21_BOOKS_ENGINEERING_MACHINES_EnglishTranslation_PartV

The three Books Of the fifth part which the Catholic King Philip the second ordered his chief engineer Juanelo to write and explain

Consecrated to his Catholic Majesty by the hand of his majordomo Juan Gómez de Mora.

FIFTH VoLUME

The Nineteenth Book deals with constructions in the sea: how they are to be built and fitted out in various ways.

The Twentieth Book deals with making defences for ports so that fleets can not enter

The Twenty-First Book deals with divisions of water, as well as islands and other things concerning water

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NINETEENTH BOOK Introduction Harbours The constructions in the sea to which the title refers are harbours, their moles, jetties and sea-walls. This book, and Book 20, comprise the most extensive study of harbour design and construction to bave survived from any time earlier than the eighteenth century.

Indeed these two 'libros' were the subject of Vigueras Gonzalez' monograph on Spanish port technology of that era, (Vigueras Gonzalez 1979), in which he presents a detailed analysis of these books in their historical and engineering context.

The extension of natural harbours into the sea by building moles goes back to Antiquity, and remains are found on sites around the Mediterranean. The Romans however were more ambitious in such enterprises than any of their predecessors, and theirs are the ports whose traces can still be seen in Spain, and beyond, in Britain, for example, as well as eastward as far as Caesarea in Israel. O ur text therefore looks to Rome for exemplars and inspiration, as so often. Vitruvius has a chapter on harbours but it is mainly devoted to the cofferdams that will be required for any building into the sea.

Alberti also deals with the subject as part of architecture, and bis treatment is much broader; he offers his observations on marine erosion and deposition, and suggests how harbours can be protected (X.12). Earlier (IV.8) he had set out his views on tbe ideal port.

This was a period of enthusiastic enlargement and improvement of ports in many parts of Europe, such as Dover barbour in England and the new port of Le Havre in France. In Spain, too, in tbe latter part of tbe sixteenth century tbe chief ports on tbe Mediterranean began to catch up, with new moles built or old ones reconstructed at Barcelona, and furtber south at Cartagena and Malaga. During the Middle Ages the Mediterranean ports had been the country's principal outlets for overseas commerce, but once traffic across the Atlantic to the Americas got under way, they had inevitably fallen behind and were now keen to expand.

As so often, Alberti provides a starting point for our text, which opens with similar observations on erosion, and propases a method of reducing scour by means of a concave harbour wall, so tbat the waves will fall back upon themselves and disperse their energy, partly on following waves. This section [395r-398v] in effect takes up Alberti's theme, which was the first attempt ata general theory of the impact of the (551]

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sea on clifferent shorelines. Our author, for instance, develops Alberti's comment that the effects of marine action are more obvious where the sea beats against a cliff than where it advances gently on a flat beach; and that the depth of the water increases more rapidly by a rocky shore. Alberti recalls the ancient doctrine that rivers extend the land into the sea. His examples are drawn from Classical accounts, mainly Greek, although in ltaly too he could have pointed to deltas encroaching on the sea.

Although in our text erosion is portrayed as Nature's great destructive force wearing away at human structures, in fact more Ancient harbours were lost through the deposition of silt and the retreat of the shoreline. So Ostia is now inland, and traces of the Reman harbour at Tarragona, here noted as vanished, were only uncovered in the course of nineteenth century building operations. In our text, the author shows how a mountain promontory will act as a giant breakwater, setting up cross-currents and diverting the waves so as to scour the inshore bed and prevent deposition. All these observations are, it is true, generalised and qualitative; they build on what Alberti had written rather than raise original problems. Nevertheless they do present a vivid and imaginative picture of the role of the sea in shaping the coast, intended to help the architect learn how best to build any structure exposed to the sea. As usual, the Ancient philosophers must have had their opinions too, which must be heeded, here specifically on the tides. The engendering of beach sand from rocks and water is also a typically ancient Ionian concept; the image apparently implies that when sea water dries out sorne viscous residue will remain, a notion that possibly comes from looking at the high water mark detritus- and this will eventually congeal to form this 'crust'.

These ideas are utilised to propase a series of harbour designs. Alberti had ser out his ideas on the prerequisites for a harbour, which may have influenced Francesco di Giorgio to include a chapter on ports in his book of architecture, illustrated with sorne pretty designs. Here however the harbours are laid out according to geometrical principies.

