Hydraulics 

'To make water rise and remain upon the ascent! 

( With drawing of pump] 

For the bath of the duchess Isabella; a Spring. 

Made for the stove or bath of the duchess Isabella; a is in this position because the screw does not turn with its socket. c.a. 104 r. b 

( With drawings] 

Water raised by the force of the wind. 

This syringe has to have two valves, one to the pipe which draws the water and the other to that which ejects it. 

Method of making water rise to a height. 

In this way one will make water rise through the whole house by means of conduit pipes. c.a. 386 r. b 

OF THE FALL OF A RIVER 

[With sketch] 

If you should wish to know what the fall of a river is in each mile without employing any other instrument for observing levels, you should follow this method: — Be careful to choose a part of the river which has the most conformity with the general range of the course of which you wish to know the fall, and take in it a hundred braccia of bank of which the beginning and the end arc marked by two rods, as is shown above in a h, and at the beginning c launch a bladder, oak-apple, or small piece of cork, and observe how many beats of time the aforesaid object travelling with the descending wave takes to arrive at the end of the journey of the hundred braccia, and then measure many other courses, some slower and some more rapid, and afterwards measure the fall of the hundred braccia with the instrument for observing levels. And by this process, having measured different reaches of the water, you will then know how to speak only for over a hundred paces of a bank; and by observing how many beats of time your oak-apple has taken to traverse this course you will be able to calculate the fall that it makes per mile. Tr. 56 a 

[With drawing of apparatus for raising water] 

If you wish to make water rise a mile and to cause it to rest upon a mountain do as is represented above. And if you wish the stream of water to be as big as your leg make the conduit as big as your thigh. And if it is to rise a mile make it also descend two miles, and then the violence of the water which is found between b and c will be so great that it will draw up the water which is found in d e and will turn the wheel of the water pump. And you must know that no air can enter into the water chamber by the water pump, seeing that every time that the screw of the water pump turns back, the valve which is at the bottom of the reservoir closes, and even if it were not so well stopped up it could not admit the air because it finds itself two braccia under water, and consequently could not admit air unless it first admit the two braccia of water. When you wish to fill the conduit you must first of all have a small lake filled with rains, and stop up with clay the pipes at the base of it, that is at c and <?, and then let this lake discharge itself into the conduit. When the water has risen half a braccio up the wheel close the box tightly and then at the same time unstop the conduit at its base in c and make the wheel four braccia. b 26 r. 

[Drawing of machine] 
To raise water. b 54 r. 

[Hydraulic machine] 

If twelve ounces of water produce thirty thousand revolutions of a machine in an hour we believe that twenty-four ounces will produce sixty thousand revolutions per hour of the same machine if it has the same fall, and that the output will be double what it was at first. h 90 [42] v. 

[ Drawing] 

OF THE INSTRUMENT ABOVE 

Let a b be stagnant water, let a c be a screw which is turned by the 
distaff z, and the said screw carries the water into the chamber c /, and 
from the said chamber a siphon tube proceeds which carries the water 
to another chamber which is round the centre of the wheel of the first 
movement, and from there the eight spokes take the water, which after 
it has fulfilled its function falls back to the spot from whence it started. 

Forster 1 41 r. 

[Drawing] 

a the instrument above: 
m keeps c unstopped as long as it falls, and when m departs c closes, 
and when m comes to the bottom s goes to the top and draws after it 
the water of the well. Forster 1 41 v. 

[Drawings] 

The water after issuing from the pump runs by the line a c, and 
pauses at s, and there makes counterpoise and falls down together 
with the lever n m, and draws up fresh water, of which part goes in 
counterpoise and part remains up by the line b f. 

The water departs from the centre a and flows in b, and from b as 
far as c it makes a level lever, and from c it rises by the wheel of the 
screw gently and returns to the centre c; and make it with sixteen 
spokes. 

Let a b be the level of the earth, p is the lever of m, q is that of #, 
and thus first one then the other after the manner of bellows perform 
their function. 

