Notebooks (17 page)
Authors: Leonardo da Vinci,Irma Anne Richter,Thereza Wells
Tags: #History, #Fiction, #General, #European, #Art, #Renaissance, #Leonardo;, #Leonardo, #da Vinci;, #1452-1519, #Individual artists, #Art Monographs, #Drawing By Individual Artists, #Notebooks; sketchbooks; etc, #Individual Artist, #History - Renaissance, #Renaissance art, #Individual Painters - Renaissance, #Drawing & drawings, #Drawing, #Techniques - Drawing, #Individual Artists - General, #Individual artists; art monographs, #Art & Art Instruction, #Techniques
I have ten measures of time and ten measures of force and ten measures of movement and ten of weight, and I wish to raise up this weight.
If I double the weight and not the force in the movement, it becomes necessary to double the time.
If I double the weight and not the time or the force it becomes necessary to halve the movement.
If I double the weight and not the movement or the time it becomes necessary to double the force.
If I halve the weight and not the movement or the time, the force is halved.
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6. IMPETUS AND PERCUSSION117
What is primary movement
Primary movement is that which is made by the movable thing during the time when it is joined to its mover.
Of derived movement
Derived movement is that which the movable thing makes through the air after it is separated from its mover. Derived movement has its origin in primary movement and it never has swiftness or power equal to the swiftness or power of this primary movement. The course of this movable thing will conform to the direction of the mover’s course when all the parts of this movable thing have movement equal to the primary movement of their mover.
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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.
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Of impetus
Impetus is the impression of movement transmitted by the mover to the movable thing.
Impetus is a power impressed by the mover on the movable thing.
Every impression tends to permanence or desires permanence. This is shown in the impression made by the sun in the eye of the spectator and in the impression of the sound made by the clapper as it strikes the bell.
Every impression desires permanence as is shown by the image of the movement impressed upon the movable thing.
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What is impetus
Impetus under another name is called derived movement, which arises out of primary movement, that is to say when the movable thing is joined to its mover.
In no part of the derived movement will one ever find a velocity equal to that of the primary movement. For instance at every stage of movement of the cord of the bow there is a loss of the acquired power which has been communicated to it by its mover. And since every effect partakes of its cause the derived movement of the arrow lessens its power by degrees, and thus participates in the power of the bow which as it was produced by degrees is so destroyed.
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Simple impetus is that which moves the arrow or dart through the air. Compound impetus is that which moves the stone when it issues from the sling.
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I ask why field-lances or hunting-whips have a greater movement than the arm. I say that this happens because the hand describes a much wider circle as the arm moves than does the elbow; and in consequence moving at the same time the hand covers twice as much space as does the elbow, and therefore it may be said to be of a speed double that of the movement of the elbow, and so it sends things when thrown a greater distance from itself.
Thus you see clearly that the circuit described by the elbow is less by half and its speed is slower by half.
It is true that if one subtracts from the movement made by the hand an amount equal to that made by the elbow the movements are of equal slowness.
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There are two different kinds of percussion, simple and complex. The simple is made by the movable thing in its falling movement upon its object. Complex is the name given when this first percussion passes beyond the resistance of the object which it strikes first, as in the blow given to the sculptor’s chisel which is afterwards transferred to the marble that he is carving. This blow also is divided into two others, namely a simple and a double blow. The simple blow has been sufficiently described. The double one occurs when the hammer descends with force in its natural movement and flies back rebounding from the greater blow and creates an inferior blow and makes this percussion in two places, with the two opposite sides of the hammer. And this blow grows less and less in proportion to the number of the obstacles which are interposed between the final resistance, just as if someone were to strike a book on its front pages, even though its pages were all touching, the last page would feel the damage slightly.
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Of movement and percussion
If someone descends from one step to another by jumping from one to the other and you add together all the forces of the percussions and the weights of these jumps, you will find that they are equal to the entire percussion and weight that such a man would produce if he fell by a perpendicular line from the top to the bottom of the height of this staircase.
Furthermore, if this man were to fall from a height, striking stage by stage upon objects which would bend in the manner of a spring, in such a way that the percussion from the one to the other was slight, you will find that at the last part of his descent this man will have his percussion as much diminished by comparison with what it would have been in a free and perpendicular line, as it would be if there were subtracted all the percussions that were given at each stage of the said descent upon the aforesaid springs.
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Every spherical body of thick and resisting surface when moved by an equal force will make as much movement in the rebounds caused by its impact upon a concrete ground as if it were thrown freely through the air.
How admirable Thy justice, O Thou First Mover! Thou hast not willed that any power should be deprived of the processes or qualities necessary for its results; for, if a force have the capacity of driving an object conquered by it, a hundred braccia, and this object while obeying it meets with some obstacle, Thou hast ordained that the force of the impact will cause a new movement, which by diverse rebounds will recover the entire amount of the distance it should have traversed.