Ideally, the basin should be circular, but that might not be easy to build and would not allow for straight quays at which ships could moor. So the text starts with a little discourse on polygons, explaining how as the number of sides increases they approximate to the circle. His command of the terminology does seem shaky. At times 'angulas' should be translated 'sides' rather than 'angles'; and the octagon in particular gave him trouble. Severa! harbour designs are shown, and his basic design for the harbour wall; after the geometrical passage, he gives more harbour plans, and no less than six versions of the wall. Since he often compares the assaults of the sea to artillery bombardment, although well aware that there was a significant difference, that model may have given him the idea to give bis walls and embankments a batter on the seaward face. The concave wall does not seem to have been tried anywhere; perhaps it was too imaginative.

Arcaded walls too were perhaps adapted from the casemates of fortifications, and do appear in sorne later quays. Towers here are for defence andas lookout posts, so if they carry a light it is to let sailors know where to find the harbour entry, not to warn them of rocks and reefs.

Book 19 is noteworthy for the long passages which do not describe structures or artefacts but denounce incompetence and parsimony. Clearly, the author saw himself asan architect, a man knowledgeable in theory, which for him meant geometry above all, whereas ordinary master builders and military engineers are the targets of his scorn.

These lengthy tirades must surely conceal sorne personal disappointment, frustration when his good advice was not accepted, and less able men, as he believed, were given the job in his stead. In their very subjectivity these pages do let us get a little doser to the author; despite occasional asides elsewhere, this is the only place where he truly lets himself go.

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Book on constructions in the sea: and how they are to be built and /itted out in various ways

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ortifying buildings in the sea is an undertaking that demands great forethought and prudence, specially in the matter of the walls, which should be made very firm and solid, so they can resist the great fury of the waves. Ordinarily, works which are constructed where the sea will strike them, should be smooth, and have nothing to catch the waves when they strike, but must let them slide up and down, and as they go down break the fury of the next, as it comes up behind. That way they will not do so much damage as if they did not fall back. We shall make an illustration so what we are saying can be better understood. Very thick firm walls are constructed where the waves will strike, so they can better resist them; that is, those which face the sea must be battered like a barbican or with a bevel, so the waves find nothing against which to break. And if they were to be built on a concave line, that would be best [!fol. 394v].

Let us take the case of wall A which stands toward the sea, facing the waves: B is the top of the wall, the foundation, which is to be of very strong and plentiful material. The base is to begin as a curve as shown at letter D, so that the waves have nowhere to break, because the line of the wall A forms an eighth of a circle, and there is no place anywhere for the impact to be felt. So the wave flows on for a great distance borne along by its own fury, allustration 396) and goes right up in such a way asto fall back afterwards with the greatest fury and Ă­mpetus. So the waves break up by themselves, for they can not go so high asto reach B; the concave line makes them drop back without striking anything that will do any harm. [!fol. 395r] This may be dearly seen, because we observe that the flatter the sea shore the less powerfully do the waves strike it. Indeed, we see that they do not remove anything from the shore, but there discharge what they bring to land.

That does not happen when they find something high before them, for then as they see that they are resisted, they apply all their force to overcome it. That is why it comes about that we observe greater depths there than are to be found anywhere else. And no other cause or reason can be found for that, than that the sea does not want anything to oppose it, except for the air. If any other thing should be put before it, then it endeavours to break it and smash it. That is the reason why the greatest care must be taken in construction in the sea.

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Illustration 396

T o forti.fy buildings in the sea with embankments; these are very different from those made in river works, because floods are not continuous like the waves of the sea, which do not cease by day or night and thereby break clown whatever they find befo re them. Yet it does not happen quite like that, beca use the sea does become calm and quiet, and if it moves that is on account of the winds which forcibly produce its movement. That is why the waves come one behind the other in succession, and die out on land, on the shore or strand of the sea. Therefore if something that is rough and craggy but straight up stands before them on the shore or strand, then the waves will strike it with the greatest Ă­mpetus, [!fol. 395v] and with their impact they will leap up on high, and keep breaking, and when they fall back, they will drop clown shattered. Another thing: the waves keep on scouring away at the base of the work that is before them, continuously and without any intermission, and with so much violence and fury that as they fall back they will bring clown any work however firm it may be. That is so, but the depth of the bed does not show it: the sea has this character, that it levels out at the shore, but if the land keeps going down, provided that it is flat, then when it is struck by the waves, not finding any resistance, they do not scour away the ground. Therefore when the sea is disturbed, sorne of them struggle with those that come behind them, striking one another. Then the sea Ieaves off its fury and Ă­mpetus, and when the waves are calm and quiet, they go back by themselves. And if something is carried away or transported because of the movement of the sands, it is left in the calmest and quietest place. From this it may be realised that when the strand goes clown toward the sea with a gentle slope, it is daily loaded by the sea, (Illustration 397) [!fol. 396r] and so it keeps on growing and loading up to seaward. But when the sea strikes a mountain at sorne point in the manner indicated here, then the waves divide, and traverse a great distance running along the shore, crossing the waves which come from out at sea, which break those which go along the shore; so they break up themselves.