This as far as relates to the cause of its movement has similarity with 
that above, and it varies only in that screw in the centre which con- 
ducts the water upwards. Forster 1 42 r. 

[Drawings] 

Here the water having ascended by the screw will arrive by the 
pipe s at the point a, and from a b it will make equidistant lever, and 
from b n will return to the first screw, and will always repeat the same 
process, and above all it makes it wider at the end than at the be- 
ginning. 

774 HYDRAULICS 

The screw a gives the water to the screw b, and the screw b gives 
movement with the same water to the screw a. Forster i 42 v. 

[With drawings] 

The water that falls from the mouth g comes from the chamber / 
pressed by the lead d, and when the chamber / is empty the water will 
be raised into the chamber a by a valve which opens inwards. Conse- 
quently as the part below becomes lighter and the part above heavier 
it suddenly turns right over and the lead c presses the chamber a and 
so it is always in motion. Forster 1 45 v. 

The left chamber sends its water from / in b and in this b there is a 
valve opening inwards, by means of which the chamber c b a comes to 
be filled, and the air escapes by a n; but make the mouth a higher 
than the other part so that the water may not pour out. The chamber 
d will be full of air and the part e will be lead. When the chamber a 
b c shall be full it will turn right over and the lead will remain above 
and will press the water on the left, and by the time that the water 
has made its exit the lead will have gone below and the chamber will 
receive the water from the right through m s. Forster 1 46 r. 

[With drawings] 
To make water rise and remain upon the ascent. Forster 1 50 v. 

This water rises by way of a pump, and after issuing forth at the 
extremity of this pump it runs by the lever from c a and from / b, and 
having arrived at the extremity of the said lever the water that follows 
creates counterpoise. Forster 1 51 r. 

The water rises by the screw a b and falls in the chamber c, and 
from there it is drawn off by the siphon b f and carried into the 
chamber p, and from there until counterpoise is made in s, and then 
it falls into the stagnant water below. 

This wheel with the lever a n will turn and draw the water with 
the circle. But see that when the buckets are ten you make twelve of 
the lever and one of the counterlever. Forster 1 51 v. 

XXIII 
Canalization 

''Every large river may be led up the highest 
mountains on the principle of the siphon! 

CANAL OF FLORENCE 

[Plan on which are the words Florence, Prato, Pistoia, Serravalle, Lago, 
Lucca, Pisa] 
Let sluices be constructed in the Val di Chiana at Arezzo, so that in 
summer when there is a shortage of water in the Arno the canal will 
not become dried up, and let this canal be twenty braccia wide at the 
bottom and thirty at the surface and the general level two braccia or four, 
because two of these braccia serve the mills and the meadows. This will 
fertilise the country, and Prato, Pistoia and Pisa, together with Florence 
will have a yearly revenue of more than two hundred thousand ducats, 
and they will supply labour and money for this useful work, and the 
Lucchesi likewise. Since the Lago di Sesto will be navigable make it 
pass by way of Prato and Pistoia and cut through at Serravalle and go 
out into the lake, for then there will be no need of locks or supports, 
which are not permanent but require a constant supply of labour to 
work them and to maintain them. c.a. 46 r. b 

And know that this canal cannot be dug for less than four denari 
per braccio, paying each labourer at the rate of four soldi per day. And 
the time of construction of the canal should be between the middle of 
March and the middle of June, because the peasants are not then 
occupied with their ordinary work, and the days are long and the heat 
does not prove exhausting. c.a. 46 v. a 

[Plan of canal ascending hill by means of loc\s] 
[Below: 10 braccia deep and $ wide] 

Every large river may be led up the highest mountains on the prin- 
ciple of the siphon. 

