 427 

circle of its revolving movement is so much more curved as the revolv- 
ing movement is shorter. 

The bird can never move backward, because the points of the wings
when extended are never farther in front than the centre of gravity
which the length of the bird has of itself, and this must of necessity be
the case; whereas if it should move backwards its feathers would turn
right over in front and restrain the movement with their resistance; 
and this the bird shows us, for when it is resting it always turns its
beak to the wind. 

If the left horn of the tail is as far above the centre line of movement, 
and above the centre line of the weight which the bird has in the line
of its movement, as the right horn of this tail is below the said centres, 
the movement of the bird will of necessity be straight, because the left
horn of the tail is as powerful to bend the straight movement of the
bird to the right when it is above the bird as the right horn of this tail
is to bend the bird to the left when it is below the bird. 

The bird will always descend in the direction in which it weighs
most. 

The bird weighs most in the direction in which its breadth is least. 
[Diagram] Therefore it will descend by the line a b and not by the
line b a. 

I have seen the sparrow and the lark fly upward in a straight line
when they were in a level position. And this happens because the wing
raised with swift movement remains filled with holes, and only rises
with the impetus it has acquired, and this is renewed in the lowering
of the wings, for the wing then reunites and presses one feather in
beneath another, as is said in the eighth of this. 

The bird which descends with the wind that strikes it below increases
this descent by raising its tail, exposing the under part of it to the
percussion of the wind. 

The bird whenever it rests upon any spot always takes up its position
with its beak against the approach of the wind. 

It is always the under side of the branches of any plant that show
themselves to the wind which strikes it, and one leans against another. 

c.a. 160 r. b 

Unless the movement of the wing which presses the air is swifter 

428 FLIGHT 

than the flight of the air when pressed, the air will not become con- 
densed beneath the wing, and in consequence the bird will not support
itself above the air. 

That part of the air which is nearest to the wing will most resemble
in its movement the movement of the wing which presses on it; and
that part will be more stable which is farther removed from the said
wing. 

That part of the air which is nearest to the wing which presses on it, 
will have the greatest density. 

The air has greater density when it is nearer to water, and [greater
rarity] when it is nearer to the cold region, and midway between these
it is purer. 

The air of the cold region offers no resistance to the movement of
the birds unless they have already passed through a considerable space
of the air beneath them. 

The extremities of the wings of birds are of necessity flexible. 

The properties of the air are such that it may become condensed or
rarefied. c.a. 161 r. a 

No impetus created by any movement whatever can be immediately
consumed, but if it finds an object which has a great resistance it con- 
sumes itself in a reflex movement. 

The impetus acquired by the beating of the wings in the slanting
descent of birds is the reason for these birds descending for a long
space without beating their wings and for the said slant. 

Define what impetus is and what slanting movement consists in, and
which has the greater or less slant, and how the reflex movement of
birds becomes more or less slanting according to the greater or less
opening of the tail and wings. 

The impetus acquired will be more permanent when the movement
of the descent slants less. 

Impetus is a power of the mover applied in a movable thing which
causes the movable thing to move after it is separated from its mover. 

[There will never be impetus unless the resistance of the movable
thing is completely subdued by its mover.] And especially when the
dense friction of the bodies moved resists the movable thing. 

This may be seen in the case of a beam drawn by oxen which only 

FLIGHT 429 

moves so long as the oxen are in movement, and when the cause has
ceased the effect tails, that is that the movement of the beam ends
together with the movement of the oxen. 

When the friction of the movable thing over the place where it is
moved is of slight density, the power of the mover will be united for so
great a space with the movable thing, since this is separated from the
mover in proportion as the friction is of less density. So one sees a barge
drawn through the water for a certain distance of its own accord after
it has been separated from the power of its mover; and the bird, after
it has beaten its wings, moves upon the compressed air without any
further beating of its wings, carried for a long distance by its impetus. 

Movable things and movers are of three kinds, of which one moves
through as much space as the movement made by its mover, and this is
only slightly dominated by the power of the mover; another moves
through a much less space than that traversed by the mover, and this in
itself is of greater resistance than the power of its mover, not taking
into account the space that intervenes between the mover and the
movable thing; the third moves in the same time through a consider- 
ably greater space than that over which its mover is moved; and this
movable thing in itself not taking into account the intervening space
has much less power of resistance than its mover. 

There are other powers of mover and movable things, in which the
movable thing follows or is followed by its movement over such space
and direction as has that of its mover, and after the mover remains
without movement the movable thing exerts the power of the mover, 
and by means of this it moves through a long tract of space, as the
arrow does when shot from the cord of the bow, which moves for a
long time by itself, after the cord of the bow has separated itself from it. 

c.a. 161 v. a 

The bird may stay in the air without change of position, even if the
power of the wind is greater than the power of the weight of this bird; 
and it does this with a slight swift movement of the wings using them
as oars behind the flight of the wind with greater speed than that of
this wind, and so it is in a position of equilibrium. 

The bird may stay in the air without change of wings or of position, 
even if the power of the movement of the air is more powerful than 

430 FLIGHT 

the weight of the bird. And this contrast is due to its slant and it is in
a slanting line. 

When there is the same span of wing the bird which is in a more
sloping line will be the heavier in the air. c.a. 180 r. a 

The bird which beats its wings with equal movement without beat- 
ing its tail will have a straight movement; but if one of the wings drop
more than the other the straight movement will be changed to a curve
and it will circle downwards round a spot below to which the lower
wing is pointing. c.a. 184 v. c 

[With diagrams] 

Sudden changes of the wings and tail of birds make sudden changes
in the lines of their movements. For suppose the bird is moving in an
eastward direction and suddenly turns towards the west; this sudden
turn is effected by extending one of its wings on the side on which it
wishes to turn, and turning it so that it faces the percussion of the air
in the line in which it is moving, drawing the opposite wing to itself
and bending the tail in such a way that that extended wing, that is as in
the bird a d /, is flying towards you, and as it flies it immediately turns
itself backward by its right side in /, and then extends this wing d f
more than usual, displaying it more in front to the wind; and the oppo- 
site wing a c will be bent as in c b, and the tail c d will turn as in e d; 
then the fury of the impetus is struck by the air, and works more in
that part of the bird which is more remote from its centre of gravity, 
and less in that nearer to it. 

When the bird rises in a circle without beating its wings it keeps its
centre of gravity much lower than the tips of its wings, and receives the
wind underneath it from whatever side it may come, after the manner
of a wedge, that is either under its tail or its breast or each of its wings. 

If the water a b strikes the tail of the fish which is in the axis above
the centre of its accidental gravity there is no doubt that this fish will
bend round this centre; but its tail will bend more in the current of the
water than its trunk will, for this being firmer offers more resistance in
its contrary movement. 

The impetus which was circular in its commencement may follow
out in itself the same circular movement upon its axis as that of the
millstone or the revolving wheel, and may follow it circular or straight. 

FLIGHT 431 

as the wheel of the cart revolving naturally outside of its axis or as the
reflex movement made in a slanting line by the spherical bodies. Simi- 
larly the flight of birds, even though the beginning of the bird's impulse
may be caused by direct movement, may continue in circular move- 
ment for as great a distance as this impetus endures. 

The level movement of birds when they fly may swiftly be changed
either to a slanting or vertical movement towards the sky or towards
the earth. The movement towards the sky occurs when the helms of
the wings and also the tail are turned towards the earth. 

When a bird is descending it keeps a straighter course and has less
risk of being overturned if it has its wings bent beneath it than if it
keeps them straight. 

When a bird's centre of gravity is below its wings it has so much the
less risk of being turned upside down, as is seen above. 

Make a small one to go over the water, and try it in the wind without
much depth of water over some part of the Arno, with the wind
natural, and then as you please, and turn the sail and the helm. 

See to-morrow to all these matters and the copies, and then efface the
originals and leave them at Florence, so that if you lose those that you
take with you the invention will not be lost . . . 

There is as much power of movement in the water or the air against
an object as there is in this object against the air or the water. 

The centre of gravity of the fish lying level in the water or of the
bird lying level in the air is situated midway between the extremities
which offer equal resistance. 

Write of swimming under water and you will have the flight of the
bird through the air. There is a suitable place there where the mills
discharge into the Arno, by the falls of Ponte Rubaconte. 

There are two different ways in which a bird can turn in any direc- 
tion while continually beating its wings. The first of these is when at
the same time it moves one wing more rapidly downwards than the
other with an equal degree of force, the movement approximating
towards the tail; the second is when in the same space of time the
movement of one wing is longer than that of the other. Also in striking
with the wings downwards slantwise, if they become bent or moved
one lower down and the other farther back, the part which drives the
wing lower down will be higher in the first case, and the opposite part 

432 FLIGHT 

of the wings which has the longer movement backward will go farther
forward through this first; consequently for this reason the movement
of the bird will form a curve round that part of it which is highest. 

These then are all the movements made by the bird without beating
its wings, and they are each and all subject to a single rule, for all
these movements rise upon the wind, for they expose themselves to it
slantwise receiving it under their wings after the manner of a wedge. 

c.a. 214 r. d
[Figure] 

The centre of gravity of this bird forms the axis of its equilibrium. 

When this bird raises itself in circles by a single wind without beat- 
ing its wings it keeps the impetus of the wind under its wings so that
they raise it as though it was a wedge. 

When the wind enters under the left wing it passes above the right
wing, and this wind would throw the bird over, if it were not that the
tail is suddenly twisted so that the wind passes over it and makes a
wedge opposite to it, and so drives it in and turns it. 

When it has turned so much that the wind strikes it in the beak the
tail will only work in a straight line; but it bends upwards so that the
wind strikes it above and at the same time the breast and wings are
struck from below, but since the force of impact on the left wing is
greater because it is more bent the bird has to wheel round and turn
its right wing to face the wind. 

When the tip of the right wing enters into the line of the wind, 
nothing is so useful in order to make the wind strike at more equal
angles as is the bending of the head and also the neck against the
approach of this wind. 

When the tail enters into the line of the wind then this tail is struck
beneath by the movement of the wind, and the head is struck above, 
and each of the wings are struck beneath. But the right wing in twist- 
ing is more exposed to and afifected by the stroke of the wind than is
the left, and therefore it travels more with the right than with the left, 
and therefore its movement becomes a curve and continually rises being
pushed up from below by the wind. 

The movement of the wing against the air is as great as that of the
air against the wing. 

The wing which is most extended strikes against a greater quantity 

FLIGHT 433 

of air, and as a consequence descends less than the wing which is more
folded up; therefore the descent of this flying thing will be made along
the line of that wing which is more folded up. 

That wing is more delayed which is struck by the air at more equal
angles or by a greater quantity of air. 

Therefore when the bird descends in a slanting direction and per- 
ceives itself to be dropping with its left wing it will extend this wing
more than the other, that is it will bend it more in face of the air
where it strikes. c.a. 214 v. a 

[Drawing] 

A bird raises itself more swiftly when the circles in which it rises
are smaller. 

What is here set forth occurs because the bird as it rises without beat- 
ing its wings by the help of the wind receives the wind underneath
it in the manner of a wedge, and this wedge has its greater angle upon
the side that slopes less, and therefore it raises the object above it more
and more. 

The bird never moves upward unless the wind enters underneath it
and forms itself into a wedge, driving it for a certain distance along the
line of its course. 
[Diagram] 

See to-morrow morning whether the bird as it turns coming against
the wind n remains in the line a b keeping its head at b or whether
it remains in the line c d. 

Here there rises a doubt, namely, whether the wedge does not raise
the object which is situated above itself in a perpendicular line, if this
object is not supported in such a way that it has no power to fly before
the blow together with the wedge, as the bird will be able to rise above
the wind which serves it as a wedge, so that this wind will not carry it
with it; it will be so much the more difficult therefore for this bird to
rise to a height against the wind if it has not already mounted after the
manner in which water falls in an empty screw. c.a. 220 r. a 

434 FLIGHT 

HOW A BIRD LOWERS ITSELF WITHOUT THE USE OF THE
WIND OR BEATING ITS WINGS 

[Diagram] 

When the centre of gravity of the bird is in front of the centre of
resistance of the wings the bird will then descend by a slanting line
always observing this slant. 

The bird's descent will be found to be of swifter movement when
the slant is less. 

That bird travels with the longer course when its descent is inter- 
rupted by many reflex movements, that is in waves, as is shown above; 
let us say that the movement of the bird is so arranged as to go from
a to b, and when it has travelled half a mile it makes in c d as great
reflex movement as gives the nature of the impetus of such descent, 
and then brings back its wings to their first slanting position and de- 
scends afterwards in another movement of half a mile, and then rises
up again and reascends until it finishes its course at the place indicated^ 
[Diagram] 

If the bird which does not beat its wings should not wish to descend
rapidly to a depth, then after a certain amount of slanting descent it
will set itself to rise by a reflex movement and to revolve in a circle, 
mounting after the manner of the cranes when they break up the
ordinary lines of their flight and come back into a troop and proceed
to raise themselves by many turns after the manner of a screw, and
then, having gone back to their first line they follow their first move- 
ment again which drops with a gentle descent, and then return again
to a troop and moving again in a circle raise themselves. 
[Diagram] 

The bird which takes longer strokes with one wing than with the
other will progress with a circular movement. c.a. 220 v. c 

With wings expanded the pelican measures five braccia, and it
weighs twenty-five pounds; its measurement thus expanded therefore
is the square root of the measurement of the weight. 

The man is four hundred [pounds] and the square root of this figure
is twenty; twenty braccia therefore is the necessary expanse of the said
wings. 

FLIGHT 435 

The width of the wings of the pelican is three quarters of a braccio, 
so you will divide the five braccia which it measures when open into
quarters, so that there are twenty quarters in its length and three
quarters in its width, and you may say that the width is three twen- 
tieths of the length. 