The mountain is to be in the sea, and the shore is parallel to the foot of the mountain, which meets the sea, and its banks are N O. In this way, the waves at [554]

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Illustration 397 This mounrain is to stand in front of rhe wall that is struck by the sea, to illusrrate the effecrs produced by the water on impact

this place will flow from M toward N andO, on the other side opposite N. So from the point M to the O, the end of the mountain, where the strand begins, it flows toward P. And it does the same toward T, from N, and so the waves flow toward N with the greatest fury after they have struck the mountain at letter M; and from N toward T, and likewise from M to P. Thus these waves break up the rest, which come towards the shore froro the sea, without striking the shore at all.

For this reason, by this arrangement it flows for a very long stretch. Everywhere in these places, long deep channels are found, [!fol. 396v] breaking all the other waves which come crossways, so as not to leave any deposit of sand, specially at the sides of the mountain. So I say that a port that is made in this fashion, as it is drawn here below, shall never have its mouth or entry blocked or filled up. And that is quite certain. The entries can in no wise be closed because of the ingenious plan with which it is made, which diverts the water. That is the reason why it does not give any trouble, save only at letter A, for there the water has greater force than in any other part of the whole construction. There is a fortress there too.

(Illustration 398) [!fol. 397r] Sorne philosophers say that the sea has its ebb and flow by its nature, considering it in this manner: they say that no man who is on the point of death actually dies save when the tide is ebbing. This in itself almost contains the argument that the sea has in itself this nature or spirit or regular motion which corresponds to the life of man. But the increase and decrease of the sea is a very commonplace matter, even though it does vary in sorne places, since in Negroponte ít rises and falls six times 1 over the day and night, whereas at Constantinople it does not vary in the least, any more than it does in the Black Sea and the Propontic.

The sea is of this nature, that it casts up on the shore all those things which rivers carry clown to the sea, because those things that move by themselves, afterwards find a resting or stopping place where they can hold fast; so then we see that the sea regularly conveys to land a great quantity of sand, and sometimes leaves stones which it casts up on the land. The philosophers say that sand is made of mud 1 'at Negroponte it rises six times' ... this is the old Italian name for the island of Euboea, from rhe strait of Euripos whose movements baffled Ancient philosophers, more used to the mínima! tidal flow of much of the Mediterranean, here partícularly referred ro the Black Sea and the Propontic (the Sea of Marmara).

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1/lustration 398 House for munitions House for making vessels-Arsenal Warehouses for keeping merchandise

Port Houses for keeping merchandise

which has been dried out by the heat of the sun, which causes it to divide into different parts. Besides, they say that stones are engendered of sea water, because the sun heats them, and once heated, by reason of their motion they get dry, and once dry, they are joined together to form one body; and having finished by· consurning the subtler parts, they are joined in that thiclmess. Now sornetimes the sea grows sornewhat quieter, and causes in thern a certain smooth rnuddy crust. {/fol. 397v] Afterwards this crust breaks, and is continually worn away with the rnovernent, as it is lmocked about. So they are turned into a sort of clod like a sponge.

These clods are later cast up on the shore, and then take in much of the sea sand that is being moved about. They dry out with it because of the sun and the sea, and as they dry they condense upon thernselves, and in the passage of time they harden in such a way as to become stones; and that is what sorne philosophers have said. True it is that we see many stones growing at the mouths of rivers, especially if they are travelling through plains or rnovable land. And therefore rnuch sand and stone is added to many rivers from either side, in the manner of a rnound or fence; and they make the coast enter further and further into the sea, which rnay be seen in various regions.

Returning to our subject: in addition, the waves have a certain inherent nature such that when they strike a wall made of very large stones which are so laid that [556]

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the waves must strike them, there they offer the greatest resistance and opposition.