775 

776 CANALIZATION 

If the river c d b sends out a branch at the point a and it falls back 
again at the point b, the line a b will have so much greater pressure 
than the line a c that it will be able to take away so much of it as will 
serve to lead ships up mountains. c.a. 108 v. a 

If a canal of water passes beneath another river with a bend like that 
of a knee, it exerts pressure in its desire to lift the cover of its conduit. 
Now I ask what weight is required to resist the weight of the water 
that wishes to proceed in its course. c.a. 199 v. b 

OF A GOVERNOR OF RIVERS 

In order to enable each large river to maintain itself within its banks, 
it is necessary for an official to be appointed with authority to com- 
mand the people who live near to it, and so to effect repairs whenever 
it has burst its banks. 

OF THE MAINTAINING OF RIVERS 

The river which has the straightest course will best keep within its 
banks. c.a. 297 r. b 

A trabocco is four braccia, and a mile is three thousand of these 
braccia, and the braccio 1 is divided into twelve inches . . . and the water 
of the canals has a fall of two inches in every hundred trabocchi. 
Therefore fourteen inches of fall are necessary in two thousand eight 
hundred braccia of movement of the said canals. It follows that fifteen 
inches of fall give the necessary momentum to the current of the water 
of the said canals, that is one and a half braccio to the mile; and by this 
we may conclude that the water which is taken from the river of Ville- 
franche and is lent to the river of Romorantin would require . . . 

Where by reason of its lowness a river cannot enter into another it is 
necessary to raise it by a dam to such a height that it can descend into 
the one which was the higher at first. 

From Romorantin as far as the bridge at Saudre it is called the 
Saudre; and from that bridge as far as Tours it is called the Cher. 

1 Braccio — nearly two English feet. 

CANALIZATION 777 

[Map of rivers] Mon Ricardo. Romorantin. Tours. Amboisc. Blois. 

Lyons. 

You will make a test of the level of that canal which is to lead from 
the Loire to Romorantin by means of a channel one braccio wide and 
one braccio deep. 

[Map of rivers] Era (Loire). Scier (Cher). Villefranche. Bridge of 
Saudre. Saudre. Ship. 

On the Eve of Sant' Antonio I returned from Romorantin to 
Amboise, and the King [of France] 1 departed two days before from 
Romorantin. c.a. 336 v. b 

The canals of Milan have a fall of one braccio or thereabouts in every 
mile. And an inch a mile is found sufficient in respect to the surface 
movement of the water. 

Moreover reckoning a fall of a braccio in every mile, in a space of 
four hundred miles it would become necessary for the water to turn 
back, because the world . . . c.a. 352 v. a 

Let the Guild of the Wool Merchants construct the canal and take 
the receipts, making the canal pass by way of Prato, Pistoia, Serravalle 
and empty itself into the lake; and it will be without locks and more 
permanent and will produce more revenue from the places through 
which it passes. c.a. 398 r. a 

The roots of the willows do not suffer the banks of the canals to be 
destroyed; and the branches of the willows, nourished during their 
passage through the thickness of the bank and then cut low, thicken 
every year and make shoots continually, and so you have a bank that 
has life and is of one substance. Fir. 

When the pool that is [provided] for the month of June is empty, 
stop up the mouths and bend the river which has poured itself into it, 
and give it its outlet in the fall of the mill. f 13 r. 

Make a lock to the narrow canal that comes from the sea, in order to 
be able to close it against storms and the tide and to open it at the ebb. 

f 16 r. 
1 MS. di jran crossed out. 

778 CANALIZATION 

IN ORDER TO DEEPEN A CANAL 

Make this in the book of the aids, and in order to prove ic cite the 
propositions that have been proved. And this is the true order, because 
if you wished to supply a help to each proposition it would still be 
necessary for you to make new instruments in order to prove this 
utility; and by so doing you would confuse the order of the forty books 
and so also the order of the figures; thus you would have to blend 
practice with theory, which would cause confusion and lack of con- 
tinuity. F 2 3 r - 

A great weight may be deposited upon a ship without the use of 
windlasses, levers, ropes, or any force: 

In order to deposit each very heavy weight that is all in one piece 
upon a floating barge, it is necessary to draw this weight to the shore of 
the sea, setting it lengthwise to the sea at the edge of the shore. Then a 
canal should be made to pass beneath this weight and to project as far 
beyond it as the half of the length of the barge which is to carry 
this weight; and in like manner the width of this canal should be 
regulated by the width of the barge, which should be filled with water 
and drawn beneath the weight. And then after the water has been 
baled out the ship will rise to such a height as to raise the said weight 
from the ground of itself. Thus laden you will then be able to draw it 
to the sea and lead it to the place that is prepared for it. f 49 v. 