If therefore the span of the man's wings be twenty braccia you would
say that they are also three braccia in width, and three twentieths of
this length of twenty braccia, that is, where the width is greatest. 

c.a. 302 r. b 

The imperceptible fluttering of the wings without any actual strokes
keeps the bird poised and motionless amid the moving air. 

The reverse movement against the direction of the wind will always
be greater than the advancing movement; and the reverse movement
when made with the course of the wind will be increased by the wind, 
and will become equal to the advancing movement. 

The ways in which birds rise, without beating their wings but by
circles, with the help of the wind, are of two kinds, simple and com- 
plex. The simple comprise those in which, in their advancing move- 
ment, they travel above the flight of the wind, and at the end of it turn
and face the direction of the wind, receiving its buffeting from beneath, 
and so finish the reverse movement against the wind. 

The complex movement by which birds rise is also circular, and con- 
sists of an advancing and reverse movement against the direction of
the wind in a course which takes the form of a half circle, and of an
advancing and reverse movement which follows the course of the wind. 

The simple circular movement by which birds rise is also circular, 
and consists of an advancing and reverse movement against the direc- 
tion of the wind in a course which takes the form of a half circle, and
of an advancing and reverse movement which follows the course of the
wind. 

The simple circular movement of rising without beating the wings
will always occur when there is great agitation of the winds, and this
being the case it follows that the bird in so rising is also carried a con- 
siderable distance by the force of the wind. And the complex movement
will be found to occur when there are light winds, for experience shows
that in these complex movements the bird rises through the air without 

436 FLIGHT 

being carried too far by the wind in the direction in which it is travel- 
ling. 

The down and feathers underneath the wings are plentiful, and at
the ends of the wings and tail the tips of the feathers are flexible or
capable of being bent, whilst those on the front of the wing, where it
strikes the air, are firm. c.a. 308 r. b 

My opponent says that he cannot deny that the bird cannot fall
either backwards or with head underneath in a perpendicular line; but
that it seems to him that its descent may be sheer if it keeps the wings
wide open and has one of the wings as well as the head below its centre
of gravity. 1 To this argument the answer is the same as to what pre- 
ceded it; that is, that if this bird being in such a position without hav- 
ing other means of aiding itself were to drop perpendicularly, it would
be contrary to the fourth part of the second book of the Elements, 
where it was proved that every body which falls freely through the
air will fall in such a way that the heaviest part of it will become the
guide of its movement; and here the heaviest part is found to be mid- 
way between the extremities of the open wings, that is midway between
the two lightest parts, and therefore, as has been proved, such a descent
is impossible. 

We have therefore proved that when a bird has its wings spread out
and its head somewhat raised, it is impossible for it ever to fall or
descend in a perpendicular line; on the contrary, it will always descend
by a slanting line, and every tiny movement of wings or tail changes
the direction and slanting descent of this line to the reflex movement. 

Nature has so provided that all the large birds can stay at so great an
elevation that the wind which increases their flight may be of straight
course and powerful. For if their flight were low, among mountains
where the wind goes wandering and is perpetually full of eddies and
whirlwinds, and where they cannot find any spot of shelter by reason
of the fury of the icy blasts among the narrow defiles of the mountains, 
nor can so guide themselves with their great wings as to avoid being
dashed upon the cliffs and high rocks and trees, would not this some- 
times prove to be the cause of their destruction? Whereas at great alti- 

1 The MS. has here an explanation of a diagram: 'that is, it will drop in the line a b, 
the wings d c being wide apart at their natural extension'. 

FLIGHT 437 

tildes whenever through some accident the course oi the wind is
changed in any way whatsoever the bird has always time to redirect its
course, and in safety take a calm flight, which will always be entirely
free; and it can always pass above clouds and thereby avoid wetting its
wings. 

Inasmuch as all beginnings of things are often the cause of great
results, so we may see a small almost imperceptible movement of the
rudder to have power to turn a ship of marvellous size and loaded with
a very heavy cargo, and that, too, amid such a weight of water as
presses on its every beam, and in the teeth of the impetuous winds
which are enveloping its mighty sails. Therefore we may be certain in
the case of those birds which can support themselves above the course
of the winds without beating their wings, that a slight movement of
wing or tail, which will serve them to enter either below or above the
wind, will suffice to prevent the fall of the said birds. c.a. 308 v. b 

The thrushes and other small birds are able to make headway against
the course of the wind, because they fly in spurts; that is they take a
long course below the wind, by dropping in a slanting direction
towards the ground, with their wings half closed, and they then open
the wings and catch the wind in them with their reverse movement, 
and so rise to a height; and then they drop again in the same way. 

c.a. 313 r. b 

When the slanting movement of the bird as it drops against the
wind makes the weight of the bird more powerful than the wind that
strikes it in front, the movement of this bird will become swift against
this wind. 

The bird which descends under the straight approach of the wind
turns the wing somewhat over from the shoulder to the tip; and it does
this in order to have as much leverage as possible in the more slanting
movement against the wind. c.a. 353 r. c 

The swallow has its wings quite different from those of the kite, for
it is very narrow in the shoulder and long in the span of the wing. Its
stroke when it flies is made up of two distinct actions, that is the span
of the wing is spread out like an oar in the direction of the tail, the
.shoulder towards the earth; and in this way while the one movement 

438 FLIGHT 

impels it forward the other keeps it at its height, and the two combined
carry it a stage onward wherever it pleases. c.a. 369 r. a 

The movement of the air against a fixed thing is as great as the move- 
ment of the movable thing against the air which is immovable. 

And it is the same with water which a similar circumstance has
shown me to act in the same way as does the air, as with the sails of
ships when accompanied by the lateral resistance of their helm. 

c.a. 395 r. b 

[Of the flight of the bat and of the eagle] 

I say that if the bat weighs two ounces and measures half a braccio
vvith wings expanded the eagle ought according to this proportion to
measure with wings expanded not less than sixty braccia, and we see
by experience that its breadth is not more than three braccia. And it
would seem to many who neither see nor have seen similar creatures
that one of the two would not be able to fly, considering that if there
exists the proper proportion between the bat's weight and the breadth
of its wings then in the case of the eagle they are not large enough, and
if the eagle is properly equipped the other has them too large and they
will be inconvenient and unsuitable for its use. We see however both
the one and the other borne with the utmost dexterity by their wings, 
and especially the bat which by its swift turns and feints overcomes the
rapid twists and retreats of the flies and gnats and other similar
creatures. 

The reason why the eagle supports itself with its small wings as the
bat does with its large ones is contained in the comparison. . . . 

When a single rush has the same proportion between its size and its
length as a bundle of similar rushes has, it will in itself have the same
strength and power of resistance as the said bundle. Therefore if the
bundle has nine heads and supports nine ounces a single one of these
similar rushes of which there are nine heads will by chance support one
ounce. 

Place on the top of a rush a danaro 1 as a weight and you will see it
bend down as far as the ground. Take a thousand of these rushes and
tie them together stretched out, fix them at the foot and make the heads
level and load them; you will perceive that whereas by the first reason 

1 A small coin, about 20 grains Troy in weight 

FLIGHT 439 

it ought to support about three and a half pounds it will in fact support
more than forty. 

So for this reason it follows that the expanse of air that supports the
bat which weighs the two hundred and twentieth part of the weight of
an eagle, if it had to be trodden down and pressed by the beating of the
wings of the eagle would need to be sixty times larger. b 89 v. 

When a bird in beating its wings raises them higher above its centre
of gravity than it lowers them beneath it it will have its head higher
than its tail during its movement. This is proved by the fourteenth of
this: — the movable thing will bend its straight movement more towards
the side where its movement is less impeded than to that where it is
more impeded; and by the eighth which says: — it is as much to move
the air against the immovable thing as to move the thing against the
immovable air. Therefore the wing when it moves farther downward
than upward makes more percussion with the air that borders on it
below than with that which touches it above; and for this reason its
straight movement will slant upwards. 

If the bird while moving its wings an equal distance below and
above its centre of gravity moves them more rapidly downwards than
upwards it will curve its level movement upwards. This is proved by
the ninth of the foregoing which said : — Of the equal movements made
by the wings of birds those which are the most rapid will have most
power to compress the air which borders on them below; and by the
seventeenth which says: — the percussion of a movable thing is more
deflected which has struck against a spot that offers more resistance; 
therefore it is concluded that if the wing making equal movement
downward and upward moves down more rapidly than up it will
curve its level movement upwards rather than downwards. 

And by the converse of what has gone before if the wings while
making equal movement below and above the bird's centre of gravity
should rise more swiftly than they fall, the bird's movement will slant
inclining towards the ground. e 21 v. 

The inclination of the wings of birds desiring to move with equi- 
distant movement to the earth must necessarily always produce as
much more fatigue when moving downwards than upwards, as the
bird weighs more downwards than in the movement of equality. This 

440 FLIGHT 

is proved by the thirteenth of this where it is said: — the weight of
every heavy thing is in the line of its movement and so much more or
less as this movement is swifter or slower. 

Definition of impetus 

Impetus is a power created by movement and transmitted from the
mover to the movable thing; and this movable thing has as much
movement as the impetus has life. 

The wings of birds feel as much more effort downwards than up- 
wards when the bird wishes to rise upwards, in proportion as the bird
weighs more downwards than upwards. e 22 r. 

A bird supporting itself upon the air against the movement of the
winds has a power within itself that desires to descend, and there is
another similar power in the wind that strikes it which desires to raise
it up. 

And if these powers are equal one to the other so that the one can- 
not conquer the other, the bird will not be able either to raise or lower
itself, and consequently will remain steady in its position in the air. 

This is proved thus : — let mbea bird set in the air in the current of
the wind a b d c. As this wind strikes it under the slant of the wing n f
it comes to make a wedge there which would bear it upwards and
backwards by a slanting movement if it were not for the opposing
power of its weight, which desires to drop down and forward, as is
shown by its slant g h, and since powers that are equal to each other
do not subdue but offer a complete resistance the one to the other, for
this reason the bird will neither raise itself nor lower itself; therefore
it will remain steady in its position. 
[Figures] 

If the bird shown above lowers its wings it makes itself more stable
upon the air and supports itself with less difficulty, because it oc- 
cupies more space by keeping its wings in a position of equilibrium
than in either lowering or raising its wings. In keeping its wings high
however it cannot bend them either to the right or the left with the
same ease that it would if it kept them low. But it is more certain
not to be overturned in keeping its wings high than in keeping them 

FLIGHT 441 

low and bending them less to the right or the left, because as it lowers
itself on the right side, through using its tail as a rudder, there is an
increase of resistance, because the wing embraces more air than the
other wing on the side on which it descends abruptly in returning to
a position of equilibrium. Consequently it is a good expedient to
descend with a straight and simple slant, and this it would not be
able to do if it held its wings lower than its body, for if it were to bend
itself about one of its sides by using its tail as a rudder it would im- 
mediately turn upside down, the wing that is farther extended em- 
bracing more air and offering more resistance to the slanting descent
than the other. e 22 v. 

The extremities of the wings bend much more in pressing the air
than when the air is traversed without the beating of the wings. 

The simple part of the wing is bent back in the swift slanting descent
of the birds. This is proved by the third of this which says: — among
things which are flexible through the percussion of the air, that will
bend most which is longest and least supported by the opposite side. 

Therefore the longest feathers of the wings not being covered by
the other feathers that grow behind them and not touching each other
from their centre to their tip will be flexible, and by the ninth of this
which said: — of things equally flexible that will bend the most which
first opens the air. And this we shall prove by the eleventh which
says: — of equal and similar things bent by the wind that will bend the
most which is struck by air of greater density. 

The helms placed on the shoulders of wings are extremely necessary
for it is these parts which keep the bird poised and motionless in the
air facing the course of the winds. 

[ With drawing of wing] 

This helm a is placed near the spot where the feathers of the wings
bend, and through being very strong it bends but little or not at all, 
being situated in a very strong place and armed with powerful sinews
and being itself of hard bone and covered with very strong feathers, 
one of which serves as a support and protection of the other. 

e 23 r. 

442 FLIGHT 

Simple slant 

If the slanting movement of the bird be made simply according to
the direction of its length this slant will be rectilineal. 

Compound slant 

But if to the slant of the length of the bird there be added the slant
of the breadth of its open wings the movement of this bird will be
curved, and the curve will have its concave side in the direction of the
lower wing. 

Irregular movement 

And if the bird is struck by the wind on the tip of its lower wing its
compound movement with its slanting curve will become broken and
will merely form a straight slant. 

The wing of the bird is always concave in its lower part as far as
the part that extends from the elbow to the shoulder, and in the rest
it is convex. 

In the concave part of the wing the air is whirled round, and in the
convex it is pressed and condensed. e 23 v. 

WHY THE BIRD MAKES A REVOLVING MOVEMENT BY
BENDING ITS TAIL 

All the bodies that have length and move through the air, with their
lateral extremities equidistant from the central line of their bulk, will
make straight movements; the power of the impetus which impels
these bodies varying neither in the natural movement nor even in the
violent or the semi-natural movement. 

If however the lateral extremities of the bodies that have length are
at an uneven distance from the central line of their bulk the move- 
ment of the body will form a curve in the air as it moves; and such
curve will have its concave part on the side on which the extremity
of the body mentioned is more remote from the said central line. 

FLIGHT 443 

Concerning complex slants in birds' flight 

A complex slant is said to be that which birds make when they move
in the air keeping their tail higher than their head and one wing
lower than the other. 

When a bird flies in a complex slant the movement in the one slant
will be so much swifter than in the other as the one is less oblique
than the other. 

The movement made by birds that fly with a complex slant is curved. 