So the more they go up the more they want to come down and dig away the foundation and the sand underneath this wall. This may be seen in places where there are cliffs, for there the water of the sea is usually found to be much deeper, [/fol. 398r] and in such places the sea strikes more powerfully than where it does not encounter anything. The more it knocks into something befare it, the more it endeavours to tear it to the ground. Only a flat coast is not so much troubled by the waves as that which is elevated. With this matter of shores that are naturally flat, it will be a question of the greatest ingenuity to know how to control and tame the furious waves of the sea. For that cause and reason, the sea greatly deceives men. There is so much art in it that if the hands of men are to do it at all, they will not curb the waves so easily, as many think they can, especially in the matter of the sea. It will be a great help to give these buildings large bases; that is to be understood of the foundations, which are to be made in the manner that has been spoken of in respect of the foundations of the piers of stone bridges.

If the need should arise to fortify a port, or protect it, or sorne mole should have to be made in the sea, embankments would have to be made, or in case they have to be reconstructed anew, then you should begin on land, out of the water, I mean where it ís dry. From there we begin to excavare the foundations raising walls of a good size, properly made, stout and robust. And so proceed, working on and entering the sea, excavating and making proper embankments for defence against the water, [!fol. 398v] according to the instructions we have given for the piers of stone bridges. It ought not to be done all at once, but piecemeal, now one side, now the other. The first thing that ought to be done, is to excavare the foundations as deep as possible, so that there may be a fi.rm base, where thís wall, or very thick strong rampart is required- because it is to be twelve to fifteen feet thick, and the stones as large as can be. This wall is to be built toward the sea with a batter like a barbican, as figure A shows. (Illustration 399) It should have this batter or slope like a barbican, made with artífice and arrangement of geometry [!fol. 399r] so the striking of the waves will not crash against anything straight. The Illustration 399 Sea Foundation

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11/ustration 400 No barbican or glacis for barbicans should be made from E clown. In cities they are made from K to 1, in the walls of harbours from H to C; from there on downward they get so flat that anyone may get up them, and they would be good for nothing

e D

most appropriate line, is to take a perfect square, and divide it from angle to angle.

It is true that it inclines more against the ground, as may be seen in square M- the diagonalline that divides it is A B- that is the line that is used in the barbicans of city walls, because nobody can climb up by that line. But if another line were drawn, lower than A B, that is A e, it would be much better; the water will travel along it very well. And if another lower line were drawn, that is from Ato D, the water would find so much the less resistance as it travelled along it.

From B downward no more lines are to be made, for walls or barbicans: if I have made the other lines, it was more to show how much more level the water would flow along those lines, through finding less resistance in walls like that. But if another should be drawn lower than from A to E, the water would flow along it with greater ease, and more from A to F allustration 400) than any of those above it. The waves slide along more easily and break up those which come behind them; and in this way the waves will do less damage [!fol. 399v] since the waves that affect wall A would find nothing to offer resistance. If this wall were to be made plumb upright, it would resist the waves with more violence than wall A, whĂ­ch is inclined toward the ground, so the danger is plain to see. As the struggle of the waves is continua!, never ceasing day or night, the walls suffer great damage from their opposition. That is why it has been stated that they ought to be battered, or have a scarp, or a barbican, or a glacis, or talus, or whatever you like to call it. In my judgement there is no better kind of wall to resist the wild fury of the waves. The lines are marked on the square M, even though sorne of those are better than others, according to the instructions I have given for each particular one. The waves then travel along these lines not as a body that breaks, but as a body that slides along by itself, as I have said, and travels very gently. Thus the wave will turn back on itself, and receive the impact of the others. And that is why they become slower, checked as they strike, and they meet wall A with less force.

A is the defence of the harbour E. B e are two entries, so that if the winds are contrary the ship has a place where she can take refuge. D is the ship's entry to the harbour. The two docks F G are used to keep old vessels and galleys, at least that is F, {/fol. 400r] and G is for caulking and fitting ships out properly. L is the entry of dock F, M is that of G; at K there are bases of columns to tie ships up. H is the warehouses or stores to keep merchandise: I performs the same office. allustration 401) N is a tower which has two functions2, the first to give light by night to guide sailors, so that they realise where they are going and can make harbour. The second is to defend the harbour against enemies, and attack them: and to be recognisable from afar. B is a chain to close the harbour. O is the eustoms-house, where the 2 'a tower which has two functions' ... such towers appear on many contemporary depictions of harbours. A few have survived, for instance at La Rochelle in France, where the chain that was once slung between two of them has also been preserved. Th.e light however was carried on a third tower nearby.