OF THE CANAL OF MARTESANA 

By the making of the Martesana canal the amount of water in the 
Adda is lessened owing to it being distributed over many districts in 
order to supply the meadows. A remedy for this would be to make 
many small channels because the water which has been drunk up by 
the earth does no service to anyone, nor any injury because it has been 
taken from no one; and by the construction of such channels the water 
which before was lost returns again and is once more of service and 
use to mankind. And unless such channels have first been constructed 
it is not possible to make these runlets in the lower-lying country. We 
should say therefore that if such channels are made in the Martesana, 

CANALIZATION 779 

the same water, drunk in by the soil of the meadows, will be sent back 
upon the other meadows by means of runlets, this being water which 
had previously disappeared; and if there were a scarcity of water at 
Ghiara d'Adda and in the Mucca and the inhabitants were able to 
make these channels it would be seen that the same water drunk in by 
the meadows serves several times for this purpose. f 76 v. 

CANALS CONCAVE AND CONVEX 

It is possible that in a canal concave in its length the water flows 
with uniform depth. 

It is impossible for the water in a convex canal to flow with uniform 
volume although the canal is of uniform width. f 

v. 

THE CANAL OF MARTESANA 

A fall of two inches every hundred trabocchi, and these hundred 
trabocchi are four hundred and fifty braccia. 

The greatest depth of the rivers will be beyond the current where the 
water is at rest. H 65 [17] r. 

The more the water falls, the more it leaps. 

On the second day of February, 1494, at the Sforzesca I have drawn 
twenty-five steps, each of two thirds of a braccio high and eight braccia 
wide. 

The greatest depth of water will be between the percussion and the 
gurglings which result from it. h 65 [17] v. 

No sluice should be narrower than the general width of the canal, 
because the water in this event forms eddies and breaks the bank. 

h 76 [28] v. 
[Estimate for canal] 

The canal which is sixteen braccia in width at the bottom and twenty 
at the top may be said to average eighteen braccia over its whole width; 
and if it is four braccia in depth and costs four denari per square braccio 
it will cost per mile for excavation alone nine hundred ducats, the 
square braccio being calculated in ordinary braccia. 

But if the braccia are such as are used to measure land, of which 

780 CANALIZATION 

every four are four and a half, and if the mile consists of three thousand 
ordinary braccia and these are converted into those used to measure 
land, then these three thousand braccia lose a quarter so that there 
remain two thousand two hundred and fifty braccia; and therefore at 
four denari the braccio the mile comes out at six hundred and seventy 
five ducats; at three denari per square braccio the mile works out at five 
hundred and six and a quarter ducats, and therefore the excavation of 
thirty miles of the canal will work out at fifteen thousand one hundred 
and eighty seven and a half ducats. h 91 [43] r. 

The water that falls over its embankments lays them bare and breaks 
them down on the opposite side. h 116 [27 v.] r. 

GARDEN OF BLOIS 

[With diagram] 

a b is the conduit of Blois, made in France by Fra Giocondo; b c is 
what is lacking in the height of this conduit; c d is the height of the 
garden of Blois; e f is the fall of the siphon b c e f; f g is where this 
siphon discharges into the river. 1 k 100 [20] r. 