The curve created by the complex movement made by birds as they
fly will be greater or less as the lateral slant is less or greater, e 35 v. 

The flight of birds has but little force unless the tips of the wings
are flexible. This is proved by the fifth of the Elements which says: — 
lateral power checks the descent of heavy things; as may be seen in
the case of a man pressing with his feet and back against two sides
of a wall as one sees chimney sweepers do. Even so in great measure
the bird does by the lateral twistings of the tips of its wings against the
air where they find support, and bend. 

When the bird in its direct descent is struck by the wind under its
wings this descent will become so much more slanting as the wind is of
greater power. Proved by the ninth of this which says: — of direct
descents which similar and equal heavy bodies make in the air that
will slant most which is struck by the wind with most impetus. 

If a bird fly with its wings at equal height and lower one of the sides
of its tail its direct flight will become curved, and this curve will have
its concave side towards the lowered side of the tail, and the wing on
this side will be as much slower than the opposite wing as the move- 
ment of the bird is more curved. 

This is proved by the seventh of this which says: — that part of a
wheel as it revolves will have least movement which is nearest to the
centre of this revolution. As therefore the tip of the wing a touches a, 
the centre round which it revolves, it will have less movement, and the
opposite wing will have its extremity d with the movement g b. 

e 36 r. 

The descent of birds is of two kinds, of which one is with certainty
upon a fixed position, the other is uncertain upon two positions or 

444 FLIGHT 

more. In the first its wings are open and the points are raised above
the back, and with these at equal height it drops with straight simple
slant to its appointed place. The second bird as it descends has the
points of its wings held lower than the breast and bends its tail now
to the right now to the left, with slant now simple now complex and
sometimes irregular. 
[Figure] 

The bird that is struck on its side by the wind moves the wing that
is towards the wind with greater swifter motion than it does the other
as the wind is more impetuous in its movement. This may be proved : — 
let a b c be the bird that moves along the line a f and to the wind d, 
which strikes it at the side on the wing a b, and would carry it along
the line of its course if the wing a b was not swifter in its movement
than the wind. And this is why when the wind has struck the side of
the bird and by some eddying recoil has folded itself up against the
wing which has closed itself by flapping, this wing has thus had a
second support against the said bending of the straight movement of
the bird. It must therefore be concluded that the wide swift move- 
ment, which the wing that is struck by the wind makes in excess of
that made by the opposite wing, at the same time as the wind which
has struck the bird and been bent back against the said wing, is that
which prevents the straight course of birds from being deflected by
the wind. And moreover unless the opposite wing was slow and of
little movement it would strike into the course of the wind and the
wind [would strike] against it; and thus the wind would be most
powerful to accompany this bird in its course. e 36 v. 

WHY THE FLIGHT OF BIRDS WHEN THEY MIGRATE IS MADE
AGAINST THE APPROACH OF THE WIND 

The flight of birds when they migrate is made against the move- 
ment of the wind not indeed in order that their movement may be
made more swiftly but because it is more lasting and less fatiguing. 
And this comes about because with a slight beating of their wings
they enter the wind with a slanting movement, this movement being
below the wind. After this impetuous movement they place themselves
slantwise upon the course of the wind. 

FLIGHT 445 

This wind alter entering under the slant of the bird alter the manner
of a wedge raises it up during such time as the acquired impetus takes
to consume itself, after which it descends afresh under the wind and
again acquires speed; then repeating the above-mentioned reflex move- 
ment upon the wind until it has regained the elevation that it lost, and
so continuing in succession. 

WHY BIRDS SELDOM FLY IN THE DIRECTION OF THE
CURRENT OF THE WIND 

It very seldom happens that the flight of birds is made in the direc- 
tion of the current of the wind, and this is due to the fact that this
current envelops them and separates the feathers from the back and in
addition to this chills the bared flesh. But the greatest loss is that after
the descent slantwise its movement cannot enter upon the wind and by
the help of it be thrown back to the elevation it has left unless it has
already turned backwards, which would not help it to make progress
in its journey. 

The bird spreads out the feathers of its wings more and more as its
flight becomes slower; and this is according to the seventh of the
Elements which says: — that body will become lighter which acquires
greater breadth. e 37 r. 

A bird descending makes itself so much swifter as it contracts its
wings and tail. This is proved by the fourth of Gravity, which says : — 
that heavy body makes a more swift descent which occupies a less
quantity of air. 

That bird is more rapid in its descent which descends by a less slant- 
ing line. This is proved by the second of Gravity, which says: — that
heavy body is swiftest which descends by the shortest way. 

A bird in descending lessens its speed more and more as it is more
extended. This is proved by the fifth of Weight, which says: — that
heavy body is most checked in its descent which is most extended. 

A bird in making a reflex movement rises in proportion as it acquires
greater breadth. This is proved by the fourteenth of Local Movement, 
which says : — the heavy body that occupies a less space of air in the line
of its movement penetrates it more rapidly. Therefore the widest expan- 

446 FLIGHT 

sion of the wings produces the greatest diminution in the bulk of the
whole bird, and in consequence the impetus of its reflex movement is
less impeded; and therefore it rises farther at the end of this reflex
movement. 

When the bird descends upon the spot where it wishes to settle, it
raises its wings and spreads out the half of its length and so descends
slowly upon the aforesaid low place. e 37 v. 

There is as much to move the air against the immovable thing as to
move the thing against the immovable air. 

When the bird moves with slow descent on a long course without
beating its wings and the incline leads it more quickly to the ground
than its intention is, it then lowers its wings and moves them against
the immovable air, and this movement raises the bird up just as though
a wave of wind struck it below: and this is proved by the last but one. 

OF TWO CONTRARY SLANTS OF WHICH ONE IS DESCEND- 
ING AND THE OTHER IS A REFLEX MOVEMENT 

The movement of the bird that descends by two contrary slants will
be longer in proportion as the slant on which it rises more resembles
the slant by which it descends. 

This may be proved : — suppose that of itself the slant with which the
bird descends makes a hundred miles an hour in order to descend to
earth with a descent of a hundred braccia, and that the opposite slant
along which it makes its reflex action at this time spares it the half of
this descent, I affirm that the movement which was a hundred miles an
hour will become fifty, as is proved in its place. e 38 r. 

Birds always fly more slowly when they raise their wings than when
they lower them. This is caused by the necessary period of rest that is
required after the adjacent fatigue of the tired limbs, and moreover
speed is not necessary in raising these limbs as it is in lowering them, 
seeing that the impetus that carries the bird is generated through a
long space of movement in this bird. It is sufficient merely for it to
have raised its wings from where they first descended when the said
impetus commences to decline, which reveals itself through the falling
of the bird. But when the bird wishes to acquire speed it resumes the 

FLIGHT 447 

impetus nearer to its inception and beats its wings more frequently
and with the longest and most rapid movement possible. 

OF THE CIRCLING MOVEMENT MADE BY THE KITE
IN RISING 

The circling movement made by birds as they rise above the wind
is produced by the bird entering upon the wind with one of its wings, 
and balancing itself with the other in the direct line of the wind. 

In addition to this it lowers one of the corners of its tail towards the
centre of its circular movement, and because of this the wind that
strikes it on the inside checks the movement of the side that is lower
and nearer to the centre of this circle. And this is the cause of the
circling movement, and the wing held above the wind causes the bird
to rise to the maximum height of the wind. e 38 v. 

The simple movement which the wings of birds make is more easy
when they rise than when they are lowered. And this ease of move- 
ment springs from two reasons of which the first is that the weight in
falling somewhat raises the wings up of themselves, the second is due
to the fact that owing to the wing being convex above and concave
below the air flows away more easily from the percussion of the wings
as they rise than when they are lowered, for then the air being pent
up within the concavity of the wing becomes compressed more easily
than it escapes. 

OF THE EXPANSION OF THE TAIL IN THE REFLEX
MOVEMENT OF BIRDS 

Birds spread out their tails in their reflex movement because the air
is compressed beneath them and resists the penetration of the bird in
its maximum breadth, so that the impetus is consumed with just the
edge or front of the wing. If this were not so the impetus acquired in
the falling movement would consume itself partly in the direction of
the earth and partly in the reflex movement; and then this reflex move- 
ment would be as lacking in height as that which drops down by keep- 
ing the tail straight. 

448 FLIGHT 

The bird acquires more lightness the more it spreads itself out and
expands its wings and tail. 

That heavy body shows itself lightest which extends in greatest
breadth. 

From this conclusion one infers that by means of a wide expanse of
wings a man's weight can support itself in the air. 

That body shows itself less heavy which extends in greater breadth. 

E 39 r. 

OF THE CAUSE OF THE CIRCULAR MOVEMENT OF BIRDS 

The circular movement of birds is produced by the unequal move- 
ment of their wings, and this is caused by the percussion created in the
air by one of the corners of the tail that projects above or below the
route made by the bird in the air traversed by it. 

Of the things that are moved by others with simple movement the
thing moved is as swift as the swiftness of its mover: therefore the bird
carried by the wind in the same direction as this wind will have a speed
equal to it. 

But if the objects carried by the wind slant more towards the ground
than the direction of the course of this wind the thing moved will be
swifter than its mover. And if the slant of the objects carried by the
wind turns towards the sky this is a clear sign that the movement of
the thing moved is slower than that of the wind. The reason is that
when the slant is turned towards the ground it produces this move- 
ment by reason of its gravity and not by the help of the wind. But
when the slant of the movement made by the thing moved is towards
the sky, this slant is caused merely by the shape of the thing moved, 
for it bears itself like a leaf which caught by the wind in its breadth
raises itself up merely by the help of the wind, and moves as much as
its mover, as has been shown in its place. e 39 v. 

When the bird is driven by the wind and has a more slanting course
than the course of the wind it is so much swifter than the said wind. 

When the bird driven by the wind has its movement parallel to that
of the wind it also has a speed equal to that of the wind. 

When birds are driven by the wind without beating their wings the 

FLIGHT 449 

bird is swifter than the wind in proportion as its course is more slanting
than that of the wind. This is proved as follows: suppose the wind in
a position ot" equality to move one degree of space in one degree of time
and the bird driven by the same wind to move the same degree in the
same time, these movements up to this point will be equal. But on ac- 
count of the slant in the bird's movement let us assume it to acquire
a second degree of movement in the same time that the wind is ac- 
quiring its first degree; it follows therefore that the bird in the same
time can be twice as fast as the wind that drives it. 

But this same slanting movement does not acquire its distance within
a position of equilibrium, but between this position of equilibrium and
the centre of the earth, as if the position of equilibrium was the line
a c along which the wind moves from a to c, and the bird moves by
the help of the wind and by help of its gravity from a to d. I say that in
the same time in which the bird shall be moved (without the help of
its gravity) from a to b, it will be moved by the help of the wind and
of its gravity from a to d, the one movement being in the proportion
of one and a half as compared with the other, from a to d upon the
movement a b. But as regards the distance of the aspects, a d is the
same as a b, as is shown us by the perpendicular b d. e 40 r. 

OF BIRDS WHICH FLY IN COMPANIES 

When the birds which fly in companies come to make long journeys, 
and the wind chances to strike them on one side, they are greatly
helped in their flight because the flight is made in loops without work- 
ing their wings; because the falling movement is made beneath the
wind, with the wings somewhat close together, and in the direction in
which they are travelling. But the reflex movement is made above the
wind; and with the wings held open it rises up as the wind meets it, 
and consequently, the wind entering beneath the bird lifts it up towards
the sky, after the manner of a wedge, when it penetrates beneath a
heavy body which is set above it. By this means, after the birds have
been lifted up to their proper height, which is the equivalent of that at
the beginning of the falling movement, they return to their first 

450 FLIGHT 

course, recommencing always in this course their falling movements; 
and their reflex movements are always made against the wind. 

e 40 v. 

OF FLYING THINGS 

Before birds start on long journeys they wait for the winds favour- 
able to their movements, and these favourable winds are of a different
kind with different sorts of birds, because those which fly in jerks or
bounds are obliged to fly against the wind, others receive the wind
on one of their sides at different angles and others receive it on both
sides. But the birds that fly by jerks such as fieldfares and other birds
like these which fly in companies, have the feathers of their wings
weak and poorly protected by the lesser feathers which form a covering
for the larger ones. And this is why it is necessary that their flight
should be against the course of the wind, for the wind closes up and
presses one feather upon another and so renders their surface smooth
and slippery when the air tries to penetrate it. It would be the contrary
if the wind were to strike these birds towards the tail, because then it
would penetrate under each feather and turn them over towards the
head, and thus their flight would have a confused movement, like that
of a leaf blown about in the course of the winds which goes perpet- 
ually whirling through the air continually revolving, and in addition
to this their flesh would be without protection against the buffeting
of the cold winds. And in order to avoid such accidents they fly against
the course of the wind with a curving movement, and their bounds ac- 
quire great impetus in their descent, which is made with wings closed
under the wind. And the reflex movement proceeds with wings open
above the wind, which brings the bird back to the same height in the
air as that from which it first descended, and so it continues time after
time until it arrives at the desired spot. 

The reflex movement and the falling movement vary in birds in two
ways, of which one is when the reflex movement is in the same direc- 
tion as the falling movement, the second is when the reflex movement
is in one direction and the falling movement is in another. 

The bird in the falling movement closes its wings and in the reflex
movement it opens them : it does this because a bird becomes heavier in 

FLIGHT 451 

proportion as ii tokls its wings and so much Lighter as it opens its
wings more. 

The reflex movement is always made against the wind and the fall- 
ing movement is made in the direction in which the wind is moving. 

e 41 r. 

If the flight of the bird turns to the south without beating its wings
when the wind is in the east, it will make the falling movement recti- 
linear with its wings somewhat contracted and underneath the wind. 
But the reflex movement which succeeds this falling movement will
be with the wings and tail open and it will have been directed towards
the east. 