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I/lustration 401

A

150 paces 600 paces in diametes

150 paces

various merchandise is registered, I mean what they bring into the country and what they take out of it.

The engineer will be well-advised- and if he does so highly to be praised[/fol. 400v] if before he sets hand to the job, he first sees and discusses whether such an edifice can be constructed, for it would be rash to try and undertake things inherently impossible, which would be contrary to their very nature, as that nature would always strive to defeat its opposite rather than be defeated and overcome.

But on the contrary we see that men take no account of any of this, but undertake such important works thoughtlessly and on the spur of the moment, with all good counsel set aside, to suit their own judgement; for we see them revolving and twisting with great ingenuity a little of what is its own proper nature. In that way such men are humiliated, leaving a bad name, and their credit fallen, because they built a work which Nature managed to cast down in a short time, for she has no patience to endure any obstacle before her. And there she exerted all the opposition she could to put her adversary to flight and annihilate him, until she saw him yield ... I do believe I have saĂ­d a deal too mu eh, as I would not laek examples to prove my purpose: so I shall deliver myself from slander and respect the reputatĂ­on and honour of all engineers without abusing anybody. Nor I think, will 1 be blamed for having enlarged on this so much, for it was not beside the point to condemn in general without naming anybody, as it is known that there are sorne people so thoughtless, as that man who wanted to make a bridge of boats that would go right across the sea. Let no critic or libellous satirist snap at [559]

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me; whoever wants to make use of me may learn, and the wise may praise my labours and my zeal. That all that has been said is the truth, I shall bring examples to illustrate; I have truth in view.

[!fol. 401r] What became of those ports that were so imposing and renowned, in that golden age, the work which the ancients made with so much ingenuity, subtlety and beauty? Let the waves of the ravaging sea tell of it; now they are no more to be seen, there is no memory of them. Gone is the port of Claudius near Ostia3, close by Terracina, Hadrian's port has lost its works, andas for that of Julius Caesar its buildings are overthrown, although the place where it was built may still be seen today, whereas nota sign is left in Tarragona. They were works which it seemed were to last for ever and would never have an end. But the sand and the force of the water has choked them and closed up their entries and left them high and dry, to such an extent that the harbour which Julius Caesar made, or the place where stood the one at Tarragona, are now entirely dry, for today all is gardens which once served for the safety and laying up of ships. What has done it? Time and the force of water, which never stops attacking and fighting against whatever is opposed to it without ceasing for a moment until it gains the victory.

Let builders then take good note, and with reason, if such excellent designs and constructions raised by such sublime judgement we now see levelled to the ground without leaving any trace of them, what then will happen to those which we now presume to erect, so rashly, and in plain madness. Now that it has been shown how valuable these buildings are, and how important it is to leave them secure and in complete perfection, so they will by themselves shake off their opponent, who líes in perpetua! ambush for them, and assails them [/fol. 401v].

That would be a good reason why anyone who builds such a structure should think well how to undertake it, what place and site to choose, the stores and materials he should employ, and how he may bring his work to its due conclusion.

For eventually it will have to be left alone, subjected to the injuries of time and raging storms of the sea, which will beat against it with their continua! motion. And there may not happen to be anyone in charge who knows how to repair the damage it has received. Let each man then consider that although he is prudent and experienced and very self-confident, it can happen to him as to the wisest: for he is in conflict with an element so powerful that it is going to harass and undo his handiwork with its sudden and continua! attacks. Although he on his part may have done whatever was possible, nevertheless there will be something for which he may be blamed: yet he had finished the work properly and set it up right; then let them say what they will, if there should be something, it will not be his fault, but due to the carelessness of the inhabitants or the landowners who took no care to inspect and repair the structure which was so important for them. For the engineer has already made good account of his talent by leaving the work in a suitable state; it is not his business to make it perpetua!. So let them keep the structure in good repair, nor spare their purses, for the materials which these gentlemen gave the engineer were what he used: and they are perishable, not 3 'gone ís the port of Claudius near Ostia'... our author may have vísited the site of Ostia, with the hexagonal basin added by the emperor Trajan (2nd century AD), in the light of his drawing and descriptíon (425v): although it did not have the zigzag passage co the sea whích appears in the sketch. Possibly this reconstruction is an interpretation of other 1uins or dikes in the neíghbourhood: which may also be the case of the port at Terracina, a long way from Ostia or the other great Roman Imperial port at Cívítavecchia.