RIVERS AND CANALS 

[With drawing] 

To ensure that the mouths of the canals which hollow themselves out 
from the rivers do not become filled up with shingle, and also to 
prevent the shingle from remaining in the middle of the dam that has 
been constructed against it, it should be made with a transverse descent. 

k 101 [21] r. 
[Canal of the Ticino] 
[Diagram] 

The declivity of the canal with the small outlets at its bottom. 
I Diagram ] 

All the water a b is that which enters into the canal having outlet 

1 This technical note as to the work of the Veronese architect Fra Giocondo in the 
garden of the chateau of Blois was most probably written by Leonardo while at Milan 
during the French occupation, the information having been supplied him by some mem- 
ber of the French court. 

CANALIZATION 781 

through the openings placed at the bottom; and all the water a C is that 
which enters in the canal having the openings near the surface of the 
water. The water c b having no outlet does not move its mass, and not 
moving it does not enter into the other mass but [this other] will go 
into the Ticino. 

And in order thus to raise the openings make the course of the 
water more [less?] slanting, and make the course slower in conse- 
quence. Then this course in the same time draws a less quantity of 
water in the canal, and the mills receive less than at first although they 
receive the whole of it, and the outlets become full of impurities and 
choked up. 

However I shall maintain the water in the canal at a height of one 
braccio and a half as at first, and the outlets at the bottom as at first, 
and I shall let in the water by degrees. 

k 109 [29-30] r. and 108 [28] v. 

[Notes with drawing of section of Loire] 

LOIRE RIVER OF AMBOISE 

The river is higher behind the bank b d than beyond this bank. 

Island where there is a part of Amboise. 

The river Loire which passes by Amboise passes by a b c d, and after 
passing the bridge c d e doubles back on its course by the canal deb], 
in contact with the embankment d b which comes between the two 
opposite movements of the above-mentioned river a b c d, d e b /. Then 
it turns back by the canal / / g h n m and reunites with the river from 
which it was formerly divided, which passes by \ n and makes \m r t. 
But when the river is swollen it then runs all in one direction, passing 
the embankment b d. b.m. 269 r. 

[French canal — project] 

The main channel of the river does not take the turbid water, but 
this water runs in ditches on the outside of the town with four mills at 
the entrance and four at the exit; and this will be constructed by 
damming the water above, at Romorantin. 

The water may be dammed up above the level of Romorantin at 
such a height that it works many mills in its descent. 

782 CANALIZATION 

The river at Villefranche may be led to Romorantin, and this may 
be done by the people who live there, and the timbers which form their 
houses may be taken on boats to Romorantin, and the river may be 
damned up at such a height that the water can be led down to 
Romorantin by an easy gradient. 
\ Sketch map of Loire with tributaries] 

If the river m n, a tributary of the river Loire, were turned into the 
river of Romorantin with its turbid waters it would enrich the lands 
that it irrigated and make the country fertile, so that it would supply 
food for the inhabitants and it would also serve as a navigable canal for 
purposes of commerce. 

HOW THE RIVER IN ITS COURSE SCOURS THE BED 
OF THE STREAM 

By the ninth of the third : that which is swifter consumes its own bed 
more, and conversely the water that is slower leaves more behind of 
that which causes it to be turbid. 

Therefore when the rivers are in spate you ought to open the flood- 
gates of the mills so that the whole course of the river may . . . there 
should be many floodgates for each mill so that . . . may open and 
give a greater impetus and thus the whole bed will be scoured. 

And let the sluice be made movable like the one that I devised in 
Friuli, where when the floodgate was open the water which issued forth 
from it hollowed out the bottom; and below the two sites of the mills 
there should be one of these floodgates, one with movable sluices being 
placed below each of the mills. b.m. 270 v. 

Here there are, my lord, many gentlemen who will undertake this 
expense between them, if so be that they are allowed to enjoy the use of 
the waters, the mills and the passage of ships; and when the price shall 
have been repaid them they will give back the canal of the Martesana. 

Forster in 15 r. 