At the end of this movement it will turn its front back again to the
south and with its wings folded it will create again the succeeding
falling movement which will be of the same nature at the first, desiring
to make a long course with the help of this wind; and the junction of
the falling movement with the reflex movement will always be of the
nature of a rectangle, and so will be that of the reflex movement with
the falling movement. 

There are two ways in which the wind causes birds to become sta- 
tionary in the air without beating their wings. 

The first is when the wind strikes against the sides of steep moun- 
tains or other rocks by the sea, as the bird then sets itself at such an
angle that it carries in front as much of its weight against the reflex
wind as this wind in front has power in its resistance. And since equal
powers cannot prevail over each other it follows that in such a position
a bird through its imperceptible vibration remains motionless. The
second way is when the bird sets itself at such a slant above the course
of the wind that it has as much power to descend as the wind has to
resist its descent. 

When by the help of the wind the bird rises without beating its
wings and makes a circular movement, and when it spreads its tail at
the uprising of the wind, it is being driven by two powers, one of
which is that of the wind which strikes the wings in the hollow be- 
neath them and the other is the weight of the bird which is descend- 
ing by a complex slant. And from the fact of its acquiring such velocity
it comes to pass that as it turns its breast to meet the onset of the wind 

452 FLIGHT 

this wind acts under the bird after the manner of a wedge which lifts
up a weight; thus the bird makes its reflex movement much higher
than the commencement of its falling movement; and this is the true
cause why birds rise some distance without beating their wings. 

e 41 v. 

DEFINITION OF THE MOVEMENTS 

Straight movement is that which extends from one point to another
by the shortest line. 

Curved movement is that in which there is found some part of
straight movement. 

Spiral movement is formed out of slanting and curved lines in which
the lines drawn from the centre to the circumference are all found to
be of varying length, and it is of four kinds, namely convex spiral, 
level spiral and concave spiral and the fourth is a spiral in cylindrical
form. There is also the circular movement always made round about a
point at equal distance, which is said to be revolving, since there are
there irregular movements which although they are infinite are made
up of a blend of each of the aforesaid movements. 

The commencement of the simple falling movement is always higher
than the termination of its simple reflex movement, the mobile genera- 
tor of these movements being immobile in the air. 

But the complex falling movement in conjunction with the complex
reflex movement will have the contrary result to the simple, provided
that the falling movement is lower than the reflex movement, and this
arises out of the fact that the bird which below the wind creates this
falling movement presses down and lowers the course of this move- 
ment; but the reflex which is produced above the wind with wings open
raises it considerably higher than the commencement of this falling
movement. e 42 r. 

DEFINITION OF THE WAVES AND IMPETUS OF THE WIND
AGAINST FLYING THINGS 

The bird maintains itself in the air by imperceptible balancing when
near to the mountains or lofty ocean crags; it does this by means of the
curves of the winds which as they strike against these projections, 

FLIGHT 453 

being forced to preserve their fust impetus bend their straight course
towards the sky with divers revolutions, at the beginning of which the
birds come to a stop with their wings open, receiving underneath them- 
selves the continual bufferings of the reflex courses of the winds, and
by the angle of their bodies acquiring as much weight against the wind
as the wind makes force against this weight. And so by such a condi- 
tion of equilibrium the bird proceeds to employ the smallest beginnings
of every variety of power that can be produced. 

Of the movement and the eddies made by the current of the air
striking upon various projections of the mountains, and how the birds
steer themselves in the various tempests of the winds by the impercep- 
tible balancing of their wings and tail: 

The falling movement is always united with the reflex movement
and the beginning of the reflex movement is united with the end of
the falling movement; and if such movements form a continuous suc- 
cession always following each other, one will be the cause of the other, 
and the death of one will immediately produce the other, so that they
will never both exist at the same time; and the falling movement has
a weak beginning and is continually increasing and the reflex move- 
ment is the opposite. 

HOW THE TAIL OF THE BIRD IS USED AS A RUDDER 

When the bird lowers its tail equally it descends by a straight slant- 
ing movement. But if it is more lowered on the right side then the
straight line of the descent will become curved and will bend towards
the right side with a greater or less curve of movement in proportion
as the right point of the tail is higher or lower, and if the left point of
the tail is lowered it will do the same on the left side. 

But if the tail is raised equally a little above the level of the back of
the bird it will move along a straight line slanting upwards; but if it
raises the right point of the tail more than the left this movement will
be curved towards the right side, and if it raises the left point of the tail
this straight movement will curve on the left side. e 42 v. 

When two movements of impetus meet, the percussion is more
powerful than if they were without encounter. As therefore the im- 

454 FLIGHT 

petus of the bird encounters the impetus of the wind its simple impetus
increases and the reflex movement is greater and higher. 

The bird moves against the wind without beating its wings and this
is done beneath the wind as it descends, and then it makes a reflex
action above this wind until it has consumed the impetus already ac- 
quired, and here it is necessary that the descent should be so much
swifter than the wind that the death of the acquired impetus at the end
of the reflex movement may be equal to the speed of the wind that
strikes it below. 

WHY SMALL BIRDS DO NOT FLY AT A GREAT HEIGHT
AND LARGE ONES DO NOT LIKE TO FLY LOW 

This arises from the fact that the small birds being without feathers
cannot endure the intense cold of the great height of the air at which
fly eagles and other large birds which have more power of movement
and are covered with many rows of feathers. Also the small birds hav- 
ing feeble and simple wings support themselves in the lower air which
is thick and would not support themselves in the rarefied air which
offers less resistance. 

The end of the reflex movement is much higher (for the birds which
fly against the wind) than the beginning of their falling movement; 
and by this Nature does not break her own laws, and this is shown by
what has gone before. e 43 r. 

HOW THE BIRD RISES BY MEANS OF THE WIND WITHOUT
BEATING ITS WINGS 

The bird rises to a great height without beating its wings by means
of the wind, which strikes it in a great mass underneath its wings and
tail placed slantwise and above its back placed at an opposite slant. 

This may be proved: — suppose the wind compressed beneath the
bird to have the same effect beneath it that one sees happening when a
wedge is driven beneath a weight, for the wedge at each degree of its
movement causes the weight to acquire a degree of height. But since
the opposite slant of the body which the bird has is disposed to descend
against the approach of the wind with the same, power as that with 

FLIGHT 455 

which the wind raises it up, through the slant of the body being con- 
trary to that of the wings, it is covered as much. 
[A il raiting of a sector] 

Here it is necessary to calculate the degrees of the slant, for in no
degree of slant either of an object upon the water or a bird in the air
do they stop, but their speed will be greater or less as their position
slants less or more. 

The bird weighs less which spreads itself out more, and conversely
that weighs more which draws itself together more tightly; and the
butterflies make experiments of this in their descents. e 43 v. 

HOW THE BIRD FALLING HEAD DOWNWARDS HAS TO
GUIDE ITSELF 

The bird that falls head downwards guides itself by bending its tail
towards its back. This is proved by the tenth which says: — the centre
of a heavy object that descends in the air will always remain below the
centre of its lightest part. Therefore as c d the central line of the gravity
of the bird is at a distance from a b the central line of the levity of the
tail of this bird, the two lines will necessarily form the same line over a
short space of the descent of this bird. And this being so one must
needs admit that the direct descent will of necessity become a slant
and in becoming a slant the descent will be as much slower as the
movement is longer, or that the movement will be as much longer as
the descent is slower, and as much longer and slower as the descent
is more slanting. 

HOW THE BIRD STEADIES ITSELF AS IT FALLS BACKWARDS 

But if the bird turns over in the air because of the wind the tail
ought to close up as much as it can and the wings rise behind the head. 
And with the part in front of the centre it becomes heavy and with
that behind light, the centre of gravity not being in the centre of its
volume; and by the ninth which says: — the fact that the centre of the
volume is not concentric with the centre of gravity is the reason why
the body in which these centres are contained will never remain in a
state of equilibrium with its greatest breadth; and by the tenth of 

456 FLIGHT 

this: — the centre of the gravity of bodies suspended in the air will al- 
ways be below the centre of the volume of the same bodies, e 44 r. 

Why the bird makes use of the helm placed in the front of the wings
although it has other ways of curving its straight movement: 

The bird only makes use of one of the helms placed in the front of
its wings when it wishes to bend its straight movement into a level
position. 

When however it comes to pass that this bending process is complex, 
that is it is a slanting curve, it will then draw in one of its wings a
little, and thus will make a curved movement which will descend on
that side on which the wing is drawn in, showing there the convex
movement. 

But such a process as this involves the danger of its turning over on
its side and leaving the point of the wing extended towards the sky, 
and as a means of protection against this it is necessary to extend the
wing that is drawn in, always showing the under side of the wing to
the ground, for if you were to show it the right side the bird would
turn upside down. When therefore in these conditions you have ex- 
tended the folded wing towards the ground you will at the same time
gather up the upper wing which was extended, until such time as you
return to a position of equality. 

In having shown one of the dangers which occur to deflect the
straight movement of the birds in the air, by disturbing the equal re- 
sistance which wings make when they are equally open upon the air
and have their centre of gravity between them midway between their
extremities, we have at the same time proved that it is safer to bend
one of the two helms of the winds than it is to bend one of the two
wings. e 44 v. 

WHICH OF THE MOVEMENTS OF THE WINGS IS THE- 

SWIFTEST 

The movement of the wings is twofold inasmuch as part of tru. 
movement descends towards the earth and part towards the place from
whence the bird is flying. But that part of the movement which is 

FLIGHT 457 

made inwards the earth checks the bird's descent and the backward
movement drives it forward. 

What it is in the bird that causes it to bend its straight movement
without it either descending or raising itself: 

The bird bends its straight movement made in a position of equi- 
librium without raising or lowering itself, by means of the right or
left helm placed in the front part of the wings. This is proved thus: 
let a p o g be the bird which moving in a position of equilibrium
bends the straight movement m p a to the curving movement a b
by means of the helm t which is set in the front part of the left wing, 
and this comes about by the ninth of this which says : — the bodies with
equal sides about the central line of their gravity will always keep the
straight line of their movement in the air — and if the volume of one of
the sides is increased or diminished the straight movement will de- 
scribe a curve, showing the concave part of the curve on the side of
the greater inequality of the thing that is moved. e 45 r. 

OF THE UNDERSIDE OF THE WINGS [with drawing] 

They form coverings one to the other b to a, the resisting parts of
the feathers beneath the wings of the birds behind the flight of the air
or wind, so that this air or wind shuts up a part of the feathers that
offer weak resistance upon the opposite feathers which offer powerful
resistance. 

WHY THE FEEBLE RESISTANCES ARE BENEATH THE
POWERFUL ONES 

The feathers that offer a feeble resistance are set beneath those which
ofTer a powerful resistance with their extremities turned towards the
tail of the bird, because the air underneath flying things is thicker than
it is above them and in front than it is behind; and the necessity of
flight brings it about that these lateral extremities of the wings are not
found by the stroke of the wind because then they would immediately
become spread out and separated one from another, and would be
instantly penetrated by the wind. Consequently these resistances being
so placed that the parts which have a convex curve are turned towards 

458 FLIGHT 

the sky, the more they are struck by the wind the more they lower
themselves and draw closer to the lower resistances with which they
are in contact, and so prevent the entry of the wind beneath the front
of the lateral parts of these resistances. 

WHAT TEXTURE OF AIR SURROUNDS BIRDS AS THEY FLY 

The air which surrounds the birds is as much lighter above than the
ordinary lightness of the other air as it is heavier below, and as much
lighter behind than above as the bird's movement is swifter in its
transverse course than is that of its wings towards the ground, and
similarly the heaviness of the air is greater in front of the contact of
the bird than below it in proportion to the two above mentioned
degrees of lightness of the air. 

The straight movement of birds in the air forms a curve towards the
side on which the wing is drawn together, and this arises entirely out
of the fact that every heavy body descends on that side on which it has
less resistance; this movement therefore may be described as a complex
curve formed out of a lateral curve and the declining curve made by
the bird upon that side which is lower than itself. e 45 v. 

OF RAISING AND LOWERING THE WINGS 

Birds raise their wings when open with greater ease than they lower
them. And this is proved by the third of this which says: — parts of
bodies which are convex are more suitable for penetrating the air than
those which are concave. 

It follows that as birds have their wings convex on the side that is
uppermost and concave on the side below they will raise their wings
with greater ease than they lower them. 

OF THE SPREADING OUT OF THE FEATHERS AS THE
WINGS ARE RAISED 

The feathers spread out one from another in the wings of birds when
these wings are raised up, and this happens because the wing rises and
penetrates the thickness of the air with greater ease when it is per- 
forated than when it is united. 

FLIGHT 459 

OF THE CLOSING UP OF THE FEATHERS AS THE WINGS 

ARE LOWERED 

The spaces between the feathers in the wings of birds contract as the
wings are lowered, in order that these wings by becoming united may
prevent the air from penetrating between these feathers, and that with
their percussion they may have a more powerful stroke to press and
condense the air that is struck by these wings. 

OF THE RESISTANCES OF THE FEATHERS IN THE WINGS 

OF BIRDS 

The resistances of the feathers in the wings of birds form with their
powerful curves shields one of another in the upper part against the
penetration of the air or the onset of the wind, so that this wind may
not as it enters cause them to spread themselves out and raising open
them and so separate the feathers one from another. 

It is shown here below how as the feathers under the wings in order
to support themselves have to rest and rub themselves upon the air
which sustains them, part of the resistance that there is in the feathers
remains beneath the strong part of the other feathers, for the feathers
underneath the wings have their long weak portions situated under- 
neath the short strong parts of the next row of feathers. 