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Nineteenth Book eternal, and so must cometo an end. Let them mend it every day, and so preserve it without ever seeing it a ruin. Considering all this, let whoever is in charge see if his talent and deverness are really so great that he can achieve his enterprise alone, and if not, [!fol. 402r] consult learned engineers, and submit to their opinion, without ever relying on himself alone, otherwise there will be nothing that looks right and ís useful. Let him observe too, who has ordered the work to be carried out, and in what place, let him ask freely for whatever is necessary, and not accept any scrimping. But let the material be good and perfect, with good and intelligent men overseeing the workers- let him not rely on them, but keep looking at what they are doing all the time, and make sure of his work until it is left in a condition that satisfies him. If he does all this well, he can undertake any job whatsoever, as he resolved to make a beginning of his construction with so much discretion and sagacity, and ata measured pace.

The most important key of a city is its harbour; which serves to defend it from its enernies, to supply it with the means of subsistence, and with all those things necessary for a community, because merchants will not fear to come there with their heaviest ships, laden with many different kinds of goods, seeing they are going to find a safe harbour for their ships. Let us then call the harbour a receptade of ships or different kinds of vessels, where they may be safe from the storms and great tempests at sea, which could afflict them. The harbour serves also as a great ornament to cities. What a fine thing it is to see the harbour full of different types of craft ladeo with uncountable merchandise, and goods brought from various remote nations. What beauty, what satisfaction for the residents to see so many provisions enter their native place without having to send for them; [!fol. 402v] and to see such a diversity of nationalities buying their merchandise, free of every risk and danger, without their having to go to any expense, orto tire themselves out on roads! Even if the harbour serves for nothing else but to be a suitable place where Kings can keep their fleets sheltered and free from any storm, that alone would be enough for us to understand how essential and ímportant a construction is a harbour. (Illustratz"on 402) A harbour built as a hexagon has less sídes than one made with eight sides: thas harbour is not so much of a haven as those which have more angles to protect more ships from storms. The entry to the harbour is A, where the chain is made fast; it is drawn up into the tower C-1. D are bases of columns for tying up ships. F is a level area which goes all round the harbour, andE a colonnade in front of those warehouses G, for keeping merchandise. The part H is the house where the merchandise is regístered; the entry of the harbour is near land. [!fol. 403r] When a harbour is to be founded, it should be made fírm and secure from every wind that could trouble it. Let its sides be very strong and high, so they can resist every storm, let it be of great width, and level so that ships may have a free entry, and be sheltered from all harassment by the weather. All these things must always be kept in view in order that the work may go well, and thus there will be nothing to desire, unless it be a fitting place so formed by its own nature- as was the one the city of Athens had, which had three harbours4 made by the Most High and Vast 4 'the one the city of Athens had, which had three harbours' ... near the m a in harbour of Piraeus there are two smaller coves, k.nown in Antiquity as Zea and Munychia. Alberti describes all three as «naturales», which Bartoli translates as «fatti da Natura>>- here they are made by God the Creator. .. so when the forces of nature work to our disadvantage, by destroying ports, Nature is to blame; when they serve our convenience, God gets the credit.

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Volume V Illustration 402

Maker of the Universe. These three harbours were so excellent that it often carne about that mariners did not know in which one to disembark, since all were so good that they could enter any of them in safety. It is very evident that there are sorne passages so dangerous that they can not be navigated because of the winds, nor, since they are so troublesome, is it possible to go in or out of harbour in any way, but only to wait for a few days until entry or depru.ture may be safe. So always ensure that the harbour is secure so that ships will go to it for that reason and sailors may say 'let us go to that harbour which has safe and gentle winds'. The north or boreal winds they say are very convenient; after the wind has stopped, the swell does not stop. When the sea is moved by the wind called grieg<Y, when it stops blowing, [!fol. 403v] the swell stops too. With the south or austral winds, although they may have left off blowing, the swell does not stop, bur rather seems to grow more violent.

You ought to choose those places and materials that suit ships best; as are places of great depth. And let the harbour have a good entry so as not to obstruct ships which come loaded with a very great weight. Care is to be taken to clean out the harbour so that no weeds, nor anything else harmful may grow there. Although we do see that often weeds provide sorne advantage, for anchors take better hold there, although it is very belatedly, I say that I would wish the harbour kept clean ' 'the wind called griego' ... the north-east wind- for Italians the Greek wind.