And if you were to measure the track made by these bounds you will discover it to be of the same length as that made by a similar object impelled freely through the air by the same force.
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Why it is first the blow rather than the movement caused by it; the blow has performed its function before the object has started on its course.
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The blow is born by the death of motion, and motion is born by the death of force.
Force is caused by motion injected into the weight, and likewise the blow is caused by motion injected into the weight.
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Of the blow and the displacement caused by weight or by force.
I maintain that the displacement caused by the weight which falls is equal to the displacement caused by the force.
The body that receives the blow is not injured as much in the part opposite as it is in the part which is struck. The proof of this is shown when a stone is struck while lying in a man’s hands, for the hand is not injured when it is holding the stone as much as it would be injured if it actually received the blow.
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Ascertain always the proportion of the blow to the object which receives it.
Since one hundred pounds applied at a single blow makes a greater percussion than a million applied one by one, I advise that when you train the battering ram against the castle you cause the blow to be raised in the air by the weight of the men and then you pull it back after the manner of a catapult or crossbow, and you will have a good result.
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A blow is an end of movement created in an indivisible period of time, because it is caused at the point which is the end of the line of the movement made by the weight which is the cause of the blow.
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If a ten-pound hammer drives a nail into a piece of wood with one blow, a hammer of one pound will not drive the nail altogether into the wood in ten blows. Nor will a nail that is less than a tenth part (of the first) be buried more deeply by the said hammer of a pound in a single blow although they may be in equal proportions to one another as those first named, because the hardness of the wood does not diminish the proportion of its resistance, that is it remains as hard as at first. If you wish to treat of the proportions of the movement of the things that have penetrated into the wood when driven by the power of the blow, you have to consider the nature of the weight that strikes and the place where the thing is struck.
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I say that every body moved or struck keeps in itself for a time the nature of this blow or movement, and keeps it in proportion as the power of the force of this blow or movement is greater or less. Observe a blow given on a bell how it preserves in itself the noise of the percussion.
Observe a stone projected from a bombard how long it preserves the nature of the movement. . . .
The eye keeps within itself the images of luminous bodies for a certain time.
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I say that percussion is the end of the swift motion of bodies against resisting objects. It is also the cause of all sounds and the breaker and transmuter of various things and the product of a second motion. There is nothing of greater power and it goes on transmuting according to circumstance.
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The stroke in a bell leaves its likeness behind it impressed as the sun in the eye or the scent in the air; but we wish to discern whether the likeness of the stroke remains in the bell or in the air and this is ascertained by placing your ear to the surface of the bell after the stroke. The stroke given in the bell will cause response and some slight movement in another bell similar to itself; and the string of a lute as it sounds will cause response and movement in another similar string of like tone in another lute; and this you will see by placing a straw on the string similar to that which has sounded.
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III. MECHANICS135
REFERENCES TO BOOKS ON APPLIED MECHANICS
Speak first of motion then of weight as produced by motion, then of the force that proceeds from weight and motion, then of the percussion that springs from weight, motion and often from force.
Speak of motion and impetus.
Speak of wheels rotating one way.
You will speak of wheels that turn and return.
Speak of the wheel that augments.
Speak of the perpetual screws.
Speak of mills and other machines that move and throw.
Speak of teeth.
You will first speak of poles.
Then of wheels and battens without teeth.
Then of wheels and battens with rope and with teeth.
And you will say what teeth are most praiseworthy in nature and movement and setting.
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Now look in the book on Elements in mechanics and you will find the definition of the screw.
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1. FRICTION137
Friction
Friction is divided into three parts: these are simple, compound, and irregular.
Simple friction is that made by the thing moved on the place where it is dragged.
Compound friction is that which the thing moved makes between two immovable things.
Irregular friction is that made by the wedge of different sides.
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Of friction
The movement of friction is divided into parts of which one is simple and all the others are compound. Simple, when the object is dragged along a plane smooth surface without any intervention. This is the only friction that creates fire when it is powerful—that is to say it generates fire—as can be seen at waterwheels when the water is removed between the whetted iron and the wheel. The other frictions are compound and are divided into two parts; the first is when any greasiness of some thin substance intervenes between the bodies that rub together; and the second is when an additional friction is introduced, as would be the friction of the poles of the wheels. The first of these is again divided into two parts, namely the greasiness, that is interposed, and the balls and such things.
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The resistance created by friction to the movement of weights is separate and remote from this weight.
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The resistance created by friction to the movement of weights is separate and remote from this weight.
Reason
This is shown by the things said before, namely that it is obvious that the movement made by weights along horizontal lines does not of itself offer any other resistance to its mover than its own friction which it makes with the surface where it touches it; which movement is more difficult in proportion as the surface is more scoured and rough.
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