Why the sinews beneath the birds' wings are more powerful than
those above. It is done for the movement: 

The shoulder where the helm of the wing is placed is hollow below
after the manner of a spoon, and being thus concave below it is convex
above. It is fashioned thus in order that the process of rising may be
easy and that of lowering itself difficult and may meet with resistance, 
and especially it is of use to go forward drawing itself back in the
manner of a file. e 46 r. 

OF THE EXTREMITIES OF THE WINGS WHEN RAISED 

The extremities of the wings when raised to their maximum height 

are farther away from each other than when lowered as far as possible. 

And when these wings re-ascend their extremities continue the 

460 FLIGHT 

descent that has been begun until they straighten the curve that they
have formed, and then bend in the opposite curve and continue it
nearly to the end of their elevation; and as the wings recede from this
elevation the extremities pursue the elevation that has been begun
until the first curve has been destroyed and another has been formed
in the contrary direction. 

In the impetus made in the air by the birds it is better and easier to
bend a part of the wings than the whole. The part of the bird which
bends in the air will cause the whole of it to bend, as one sees happen
to a ship through the turning of its rudder. 

By what has been said above the points of the wings produce a
greater movement than is demanded by their length since they are not
flexible. This is proved: — let there be the movement of the points of
the wings which are flexible a c and of those which are not flexible
b d\ the movement a c of the flexible extremities of the wings exceeds
b d the movement of the non-flexible wings, and of these two lines of
movement the one is proved to be less than the other because the one
is part of the other. 

But because the points of the wings as they are raised and lowered
make a less movement than the parts of the feathers joined to them, 
and before these points of the wings commence to extend the parts of
the feathers united to these points they turn in a contrary movement, 
it is necessary for part of the extremity of these feathers to turn back
with the rest of the feather, and for the point to come forward like a
finger that raises itself as much as the hand descends, which finger one
would describe as immovable because it does not change its position; 
and for this reason we may say that the point of the flexible wing has
a movement resembling that of the wings that are not flexible. 

e 46 v. 

WHETHER THE CURVES OF THE END PARTS OF THE WINGS
ARE NECESSARY OR NOT 

The air which is underneath the curves of the end parts of the wings
as they descend is more compressed than any other portion of the air
that is found underneath the bird, and this is brought about by the
beating of the wings. This is proved bv the seventh which treats of 

FLIGHT 461 

percussion, where it is stated that percussion is greater in proportion
as the movement of that which strikes is more long continuing. There- 
fore in the case of the whole wing descending at the same time that
part has most rapid movement which is most distant from the fixed
part, and as a consequence that air is most compressed which is struck
by the swiftest blow. It follows also that the flexion of the point of
the wing is after the manner of a spring or a bow bent by force, and
that this process of bending compresses the air with which it comes in
contact. 

But when these wings rise up their points follow the line of their
descent until they straighten themselves and then they bend back in the
opposite direction, that is that if the concavity which there is in the
end of the wing as it descends turns towards the sky the concavity of
the same end as the wing rises will be turned towards the earth. 

That part of the shaft is most rapid which is furthest away from its
motive power, and the proportion of speed to speed is as the distance, 
the shaft as it moves not bending. e 47 r. 

If the movement of the wind had uniform power in its expanse the
bird would not be so often engaged in beating the wind and balancing
itself with its wings. 

The air in itself is capable of being compressed and rarefied to an
infinite degree. 

WHETHER THE FOLDS IN THE EXTREMITIES OF THE
WINGS ARE NECESSARY OR NOT 

The curve which is created in the extreme parts of the wings when
these wings strike and press upon the air which is condensed beneath
them has the effect of greatly increasing the bird's power of flight, for
in addition to pressing on the air that is below them they compress the
adjacent lateral air, by the fourth of the second which says 'every
violence seeks to undo itself on the very lines of the movement which
has produced it'; and by the seventh 'every straightness which is bent
by force has the lines of its power converging in the centre of a com- 
plete circle formed by the curve commenced by this extremity of wing'. 
As if the wing abed being curved at its extremity c d £, I come to 

462 FLIGHT 

finish the circle c d b r of which the centre is n, and from this 1 draw
the line n f touching the point of the wing; and the others will be the
lines n e and n /, and thus in the centre are the infinite images of the
others. 

And by what is said below all these lines have the same boundaries
as the curve of the wings b d c by the rule of the perpendicular; there- 
fore the force of this extremity of wing b d c is directed along the lines
b /, d e, c m> and of these b f is outside the space occupied by the bird
as the line b o informs us. e 47 v. 

OF FLYING THINGS 

If the lateral parts change from a position of equilibrium the straight
slanting movement will change to a curved slanting movement. 

The bird which after its descent is thrown back in the air will never
regain its former height unless it beats its wings and has the help of
the wind. 

The bird that drops down before the approach of the wind with a
straight slant will always have its reflex movement more raised than its
falling movement. 

The curving slant that is seen to occur when birds are flying to meet
the approaching wind with a falling reflex movement is much more
steady than the same movements made in a straight slant. 

OF REFLEX WINDS 

If the birds are driven by the wind without beating their wings and
the wind meets the wall set over against it, in avoiding this wall [the
bird] immediately encounters the reflex wind. 

If the bird moves towards the north upon the wind and the wind
wishes to turn it to the east, the bird in order not to spoil the equal
expanse of wing which keeps it at its maximum levity will lower the
right tip of the tail and receive the stroke of the wind upon it more
than it does upon the left tip, keeping thus its straight movement
direct to the north upon the wind. e 48 r. 

FLIGHT 4 6 3 

OF THE THINGS THAT MOVE IN THE AIR AND THEIR 

DESCENT 

A parallel board of uniform thickness and weight placed flat in a
position of equality in uniform resistance will descend uniformly in
each of its parts. And if this board is placed in the air in a slanting
position the descent will slant uniformly, and this is proved in its
place. 

The shape of the front part or back part of the thing that moves in
the air or water is what bends its straight course. 

An irregularity attached either in front or behind the extremities of
the equality that moves in the air is what diverts to right or left or up
or down or in some slant the straight movement of the aforesaid
equality. 

A bird which descends with a straight slant in one direction will not
change the equal position of its side parts. 

A bird in the air makes itself heavy or light whenever it pleases; and
it does this by spreading out its wings and expanding its tail when it
wishes to check its swift descent, or by contracting wings and tail
when it wishes to quicken a descent which has been delayed. 

e 48 v. 

The helms placed on the shoulders of the wings are [formed] of
very strong feathers because they bear a greater strain than all the
other feathers. 

[Figure] a b the helms of the wings come into use when the bird is
in swift descent. When it wishes to capture its prey and to turn from
one direction to another without checking its movement it uses these
helms, and if these were not there it would be necessary for it to em- 
ploy the whole wing, and this by reason of its size would greatly hin- 
der the movement commenced, contrary to its intention. 

OF THE SLANTING MOVEMENT OF BIRDS 

The bird which consumes the impetus against the coming of the
wind with its wings open without any movement, except for their
accessary balancing, if it finds itself above this wind, will always rise, 

464 FLIGHT 

but with greater or less increase of height as the impulse which moves
it is of greater or less power and of less or greater slant in itself. 

But if the bird moves without beating its wings underneath the
wind the impetus will be consumed in the descent of the bird but the
impetus will be the more permanent as the descent is less slanting. 

If the bird moves with its wings open and without beating them, at
the same time as the wind and in the same direction, this bird will
then acquire a degree of descent with each degree of movement; but
this descent will be as much more slanting as the wind is swifter, as is
proved when heavy substances are thrown into running water. 

And if a bird is struck behind and below by the wind then the bird
will rise up, but this is only done on very rare occasions by birds, be- 
cause such a movement turns the feathers over and down so that they
point towards the head of the bird. e 49 r. 

OF EVERY KIND OF FLIGHT MAKE ITS OPPOSITE 

When the bird is driven by the wind it proceeds continually to
descend by a slanting movement, and when it desires to rise to its
former height it turns backwards and uses the impetus of the wind as
a wedge. 

Science 

The impetus that the bird acquires by its falling movement may be
reflected in each direction by a movement that is either straight or a
gradual curve whichever it may be until this impetus is consumed. 

Rule 

When the bird struck beneath the right side by the wind desires to
descend upon some spot it lowers the one of its wings upon the side
where it wishes to settle. 

Science 

The bird that desires rapidly to consume the impetus it has acquired
turns its wings in their full extent against the spot where it wishes to
halt — and this it does without the help of the wind. 

FLIGHT 465 

When a bird desires to rise straight up without the wind by means
of beating its wings the turning movement is necessary. 

But if the bird's movement is to be in a straight line without the
help of the wind it is necessary that the movement should be made by
frequent beatings of the wings, and for this cause the movement will
be extremely slanting. e 49 v - 

THEORY OF FLYING THINGS 

The movement made by a movable thing which is long in shape
and of uniform sides round about its centre-line will take a straight
course through the air for so long a time as the impetus lent to it by its
mover lives within it. 

The bird which flies in a curved line in a level position moves one
wing with a longer and more rapid movement than the other, but
such movement does not raise or lower the one wing more than the
other. 

But if the curved movement of birds is made up of curve and slant, 
then in addition to the movement in one wing being swifter and
longer than in the other the one wing will also go higher and lower
than the other. And this is proved by the fourth which says, 'wings of
equal movement propel the bird in a straight line', and by the con- 
verse 'wings of which the movement is unequal in length make a
curved movement'. And if the movement of wings which are unequal
is of equal height but of varying length the movement of the bird will
then be a curve in a level position. And if the movement of the wings
in addition to being unequal in length is also unequal in height and
depth, this being more in the case of one wing than the other, this
movement is composed of curve and slant. e 50 r. 

OF THE REVOLVING MOVEMENT 

[With three sketches of a top spinning] 

The pegtop or 'chalmone' which by the rapidity of its revolving- 
movement forgoes the power that comes from the inequality of its
weight round the centre about which it revolves, on account of the
impetus that controls this body, is a body which will never have such a 

466 FLIGHT 

tendency to fall as the inequality of its weight desires, so long as the
power of the impetus that moves this body does not become less than
the power of this inequality. 

But when the power of the inequality exceeds the power of the
impetus it makes itself the centre of the revolving motion and so this
body brought to a recumbent position completes upon this centre the
remainder of the aforesaid impetus. 

And when the power of the inequality is equal to the power of the
impetus the top is bent obliquely, and the two powers contend in a
concerted movement and move one another in a great circuit until the
centre of the second variety of revolving movement is established, and
in this the impetus ends its power. e 50 v. 

The rows of feathers on the wings placed one above the other are
set there for the purpose of strengthening the largest feathers. 

Make first the anatomy of the birds, then that of their wings stripped
of feathers and then with the feathers. 

Parallel lines which between their extremities are equidistant from
the same point are always curved, and the one is shorter than the other
if they are in contact with the two sides of the same triangle. 

All the feathers of the wings that grow beneath the penultimate
feathers of the same wings are in process of bending during the bird's
flight, and the most flexible are those which do not form a covering
one to another, that is those which are pierced during the flight. 

In order that a bird flying against the wind may be able to settle on
a high spot it has to fly above the spot and then turn back and without
beating its wings descend upon the above-mentioned place. This is
proved, for if the bird should wish to abandon its flight in order to
settle, the wind would throw it backwards, and this cannot happen
when it acts in the aforesaid manner. 

If the flight of the bird is conditioned by the length of the bird and
the wind strikes it on the side the movement of its flight must needs
be between its length and the said side: as though the bird a b should
wish to fly from a to c and the wind / should strike it on the flank or
at the side, this bird will then direct its movement by the line a g, and
the wind will continually bend the movement along the curve m n c\ 
thus it will go where it wishes and will find itself at the spot marked c. 

FLIGHT 467 

But should the wind deflect the bird's course in a more pronounced
curve than its will consents to, the bird will then resume its flight
against the wind as it did at first, and then with a second curving
movement the wind will lead it to the desired place. e 51 r. 

Whether or no equal striking forces made with equal lengths of
movement at different times will create equal lengths of movement in
the objects moved: this is answered by the seventh of the ninth which
says: — among moving forces of equal powers and of movements united
with their objects moved, that which divides its movable thing most
swiftly from itself will be that which will move this movable thing
farthest from itself. At this point the adversary says that moving
forces of equal power will not vary their speed and cannot therefore
with similar movement drive one of two equal movable things farther
from them than the other. The reply to this is that there are two kinds
of moving forces of which one is sensitive and the other is not: that
which is sensitive has life, and the other is without life. But that which
has life moves its movable things by means of the expansion and con- 
traction of the muscles that form parts of its limbs, this expansion and
contraction being made with a greater or less amount of speed with
the same power, the cause that is swiftest not being the most powerful. 

No other difference is found except that the greater or less speed
compresses more or less the air through which the arm of the moving
force is exerted. But the insensitive moving force such as catapults or
mangonels or other similar engines which by means of trapezes or by
the force of cords or bent wood drive forth from themselves. . . . 

The bird which one sees, carried on by its impetus, flying higher
than the spot on which it desires to settle, spreads out its tail and
lowers it; and striking the air with it in the course of its movement it
bends its straight course and causes it to curve and makes it end upon
the spot where it settles down. 

The kite which descends to the east with a great slant with the wind
in the north wall have its movement bent to the south-east by this wind
unless it lowers the right tip of its tail and bends its movement slightly
to the north-east. This is proved thus: — let a b c d be the bird, 
moving to the east in the direction n m, and the north wind strikes it
crosswise by the line / n, and would cause it to bend to the south-east 

468 FLIGHT 

if it were not that it has the right tip of the tail lowered to meet the
wind, as it strikes it behind the centre of gravity over a longer space
than existed in front of this centre of gravity, and so its straight move- 
ment is not deflected. 1 e 52 r. 