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at all times, and free of all obstruction, because for the most part all these things do more harm than good, spoiling the air with theír foul exhalations, and so are the cause why ships which stay there a long time get spoilt, because of the seaweed, Javer, reed mace, and other plants that grow in water. We know for certain that where these plants grow, they give rise to harmful grubs and worms in ships; that happens because the water is corrupted by the rotten vapours of the plants, and ·so the place becomes unhealthy and harmful, [!fol. 404r] and all the more if the rain drains into it from mountains, because that brings clown much dirt and filth with the earth. The harbour has to have sorne spring or wells of sweet water nearby, to provide water for the ships: its entries and exits are to be free, easy and direct, and such that the ground there can not be changed nor undergo any variation on account of the deposition of sand, nor suffer obstruction from it. Besides, it should have sorne high mountain near, so that sailors can make out the harbour.

Inside the harbour, there ought to be a quay and bridge, to load and tmload most easily all the merchandise that comes by sea. The ancients customarily did all this in their works, I mean in different ways, having steps all round their harbours, and on the second step sorne pieces of columns to tíe up ships, and likewise sorne big iron rings for the same purpose. It should have considerable width all the way round, for walking along, so there will be plenty of space to put the merchandise which is being loaded and unloaded, without causing any obstructions. There are to be colonnades along the sides. There is to be a Church too, so the mariners can hear Mass and perform their devotions. Nor should there fail to be all those things that are needed to make a harbour beautiful, specially blocks for mooring, stone hooks or ties to attach the stones together. There ought to be many warehouses, [!fol. 404v] vaulted, so that every one can store his goods under cover. At the two entries there ought to be two very high towers, to hang the lantern, so that sailors can see by night where they are to make port; and to know by the lantern's light what sails, what people are coming, if they be enemies or no. At the entry of the harbour there ought to be a very strong chain to prevent the enemy getting in, and so that ~hips can not go away without paying the dues they owe. At the sides of harbours, smaller harbours should be built, to keep old or damaged vessels, and on the other·side to fit out, mend and caulk ships and other craft, so that they can be better tended there, and not become an obstruction to the other boats in the harbour. Then harbours must have a great square, for the convenience of those who sell goods. Besides, the harbour should have many points, in particular: the first is to have a very good situation; the second, the shape; the third, the material; the fourth, a good entry; the fifth, safety and strength; the sixth, a good place to load and unload; the seventh, security from enemies, to defend yourself from them, and guard your land quite safe from sudden invasion or surprise attack by any enemy. [!fol. 405r] Harbours are to be built in such a way asto have entries to suit the winds that blow in those parts; there should be sorne protection to keep the winds from being troublesome. The shape of harbours is to be on a sphericalline, as if to forro a pentagon·, which is of five sides, or else of six, eight, ten or twelve, or more according to the site, and the direction given to the winds by the position, or by the mountains that surround it. The best rule that can be given is, that it should be so arranged that the harbour is not troubled by the winds, but well sheltered from the annoyance they can cause, even if everywhere the wind is one and the same and the [563]

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Volume V mountains and rocks are one and the same, and although there is one and the same sea. We could give a general rule, but in each place a new k.ind of device should be used, in the plan, or the walls, or entry and exit, because in one part sorne winds prevail more than others, and in another land another, contrary wind prevails, and so at different times in different regions of the world clĂ­fferent effects are produced: it is the same with the seas. So I think it would not be inappropriate to set down illustrations of harbour designs, as may be seen drawn here. to show a harbour that has more than twelve angles, here below there are many more than this numberbut for my part, [!fol. 405v] I take it no harbour has ever been made with more than twelve angles, or at most two more. Indeed there are very few that have so many, because the more angles there are, the greater the difficulty in fitting them all in, specially in large things to accommodate the little. That is the reason why so few are seen, as I say, and most are of six or eight angles. But there is no doubt they could be made with countless angles with the greatest of ease, (Itlustration 403) and could be made round with less labour than with so many angles. W e should now proceed to give the method and procedure of each one of the figures drawn above, and how they should face the sea, so you can avail yourself of them. But I only want to give instructions {/fol. 406r] on the difference between one figure, and its method, and another- how each one has more or less strength in one place than in another, and how they really ought to be situated; for that is what matters for the stable construction of a harbour.