That a river which has to be diverted from one place to another 
ought to be coaxed and not coerced with violence; and in order to do 
this it is necessary to build a sort of dam projecting into the river and 
then to throw another one below it projecting farther; and by proceed- 

CANALIZATION 783 

ing in this way with a third, a fourth, and a fifth, the river will dis- 
charge itself in the channel allotted to it, or by this means it may be 
turned away from the place where it has caused damage, as happened 
in Flanders according to what I was told by Niccolo di Forzore. 
[With drawing] How one ought to repair by means of a screen a bank 
struck by the water, as below the island of Cocomeri. Leic. 13 r. 

FROM 'THE ORDER OF THE BOOK OF WATER' 

No canal which issues forth from rivers will be permanent unless the 
water of the river from which it has its origin is entirely closed up, as is 
the case with the canal of Martesana and that which issues from the 
Ticino. 

The canals ought always to be provided with sluices, so that excessive 
floods may not damage or destroy the bank and the water may always 
maintain itself in the same volume. Leic. 18 r. 

How in order to twist the line of the water one should make a twist 
in the line of the bank with a few stones : By the fourth of the second, 
where it was proved that the line of the water of the rivers was a con- 
course of the reflex movements of the water that has struck upon its 
banks, and has there multiplied and raised itself and hollowed out its 
bed beneath itself. And this is what would occur if anyone set out to 
twist the bank when the river a certain space above had shown that it 
wished to bend, and then had not continued this bending process, and 
you were to follow it up again gradually and minister to its first desire 
with an almost imperceptible curve; and thus you will proceed to make 
your attempt. But if you should try to bend the water in the direct line 
of its strength all your work will be in vain, because it will break every 
obstacle. And if with your lock you raise the level of the water so high 
that it swallows up so much in itself that the current loses its impetus 
in the expanse of water that has been formed, this can have a good 
result, and, by the fifth of the first, it will fill up all its bed with mud, 
But make it so that the water does not run along the bank. 

Leic. 27 v. 
[Of diverting a river and protecting a house] 

I have a house upon the bank of the river, and the water is carrying 
oflF the soil beneath it and is about to make it fall in ruin; consequently 

784 CANALIZATION 

I wish to act in such a way that the river may fill me up again the 
cavity it has already made, and strengthen the said house for me. In a 
case such as this we are governed by the fourth of the second, which 
proves that 'the impetus of every movabe thing pursues its course by 
the line along which it was created'; for which reason we shall make a 
barrier at the slant n m, but it would be better to take it higher up at 
o p, so that all the material from your side of the hump might be 
deposited in the hollow where your house is; and the material from the 
hump ^ would then do the same, so that it would serve the need in the 
same winter. But if the river were great and powerful the said barrier 
would have to be made in three or four attempts, the first of which, 
made in the direction that the water is approaching, ought to project 
beyond its bank a fourth part of the width of the river; then, below this, 
you should make another, distant as far as the summit of the leap that 
the water makes when it falls from the first barrier, — for in this summit 
of its leap the water leaves the summit of the mound made by the 
shingle which was hollowed out by the first percussion, made by the 
water when it fell from the first barrier upon its bed. And this second 
dam extends halfway across the breadth of the river. The third should 
follow below this, starting from the same bank, and at the same fixed 
distance from the second as the second was from the first; and it follows 
its length as far as three-quarters of the width of the river. And so you 
will proceed with the fourth dam which will close the whole river 
across. And from these four dams or barriers there will result much 
greater power than if all this material had been formed into one barrier, 
which in uniform thickness would have closed the whole width of the 
stream. And this happens by the fifth of the second, where it is proved 
that the material of one single support, if it be quadrupled in length, 
will not support the fourth of that which it used formerly to support, 
but much less. 
[Drawing] 

I find that the water, that falls at the foot of the dams of rivers, 
places material towards the approach of the water, and carries away 
from the foot of the dam all the material on which it strikes as it falls. 
Now I could wish that it would place the material where it falls, and 
thereby bank up and fortify this dam: which thing might be done in 
this way — Leic. 32 r.