When the bird desires, with its wings extended, to make a circular
movement which shall raise it to a height with the help of the wind, it
lowers one of its wings and one of the tips of its tail towards the centre
of the circle in which it is revolving. 

And when the movement of the bird is circular in order to raise
itself to a height without beating its wings it receives the wind under
one of its wings over a fourth part of this circle; and in this way the
wind makes itself a wedge and raises it up. It would turn it upside
down if it were not that the other wing supported it and sustained it
upon the air which strikes with a whirling movement underneath this
wing, which is the one that was struck and pressed together beneath
the other wing. 

THINGS THAT FLY 

The helms formed on the shoulders of the wings of birds are pro- 
vided by resourceful nature as a convenient means of deflecting the
direct impetus which often takes place during the headlong flight of
birds, for a bird finds it much more convenient to bend by direct
force one of the smallest parts of the wings than the whole of them; 
and this is why their feathers are made very small and very strong so
that they may serve as a cover for one another and by so doing arm
and fortify each other with marvellous power. And these feathers have
their base in the small and very thick bones, moved by the sinews
which bend them over their joints and which are very great in these
wings. 

The movement and position of these bones on the shoulders of the
wings is ordered and established in the same way as the thumb in the
human hand, which being in the centre of the four sinews that sur- 
round it at the base with four equal spaces between them, produces by
means of these sinews an infinite number of movements both curved
and straight. 

1 Words crossed out in MS. 

FLIGHT 469 

We may say the same of the rudder placed behind the movement oi 

the ship, imitated from the tails of birds; as to which experience
teaches ns how much, more readily this small rudder is turned during
the rapid movements of great ships than the whole ship itself. 

Why the inventors of ships do not place their rudders in front as is
the case with the rudder placed in front of the shoulders of the wings: 

This was not done with ships because the waves of the water are
thrown up in the air to such a great height when smitten by the
impetuous blow of the moving ship as would render the movement of
the rudder very difficult from the gravity it would have acquired, and
moreover it would often get broken. But since air within air has no
weight but has condensation which is very useful the rudders (or
helms) of the wings have a better use in a thick substance than in a
thin one, the thick offering more resistance than the thin. The ship
does the same in the added gravity of the water as has been said, and
for this reason the rudder has been placed behind the ship where the
water furrowed and cleft open by its course falls back from the dikes
which have been made in the depth of the hollow created, and in its
descent strikes the rudder with greater or less power as the falling
water strikes it at angles greater or less; and in addition to this the
volume of water pent up in the centre of the said concavity falls with
impetus at the blow of the rudder as has been stated. 

But at the tail of the kite there is the stroke of the air which presses
with fury closing up the void which the movement of the bird leaves
of itself, and this occurs on each side of the void so created. 

The void which the bird leaves of itself successively as it penetrates
:n the air is struck on its sides by that part of the bird which most
exceeds the space about its central line. 

If the percussion which the sides of the bird make on the sides of
the air they penetrate, with those parts that is which are at the greatest
distance from the centre line of their movement, is above the middle of
its right side, then the straight movement will curve towards the right
side, and if it is below the middle upon the opposite side this straight
movement will then curve upon the left side; it will also do the same
if struck above the middle of the left side as if struck below it on the
left (right?) side and of the side above or of that below; and of the
appearance of each we will speak in its place. 

470 FLIGHT 

The tail of the bird spread out takes the same proportion of the
bird's whole weight as is the proportion that the open tail bears to the
other parts of the bird, the bust, neck, head and open wings, — and so
much less in proportion as the centre of gravity of the whole bird is
nearer the centre of the bust than of the tail. 

[The air] runs after the vacuum which the bird leaves of itself as it
pierces the air as much as the bird flies forward in the air which con- 
tinually receives its contact. Consequently it is not the closing up of the
air behind the bird that drives the bird before it but the impetus which
moves the bird forward opens and drives the air, which becomes a
sheath and draws the air behind it. 

The bird which without moving its wings rises up by the help of the
wind descends half the distance that it rises as it moves above the
wind when its tail is turned to this wind. And as much more as the
circle is larger. e 52 v. and 53 r. 

The bird that flies with a curving movement as it beats its wings
beats the wing on the convex side of this movement more frequently
and with a longer movement than it does on the concave side. 

If the bird were to raise its wing above the wind on the side on
which it is struck by this wind, this bird would be turned upside
down, but for the fact that the opposite wing is lowered and bent
underneath the percussion of the wind beyond the centre of its gravity, 
which percussion would immediately restore it to a position of equi- 
librium in the tips of its wings. 

The bird which spreads its bulk out longer and thinner will have
its flight less affected by the percussion of the wind as it receives the
aforesaid percussion. 

When the bird has arranged itself so that it receives the percussion
of the wind slantwise, the extreme part of the lower wing bends con- 
siderably and assumes the shape of a foot and in this way it serves
somewhat as a support to the weight of the bird. 

Birds with short tails have very wide wings; by their width they
take the place of the tail, and they make considerable use of the helms
set on the shoulders of the wings when they wish to turn to any spot. 

The bird that receives the wind full in front turns over as it rises
and stretches out its neck towards the sky; and by lowering and open- 

FLIGHT 471 

ing its tail it stops itself from turning over. And this proceeds Erom the
fact that a greater volume of wind strikes the bird below its centre of
gravity than above it. e 53 v - 

In order to give the true science of the movement of the birds in the
air it is necessary first to give the science of the winds, and this we shall
prove by means of the movements of the water. This science is in itself
capable of being received by the senses: it will serve as a ladder to
arrive at the perception of flying things in the air and the wind. 

Wind 

The wind in passing the summits of mountains becomes swift and
dense and as it flows beyond the mountains it becomes thin and slow, 
like water that issues forth from a narrow channel into the wide sea. 

When the bird passes from a slow to a swift current of the wind it
lets itself be carried by this wind until such time as it has devised a
new assistance for itself, as is proved in this book. 

When the bird moves with impetus against the wind it makes long
quick beats of its wings with a slanting movement, and after thus
beating its wings it remains for a time with all its members contracted
and low. 

The bird will be overturned by the wind when in a less slanting
position it so arranges itself as to receive beneath it the percussion of
any lateral wind. 

But if the bird that is struck laterally by the wind is on the point of
being overturned by this wind it will fold its upper wing, and so im- 
mediately go back to the position of having its body turned towards
the ground, but if it fold its lower wing it will be immediately turned
upside down by the wind. e 54 r. 

OF THE BIRD'S MOVEMENT 

Of whether birds when continually descending without beating their
wings will proceed a greater distance in one sustained curve, or by
frequently making some reflex movement; and whether when they
wish to pass in flight from one spot to another they will go more 

472 FLIGHT 

quickly by making impetuous headlong movements, and then rising
up with reflex movement, and again making a fresh descent, and so
continuing: to speak of this subject you must needs in the first book
explain the nature of the resistance of the air, in the second the anat- 
omy of the bird and of its wings, in the third the method of working
of the wings in their various movements, in the fourth the power of
the wings and of the tail, at such time as the wings are not being
moved and the wind is favourable, to serve as a guide in different
movements. 

Dissect the bat, study it carefully, and on this model construct the
machine. 

OF SWIMMING AND FLIGHT 

When two forces strike against each other it is always the swiftest
which leaps backwards. So it is with the hand of the swimmer when
it strikes and presses upon the water and makes his body glide away
with a contrary movement; so it is also with the wing of the bird in
the air. f 41 v. 

Before you write about creatures which can fly make a book about
the insensible things which descend in the air without the wind and
another [on those] which descend with the wind. 

When the bird is moving to the east with the wind in the north and
finds itself with its left wing above the said wind it will be turned
over, unless at the onset of this wind it puts its left wing under the
wind and by some such movement throws itself towards the north- 
east and under the wind. f 53 v. 

AIR 

Its onset is much more rapid than that of water, for the occasions
are many when its wave flees from the place of its creation without
the water changing its position; in the likeness of the waves which in
May the course of the wind makes in the cornfields, when one sees
the waves running over the fields without the ears of corn changing
their place. 

When the heavy substance descends in the air, and this air moves in
a contrary direction in order to fill up continuously the space left by 

FLIGHT iji 

this heavy substance, the movement of this air is a curve, because when
it desires to rise by the shortest line it is prevented by the heavy sub- 
stance which descends upon it, and so of necessity it is obliged to bend
and then to return above this heavy substance and fill up the vacuum
that has been left by it. And if it were thus the air would not be com- 
pressed beneath the speed of the heavy substance, and this being so
the birds would not be able to support themselves upon the air that is
struck by them; but it is necessary to say here that the air is com- 
pressed beneath that which strikes it and it becomes rarefied above in
order to fill up the void left by that which has struck it. f 87 v. 

BIRDS IN SLANTING MOVEMENT 

The adversary says that if the bird is struck below by the wind
this bird will always rise up, and this will not fail to be the case if the
bird be flying against the wind. But if the bird and the wind go with
equal movement along the same path it must needs be that at every
degree of movement made by the wind the bird acquires a degree of
descent; we may therefore say that in such time as the wind moves a
degree in a horizontal position, a degree to which we may apply a
name . . . 

The bird that flies in an easterly direction without beating its wings
as it crosses the course of the south wind gathers in its right wing and
extends its left; and this inequality of wings is according to the ninth
of the first which says: the birds that support themselves without
beating their wings in the course of the wind, or descend through the
motionless air bend their straight movement towards the side where
one of the wings is pressed together. 

Therefore the bird p flying along the line a f with an equal expan- 
sion of wings n b will bend this movement from c f towards d, 
gathering in the right wing from m to n. g 41 v. 

The adversary says that if the movement of the bird be slanting in
the course of the wind and made in a position of equality, this bird
will be struck by the wind on the side underneath; and the bird which
is struck underneath continually rises upward. 

Birds always fly low when the course of the wind is contrary to their 

474 FLIGHT 

pprh, and this teaches us how the wind is more powerful at a height
>.Lan low down. Here the adversary says that the wind which strikes
jJie earth suddenly acquires more density than it had at first, and con- 
sequently it becomes more powerful and heavier. 

When the bird is driven by the wind it proceeds to lower itself
continually with a slanting movement; and when it wishes to raise
itself again to its former altitude, it turns back with the speed of the
impetus it has acquired; and this is consumed against the wind which
acts as a wedge and raises it to a greater altitude than it left; from
thence it afterwards descends with the slant mentioned before, after
which it acts as we said above, and so continually acquiring degrees of
altitude it raises itself at last to the spot that it desires. c 42 r. 

The bird which without beating its wings descends with a great
slant beneath the approach of the wind bends its straight course to- 
wards the side where one of its wings is contracted. g 49 v. 

OF THE END OF THE FLIGHT OF BIRDS 

The end of the flight of birds in certain species is made with a
straight and slanting movement and in others it is made with a curved
slanting movement. But in the case of that which is made with a
straight slant it is necessary that this movement should slant very con- 
siderably, that is that the slant is almost horizontal as is shown in
m n [diagram]. 

And if the movement of these birds drops very much then of
necessity this is intermingled with many reflections, and especially
toward the end as will be shown in its place. 

OF THE END OF THE FLIGHT THAT IS MADE UPWARDS 

FROM BELOW 

When it is near the end [of its flight] the bird makes itself slant only
a little in its length, and opens its wings and its tail very widely, but
the wings reach this end with frequent tiny beats in the course of
which the impetus is consumed, and so as they contract it remains for
a very brief space above the spot where it finally settles with a very
slight percussion of its feet. 

FLIGHT 475 

Bats when they fly have of necessity their wings covered completely
with a membrane, because the creatures of the night on which they
feed seek to escape by means of confused revolutions and this confusion
is enhanced by their various twists and turns. As to the bats it is neces- 
sary sometimes that they follow their prey upside down, sometimes in
a slanting position, and so in various different ways, which they could
not do without causing their own destruction if their wings were of
feathers that let the air pass through them. g 63 v. 

OF THE COMMENCEMENT OF BIRDS' FLIGHT 

When birds wish to commence their flight it is necessary for them
to do so in one of two ways, one of which commences by lowering
themselves with their body to the ground and then making a leap in
the air by extending very rapidly their folded legs. 

At the close of this leap the wings have completed their extension
and the bird immediately lowers them swiftly towards the ground and
reascends the second stage which is slanting like the first; and thus
continuing in succession it rises to whatsoever height it pleases. Some
others first raise their wings to slant forward and lower themselves as
far as they can with their breasts on the ground, and in this position
they extend their legs very rapidly leaping up and slanting forward, 
and then at the end of the effort they drop their wings so that they are
slanting downwards and backwards. Thus they find themselves con- 
siderably above and in front of the place from which they set out and
at the end of the effort they are in another; and so their movement
continues. 

There are other birds which after having lowered themselves to the
ground and having their wings extended high and forwards, lower the
wings and extend the legs at the same time, and thus the power pro- 
duced by the first beating of the wings allied to the power acquired by
extending the legs becomes very great, and this power united is the
greatest that it is possible to create for the beginnings of the flights of
these birds. 

The second method employed by birds at the commencement o f
their flight is when they are descending from a height: they merely
throw themselves forward and at the same time spread their wings 

476 FLIGHT 

high and forwards and then in the course of the leap lower their wings
downwards and backwards, and so using them as oars continue their
slanting descent. 

Others have the habit of throwing themselves forward with wings
closed and then opening the wings as they descend, and having opened
them are stopped by the resistance of the air, and then close them and
fall again. g 64 r. 

THE FLIGHT OF THE FOURTH SPECIES OF BUTTERFLIES
THE DEVOURERS OF THE WINGED ANTS 

The butterflies with four equal and separated wings (ant lions) 
always fly with the tail high using it as a rudder for any sort of move- 
ment. That is that if one of these insects wishes to descend it lowers
its tail and if it wishes to ascend it raises its tail, and if it wishes to
turn to the right or left it bends its tail to the right or left and the
same with all sorts of angles of movement which lie between the said
four principal movements. And this is the largest butterfly of the afore- 
said species, black and yellow in colour. 

It uses its four wings in short wheeling flights when it wishes to
prey on the small winged ants, moving sometimes the right forward
and the left backward and sometimes the left forward and the right
backward because the rudder formed by the tail is not sufficient to
regulate the speed of its movement. 

OF THE THREE CHIEF POSITIONS WHICH THE WINGS OF
BIRDS ASSUME AS THEY DESCEND 

Of the three chief positions which the wings of birds assume as they
descend slantwise without beating their wings, the first is a b c in
which the wings have their extremities of equal height and so also the
opposite angles of the tail, whence their movement will descend by the
slant a d. The second arrangement will be a e f, in which the extrem- 
ities of the wings and the angles of the tail are of different heights, 
the left wing being higher, and its slanting movement being a g. The
third arrangement of the slant of the same wings is the converse of the
second, for in it the left wing is lower than the right; and its move- 
ment is at a o, and the position of the wings is n m. g 64 v. 

FLIGHT 477 

A SCREEN TO PREVENT THE WIND FROM TURNING THE
BIRD UPSIDE DOWN 

I have seen the bird turned upside down by the wind on its left
when it entered above the wind with its left wing. 

In the case of all the birds that fly high as they raise their wings they
remain perforated, as is shown in its place. And as the wings descend
they remain united; so as the compressed and condensed air does not
yield place to the descent of the wings with the same speed as the
wing, it becomes necessary for the bird to have the reflex of such per- 
cussion, by which it rises and is carried to a height, by the impetus
acquired, through as great a span of height as the impetus of the reflex
has of life. And in this time the wings reopen and become perforated
with the spaces interposed between the said feathers, then the bird
lowers its wings again violently as it closes up its feathers, and so ac- 
quires anew the impetus that it had lost. And in this way all the birds
act which rise in straight movement such as the lark and the like. And
chose birds which do not possess such a wide expanse of feathers such
as birds of prey, it is necessary for them to raise themselves by turning
round, that is in the form of a screw or otherwise in circular move- 
ment. 

The butterfly and many similar insects all fly with four wings
having those behind smaller than those in front. Those in front form
a partial covering to those behind, and all the insects of this class pos- 
sess the power to rise with straight movement, for as they raise them- 
selves on these wings they remain perforated because they keep the
front wings much higher than those behind. And this continues almost
to the end of that impulse which urges them upwards, and then as
they lower their wings the larger become joined to the lesser, and so as
they descend they again acquire a fresh impulse. 

There are also other kinds of flying insects which fly with four
wings equal, but these do not cover each other in their descent any
more than in their rise; and those of this kind cannot rise with straight
movement. g 65 r. 

478 FLIGHT 

OF PERCUSSION— FLIGHT OF MAN 

Of the things that fall in the air from the same height, that will
produce less percussion which descends by the longer route: it follows
that that which descends by the shorter route will produce more per- 
cussion. 

This first movable thing formed of paper slightly curved has its
first descent with the front b and moves from a to c, in which move- 
ment a descends farther than b; consequently a at the end of the reflex
movement finds itself at c, and b is raised to d. And this is proved by
the ninth of this which says: — the thing that strikes the air with a
greater part of itself has less power to penetrate this air. And by the
tenth: — that thing is swifter in penetrating the air which strikes it
with less breadth. And by the eleventh: — the heaviest part of a body
that moves through the air becomes the guide of the movement of
this body. 

This may be proved: — let a b be the heavy substance, which, al- 
though in itself of uniform thickness and weight, being in a slanting
position, has a front that has more weight than any other part of its
breadth equal to the front which can serve as its face, and for this
reason the front will become the guide of this descent. And by the
twelfth: — that air offers most resistance to its moving thing which is
most compressed; therefore that face weighs least with its parts which
has below it the compressed air. And by the thirteenth: — the air that
has the swiftest movement moves most — it follows that the man can
descend as is shown below. 

This [man] will move on the right side if he bends the right arm
and extends the left arm; and he will then move from right to left by
changing the position of the arms. g 74 r. 

GRAVITY 

Every slanting movement made by a heavy substance through the
air divides the gravity of the movable thing in two different aspects, 
one of which is directed to the place towards which it moves and the
other to the cause that restrains it. c 74 v. 

FLIGHT 479 

[Of the wings of the fly] 

The lower wings are more slanting than those above, both as to
length and as to breadth. 

The fly when it hovers in the air upon its wings beats its wings
with great speed and din, raising them from the horizontal position up
as high as the wing is long. And as it raises them it brings them for- 
ward in a slanting position in such a way as almost to strike the air
edgewise; and as it lowers them it strikes the air and so would rise
somewhat if it were not that the creature threw its weight in the oppo- 
site direction by means of its slant. As though the slant of the fly when
stationary in the air was along the line e f, and the slant of the move- 
ment of the wings between the straight up and the straight down
position followed the lines a b, c d which intersect with the line of the
descent e f between right angles, in such movement that the power of
the descent by the slant e f is equal to the power that it has to raise
itself by the slant of the movement of the wings by the slant d b c a. 

And the back legs serve it as a rudder, and when it wishes to fly it
lowers its wings as much as possible. g 92 r. 

The ascent 1 of birds or their rebound near to any object will never
extend as far as the descent or will not exceed it. h 33 v. 

The bird rises to a height in a straight line without beating its wings
when the reflex movement of the wind strikes it from underneath. 

I have divided the Treatise on Birds into four books; of which the
first treats of their flight by beating their wings; the second of flight
without beating the wings and with the help of the wind; the third of
flight in general, such as that of birds, bats, fishes, animals and insects; 
the last of the mechanism of this movement. k 3 r. 

If one of the wings is lowered rapidly and then folded, the bird drops
a little on that side; and if it is lowered rapidly and extended the bird
drops on the opposite side; and if it is lowered slowly and extended
the bird moves in a circle round this wing, falling as it proceeds; and if
it is lowered slowly and with hesitation and folded up the bird then
descends in curves on that side. k 4 r. and 3 v. 

All birds driven by the water or by the wind keep their heads in the 

1 MS. calare. 

480 FLIGHT 

direction from whence the water or the wind is coming. They do this
in order to prevent the wind or the water penetrating up from the
extremities to the roots of the feathers, so that each of the feathers may
be pressed against one another, and thus they may remain drier and
warmer. k 3 v. 

When the bird lowers one of its wings necessity constrains it in- 
stantly to extend it, for if it did not do so it would turn right over. 
The bird when it wishes to turn does not beat its wings with equal
movement, but moves the one which makes the convex of the circle it
describes more than that which makes the concave of the circle. 

K 4 V. 

If the rudder or tail of the bird is beneath the wind the bird will be
pulled down by the wind from its middle backwards, and turned with
its front towards the wind. 

And if the bird is struck on the slant of its tail above the wind it will
be pulled down in front and turn towards the wind. k 5 r. 

The bird often beats twice with one wing and once with the other
and it does this when it has got too far over to that side. 

It also does the same when it wishes to turn on one side; it takes two
strokes with one wing backwards, keeping the opposite wing almost
stationary pointing towards the spot to which it ought to turn. 

k 5 v. 

The helms of the wings are used when the bird is struck from behind
by the wind and rests slantwise upon the air that supports it: the bird
is then struck by the wind in the front of these helms and so is driven
upwards, its reflex movement being increased by the movement of the
wind. k 6 r. 

If the extent of the slant of the tail from the centre of the bird back- 
wards is more than that of the wing from the centre of the bird for- 
wards the bird will turn to face the wind. But if the slanting part of
the wing is greater in extent than that of the tail then the tail will turn
towards the approach of the wind. k 6 v. 

The bird beats its wings repeatedly on one side only when it wishes
to turn round while one wing is held stationary; and this it does by 

FLIGHT 481 

taking a stroke with the wing in the direction of the tail, like a man
cowing in a boat with two oars, who takes many strokes on that side
from which he wishes to escape, and keeps the other oar fixed. 

k 7 r. 

Of the flexion of the tip of the wing even when the wing does not
beat. 

The helms which are on the shoulders of the wings are necessary
when the bird in its flight without beating its wings wishes to maintain
itself in part of a tract of air, upon which it is either slipping down or
rising, and when it wishes to bend either upwards or downwards or to
right or left. It then uses these helms in this manner: — if the bird
wishes to rise it spreads the helm in the opposite direction to the way
the wind strikes it; and if to descend it spreads the top part of the
helm slanting to the course of the wind. If it turns to the right it
spreads the right helm to the wind, and if it turns to the left it spreads
the left helm to the wind. k 7 v. 

The helm of the wing is used by the bird when in flying it supports
itself upon its wings raised so that by their vibration they prevent it
from descending; and in addition to this these helms or fingers show
themselves fronting the air down which the slant of the bird is gliding, 
and by thus striking upon it with these helms it resists it as it glides. 

That bird descends most rapidly which has the least distance be- 
tween the extremities of the tips of its wings. k 8 r. 

The birds which seek to penetrate within the approaching wind are
in the habit of fluttering to the right and to the left, like sailors tacking
against the direction of the winds; and this they do in order not to
make a long descent, for if the bird did not guard against descending
for any great distance, it would be driven right against the current of
the wind; and, entering under the wind slanting lengthwise, it will
present so much of its weight by this line as to subdue the resistance of
the wind. k 8 v. 

The 'hands' of the bird show themselves in front, close to the spot
where it descends by a straight slant in order to consume the impetus
it has acquired. 

482 FLIGHT 

By beating its wings in order to support itself at a height and to
advance from the 'hand' behind, it supports itself at the height and the
'hand' causes it to make progress. k 9 r. 

When the bird is carried along by the wind and wishes to turn
quickly towards it, it will then enter beneath the wind with the wing
turned towards it; and then with the feathers of the tail turned towards
the wind, it will enter upon it, and so by the help of the wind striking
upon its tail it turns much more rapidly. k 9 v. 

The wing bends so much the more in proportion as the bird is
swifter in the same space of time. 

What difference there is between the tips of the wings of birds which
bend and those which do not, and whether to bend up and down thus
is necessary for the flight of these birds or no, since one sees that how- 
ever slightly these tips are cut the bird's power of flight is almost
stopped. k 10 r. 

When the bird rises up by the assistance of the wind without beating
its wings, it spreads out and raises its wings so that they form an arch
with the concave side towards the sky, and it receives the wind under
its wings continually, in its movement to and fro, and this would cause
it to turn right over if it were not that the point of its tail is turned to
the wind as it enters beneath the wind; and this afterwards by its
power of resistance acts to prevent the said movement of turning over, 
because the wings are restrained by the tail in such a way that their
various parts are of equal power, and so the tail becomes partly lowered
and the bird is raised forward slightly. k 10 v. 

Always the wind that strikes the tail is farther removed from the
centre and more powerful than that of the wing. 

What has been set forth before is here proved. I say that if the wing
be in such a position in relation to the tail that the amount of the wind
a b which strikes the wing m o is equal to the amount of the wind b c
which strikes the tail above at o n, the bird will not turn, but will be
carried in the line of the course of the wind. But if the wind that strikes
the tail above is more powerful than the wind that strikes beneath the
wing, then the tail will move away and will be dominated by the power
of the wind, and the wing will turn to the wind which will be more 

FLIGHT 4 S > 

powerful than it was before, because the movement that the wing
makes against the wind increases in speed and power, and so the wind
entering beneath it forms a wedge there and raises and turns it. 

k n r. 

When the bird wishes to ascend it drives the centre of its gravity
behind the centre of its wings, and it does this in order to be in a slant- 
ing position. It is of the nature of an equable wind to straighten all the
uneven parts of the bird, placing it with its extremities equidistant from
the centre of its bulk, this being understood of such as support them- 
selves without beating their wings in the air by the help of the wind; 
and consequently it makes first a circling movement and then a straight
movement. k n v. 

When the bird wishes to avoid being turned over by the wind it has
two expedients, one of which is to move the wing that was above the
wind and place it suddenly below the wind, that is to say the one that
was turned to the wind; the other is to lower the opposite wing so that
the wind that strikes it on the inside is more powerful than on the
wing that faces the wind. k 12 r. 

The bird in its flight without the help of the wind drops half the
wing downwards, and thrusts the other half towards the tip back- 
wards; and the part which is moved down prevents the descent of the
bird, and that which goes backward drives the bird forward. 

When the bird raises its wings it brings their extremities near to- 
gether; and while lowering them it spreads them farther apart during
the first part of the movement, but after this middle stage as they
continue to descend it brings them together again. k 12 v. 

The point of the wing of the bird serves to guide it through the air
as the point of the oar does through the water or the arm or hand of
the swimmer beneath the water. But here arises a doubt as to whether, 
if for instance the bird be travelling along the line / a and the wing or
rather the point move backward moving from a to /, it makes its path
by a b /, driving the bird forward, and returns towards a by the path
above f c a, or whether it really acts as the hand of the swimmer does
under the water which forces itself back by the line above a c f and
returns by / b a. k 13 r. 

484 FLIGHT 

When the bird is borne along by the help of the north wind, and
moves with it to the south, it keeps one wing fixed to the north-east, a
little above the wind, and lowers the wing that is to the south-west and
makes it serve as a cover to the wind by receiving there beneath it the
percussion of the wind slantwise. It seldom beats this wing but it is
entirely by means of it that it maintains its equilibrium, whether the
wind be greater or less. 

When the bird ascends by reflex movement against the wind, if it
did not turn round on its lower wing it would by this reflex movement
turn back with its breast to the wind, and this wind would over- 
throw it. 

And ascending by reflex movement with its spine to the wind it
would turn back with its spine below the wind. k 13 v. 

The thrushes and the other birds fly readily against the wind. 

When the bird wishes to let itself fall on one of its sides it throws
its wing down rapidly on the side on which it wishes to descend, and
the impetus of this movement causes the bird to drop on this side. 

When the north wind blows and the bird is carried by the wind and
wishes to return facing the wind, it drives the wing downwards and
turns and enters with its spine beneath the wind. k 14 r. 

A bird beats its wings frequently as it settles when it has descended
from a height, in order to break the impetus of the descent, to settle
itself on the ground and to diminish the force of the impact. 

k 58 [9] r. 

When birds ascend by wheeling round with the wind they keep their
wings very high so that the wedge of the wind and of the impetus may
raise them. 

When they move in a downward direction they lower their wings
for two reasons; the first is because less air sustains them, the other
because the wind serves as a wedge above them and drives them down
and continually lowers them. k 58 [9] v. 

Many are the times when the bird beats the corners of its tail in order
to steer itself, and in this action the wings are used sometimes very
little, sometimes not at all. k 59 [10] r. 

FLIGHT 4 8 5 

When the kite rises or sinks without beating its wings, it holds them
slanting, and keeps the tail slanting in the same way but not to the
same extent, for if this were so the bird would fall to the ground by
the line of the slant of the wings and of the tail; but as this tail is away
from the centre of the bird's length it meets with somewhat more re- 
sistance than the wings, and this in consequence checks its movement, 
and so the tail has less movement than the wings. Necessity causes the
bird to move with a circular motion, and as the tail is less slanting so
in proportion the circles are less in diameter, and so also conversely. 

k 59 [10] v. and 60 [11] r. 

When the bird flies along a level line it seems that the nearer it
approaches the eye the more it rises. 
[Diagram] 

Let g h be the level line and let the bird be moving along g c s, and
let n be the eye. I say that as the images of the bird rise in every stage
of its movement in every stage of height in the pupil it seems to the
eye that this bird is rising. k 121 [41] v. 

And if the bird flies along a level line separating itself from the eye
it will seem to be descending stage by stage with the stages of its
movement. k 121 [41] r. 

The slanting movement made by the descent of birds commences
with the wings straight and low. Gradually they stretch out their wings
in order to consume the access of impetus which heavy bodies acquire
at each stage of their descent. And when such a movement is retarded
by the too great expansion of wings then this bird again contracts its
wings and so again the descent commences to become swift. 
[Drawing] 

Route made through the air by flying things which descend, with
their expansion and contraction of wings. l 54 r. 

[Slanting flight of birds] 

When the bird descends by any slant whatever it brings the humerus
of the wings near to its shoulders and draws together the points of the
wings towards the tail, and this tail is also drawn together into itself
and by so doing it meets with a less volume of air to resist its descent. 

But when this bird wishes to turn to the right or to the left it will 

486 FLIGHT 

extend its right or left wing, that is to say the wing that is on the side
on which it wishes to turn. This extended wing finds a greater volume
of air and in consequence comes to meet with a greater resistance, with
result that it slackens its pace more than the opposite wing does which
is more contracted, and as the one wing moves more than the other the
bird transforms its straight movement into a circling movement; but
if the wing which is more contracted towards the bird's body than the
other cannot expand with that ease which the bird requires, then it
spreads out its tail and twists it thus open towards the side where this
wing is contracted. This bird will then fly in a straight movement and
so as you see it will leave the circular movement. 

There are two helms on the humerus of the wings of each bird, and
these without making any change of wings have power to cause the
birds various movements between ascending and descending; it is only
in the transversal movements that the helm of the tail takes part. 

l 54 v. and 55 r. 

[The flight of birds with the wind] 

The movement of things that fly is much swifter than that of the
wind. For if it were not so no bird would move against the wind. But
its movement against the wind is as much less than its natural course
within the still air as the degrees of movement of the wind are less
than that of the bird. 

Let us say the bird moves in the still air at a speed of six degrees and
the wind of itself moves at a speed of two degrees, then this wind
following its natural course takes away two degrees of speed from this
bird and consequently of the six degrees there remain four. 

But if such bird were to fly at six degrees of speed together with the
course of the wind which imparts to it its two degrees, this bird would
be flying at eight degrees of speed. Here however one should observe
how the wing is supported in its percussion in the motionless air, the
retreating air or the air that follows after it, and guide one's self ac- 
cording to these rules. l 55 v. 

[Flight of birds — the lar1(\ 

When the bird finds itself upside down, as is seen at a, the tips of
the wings are driven towards the ground as is shown at b; and then 

FLIGHT 487 

this flying thing will straighten itself in its first position, but it bends
the tail spread out towards its spine. 

And if it falls edgewise it will raise its wings towards its spine and
then straighten itself. 

There are many varieties of birds which can only raise themselves
spirally, that is by revolving movements; the lark is an exception be- 
cause as it raises its wings it proceeds to transpierce them with air in
such a way that they oflfer no resistance being almost entirely trans- 
pierced. 

When the bird wishes to go down it throws its wings backward in
such a way that the centre of their gravity comes away from the middle
of the resistance of the wings and so it comes to fall forward. 

l 56 r. 

The flight of many birds is swifter than is the wind which drives
them. And this arises from driving the wings in the wind which car- 
ries this bird. If it were not so the birds that rest upon the wind would
not be able to fly against the wind. 

The bird in raising its wings sends them partly forward and partly
upward, and the whole wing comes to go edgewise, and each feather
of itself, and in addition to this it remains transpierced; and as it
proceeds downward it thrusts it back in face of the air or of the wind
and the transpiercing of the feathers and of the whole wing become
united. l 56 v. 

[With drawings] 

The manner of resistance of the feathers as the bird drops down. 

The resisting a b as it is flexible is bent by the line of any move- 
ment of air, and there will be the same result with paper protected as
with ribs by the stems of the reeds. l 57 r. 

[Wings of birds] 

The bird which is swifter in lowering than in raising its wings is
that which raises itself more by pressing the underpart of the wings
towards the centre of the earth. 

But if they press this underpart of the wings towards the horizon
they will make equal movements. 

488 FLIGHT 

[Drawing] 

You will note if the feathers of c a are placed above in the manner
and order of a b. 

A b n m is the position of the shutters (sportelli). l 58 r. 

The opening and lowering of the tail and the spreading out of the
wings at the same time to their full extent, arrests the swift movement
of birds. 

When birds in descending are near to the ground, and the head is
below the tail, they then lower the tail, which is spread wide open, and
take short strokes with the wings; and consequently the head becomes
higher than the tail, and the speed is checked to such an extent that
the bird alights on the ground without any shock. 

In all the changes which birds make in their lines of movement they
spread out their tails. 

There are many birds which move their wings as swiftly when they
raise them as when they let them fall: such as magpies and birds like
these. l 58 v. 

There are some birds which are in the habit of moving their wings
more swiftly when they lower them than when they raise them, and
this is seen to be the case with doves and such like birds. 

There are others which lower their wings more slowly than they
raise them, and this is seen with rooks and other birds like these. 

The birds which fly swiftly, keeping at the same distance above the
ground, are in the habit of beating their wings downwards and behind
them, downwards to the extent necessary to prevent the bird from
descending, and behind when they wish to advance with greater speed. 

The speed of birds is checked by the opening and spreading out of
the tail. l 59 v. 

When the slant of the flying thing is struck by the wind in its lower
part this flying thing will rise upwards. 

But when this slant is struck in its upper part this flying thing will
be constrained to descend from its height. 

But if the wind which strikes the said birds in the part below were
to overturn them the flying thing will then contract its wings some- 
what, with result that it will descend by its heaviest part. l 60 r. 

FLIGHT 489 

When the kite in descending turns itself right over and pierces the
air head downwards, it is forced to bend the tail as far as it can in the
opposite direction to that which it desires to follow; and then again
bending the tail swiftly, according to the direction in which it wishes
to turn, the change in the bird's course corresponds to the turn of the
tail, like the rudder of a ship which when turned turns the ship, but
in the opposite direction. 

When the wind is about to throw the bird backward the bird draws
together the shoulders of its wings, so that its weight is massed more
to the front than it was at first, and consequently the part that is
heaviest is first in its descent, while in addition the tail is spread out
and bent down. l 62 r. 

[Tail and wings of birds] 

When one of the sides of the tail of the flying body is lowered with
a swift movement, then the air where it strikes is more compressed and
as a consequence offers more resistance, whence of necessity the bird
bends with its opposite side, and so the movement of this bird is curved
circling round the part of the tail which is lower. 

But when it is sometimes the one and sometimes the other point of
the tail which impels it to lower itself sometimes to the right and some- 
times to the left, it does not make a circling movement but it is merely
a way of striking the air as wings would do. When this bird feels itself
dropping on one of the sides this tail beats the air on the opposite side
and in this way it resists this tendency. l 62 v. 

[A goose swimming and flight] 

OF MOVEMENT 

Swimming illustrates the method of flying and shows that the
weight which is largest finds most resistance in the air. Observe a
goose's foot: if it was always open or closed in the same manner the
creature would not be able to make any kind of movement. It is true
that the curve of the foot outwards would have more perception of the
water in going forward than the foot would have as it was drawn
back; this shows that with the same weight the wider it is the slower
its movement becomes. 

490 FLIGHT 

Observe the goose moving through the water, how as it moves its
foot forward it closes it and covers but little water and consequently
acquires speed, and as it draws it back it spreads it out and so makes
itself slower, and then the part that has contact with the air becomes
swifter. m 83 r. 

When one wing bends with the same speed as the other but with a
longer movement it will cause the straight movement to bend to a
curve. b.m. 43 r. 

CONCERNING THINGS THAT CAN FLY 

In the case of every heavy thing descending freely the heaviest part
will become the guide of its movement. b.m. 96 r. 

\Dr awing — bird with wings extended] 

This raises itself in circles by means of the wind. This creature is
always struck below by the wind by a slanting line; and when this
wind strikes it in front it bends its wings with its shoulders towards
the sky; and when the wind catches it in the tail it bends its shoulders
towards the ground. And so always this bird takes the wind at its
centre of gravity in front or behind or at the side. b.m. 134 r. 

The tail adds or takes away the weight from the wings of the bird. 
Every heavy substance moves by the line where it has least resistance. 
The heavy substance finds least resistance by the line in which it
weighs most. b.m. 146 r. 

That bird will raise itself in flight more readily which gets the
impetus of its movement by dropping somewhat at the beginning of its
flight. 

When a bird flies against the wind it is necessary that the progress
which it makes against the wind should be made in a slanting line
towards the earth, entering underneath the wind. And this because its
weight is more powerful than that of the amount of wind which
strikes it at unequal angles, and would wish to press it down towards
the ground if it were not that the air which is in front in the line of its
movement is far less in amount than the air which happens to be below
it and which touches it. This movement alone suffices to subdue that 

FLIGHT 491 

air which offers less resistance, and that will offer less resistance which
is less in quantity. 

Therefore from what has been stated we are certain that the bird will
move itself against that part of the air which offers less resistance and
which meets the helms of the wings, rather than against that which
meets it from below along the whole extent of these wings. 

Rectilinear movement 

But when this bird wishes to rise to a height it will enter above the
wind, and it will retain enough of the impetus it has acquired in the
descent we have spoken of, so that by means of the speed thus gained
it will lower its tail and likewise the elbows of its wings and will raise
up its helms. It will then be above the wind, and as this impetus is
constrained neither to cease nor to be consumed its nature forthwith
compels it to follow along the line where the least amount of air im- 
pedes its movement, which will be in that line in which the wings
show themselves edgewise to the air where they strike, that is along the
line where the air as it is met is always divided by the helms which are
in the thickness of the wings and never along the line of their width. 

After having done this then the bird rises up without beating its
wings, for the wind which passes underneath it raises it up as a wedge
raises a weight, and for this reason would cause it to turn backwards, 
if it were not that in this act of rising it is continually becoming slower
and consuming the impetus already acquired. And after this impulse
has been consumed the bird would be overturned by the wind which
has carried it up to a height if it did not immediately lower the helms
of the shoulders of the wings, enter underneath the wind and lower its
tail. Then the movement which has just ended commences anew, and
as it drops it acquires again the impetus which it has lost, with which it
again rises up to a height with reflex movement until it again loses the
impetus that it has acquired. 

If however such movement were circular then the bird would follow
other rules which will subsequently be defined in due order. 

b.m. 166 v. 

492 

FLIGHT 

OF THE BIRD THAT MOVES WITHOUT WIND OR BEATING 

OF WINGS 

The movement of a bird without beating of wings or help of wind is
along a line that slants steeply downwards and then rises with a reflex
movement. By this reflex movement it raises itself seven eighths of the
height of its falling movement and it goes on doing this little by little
until it reaches the ground. 

OF THE MOVEMENT AGAINST THE WIND WITHOUT
BEATING OF WINGS WHICH RAISES THE BIRD 

Here the falling movement is below the wind and the reflex move- 
ment will be above the wind. b.m. 277 r. 

rrv • bd f i 

{Diagram wing g\ 

I find in the wings of birds three causes of power, of which the first
is b which derives its strength from the muscle a; the second may be
d c\ the third may be / e; now I ask: if the part g produces its force by
means of / e what force penetrates to b a, or to put it more exactly
what weight? Forster 11 34 v. 

The reflex movement made by the bird against the course of the
wind becomes considerably greater than its falling movement; and it
is the same with the succeeding reflex movement because it is driven by
jjie same course of the wind. Quaderni 11, 16 r.