Illustration 403 Pemagon Hexagon Hepragon Ocmgon Henneagon Decagon Hendecagon Dodecagon Globc

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Let us now deal wíth each of the aforesaid figures. The pentagon is a round figure, it has less angles than any of those on which we have given instructions, although there are two other figures which have stillless, the triangle and the square. The triangle has less than any figure in geometry, and so has less capacity than any, so it was never of any use in making a harbour. And it is the same wíth the square, it too is a figure of little capacity, because of its right angles, and · therefore does not serve to make any shape, wíth one angle more than the triangle and one less than the pentagon. So this figure does not approximate the circle as the rest do; hence I do not deny, that no triangle could serve for any harbour, all the space would go into the angles, and if it should happen to be built, it would not seem right. Since it is a figure of little volume, h arbours have not and will not be made in thís shape, whose capacity is not more than half that of the perfect square. As its capacity is so slight, there is nothing in it to detain us. [!fol. 406v] The square is a perfect figure, more so than the pentagon, but it has much less volume than the other figures, for the more they approximate the circular figure the more perfect they are, and the more their sides approximate to equality, the more lines there are to the centre, and their angles and bases become more perfect.

And the more the lines drawn from this point are equal, the more perfect shall be the figures or shapes which by this equality share in the perfection of the circle.

Now this subject has been well examined, and there is no need to waste any more words on it. allustration 404) Itlustration 404

l

So I set clown here these four figures6 which are to illustrate what has been discussed on the subject of shapes, their capacity, and the differences between them . These figures are equal in their angular circumference, so that all the lines A B C D E F [!fol. 407r] proceed from the point G; that is M; and this N is the hexagon, whose angles are the same as appears at M. lt is the same with the square D whose angles are G H I K, so the line proceeding from K to G is equal to the other lines of the circle. As wíth the hexagon N, so the same lines appear in the square P and the triangle O; alllines are equal from that point G to the side of the hexagon T. And the same wíth square S proceeding from point G to base S; and likewise with triangle O from point G to L. From this it is very clearly demonstrated that line T is greater than S, and S greater than L. And from this the capacíty of all of these figures is proveo.

6 'here I set clown these four figures' ... i.e. triangle and square are one diagram, so asto demonstrate four 'figures'. The meaning might have been clearer if aJl had been shown inscribed within the ci.J:de.

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11/ustration 405 Sea Land

A

Let us then retum to the proposition with which we began. I say that the pentagon is the figure, which fits the circle more than either of the other two of which we have spoken, the triangle and the square or cube. To form or construct a harbour upon thís figure, care should be taken to lay out one of the angles of the pentagon toward the waves; and let it be done as here portrayed. (lllustration 405) I do not indícate the entry of the harbour because information should first be obtained about the winds. [!fol. 407v] I do not mean knowing how many winds there are, nor what names they may have indívidually, but about which winds are harmful for the harbour entries- since every part and region has íts own specifíc winds, which have more strength there than elsewhere, and for that reason close attention should be paid when desígning a harbour to the frequency of the winds prevailing in that province. The apex of pentagon F is placed toward the sea because of the force the angle G makes against the waves, breaking the waves which strike it, so that they will flow along the two sides H I for a great dístance, without being able to hit eíther of the two bases directly, only obliquely, and so not at full power. Besides, the other two sídes H K and I L are not affected by the waves at all because they retreat at these two places. This makes the water more peaceful there, and ít deposits the sand which it normally carries. The sea does not damage the foundations of the other two sides G H and G I, because the waves keep breaking upon themselves, almost without striking these two sides, as has been stated. Figure A has the pentagonal shape, but is placed differently than the rest with regard to the waves. For it has one base, B e, facing the waves, which strike it at full power, [!fol. 408r] so that there is nothing to protect them orto resíst the fury of the waves with the continua! motion they produce as they move the sand of the sea-bed. From this it may be seen wh at a difference results from planning one shape rather than another. It is true that the two sides B D, e E take very little punishment from the waves, as they are struck obliquely; the waves upon these two bases flow on to the end without turning back this way or that, and the others, which come up behind them continually break on those which flow along the bases B D, e E, which therefore do not take any harm. The same difference between angle G and the base B C holds good between the two distinctions, D G, B O . It is true that the angle Gis susceptible to greater damage than any other part of these two figures, but ít is there much thicker, because of the obtuse angle where 7

'the two distinctions D G, B C'... unclear.

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Nineteenth Book the two walls G H, G I, meet. So it has very great strength at that point, because the two walls serve as buttresses for the angle. That can not be done in figure A, since DB can only help angle B, and CE likewise can only help angle C, but the whole distance from B to C is left without any protection, and nothing will help it at all.

The hexagon is the second figure or shape derived from the circle, and h~s six sides; it should be so fitted, if it should be laid out to make a harbour, [!fol. 408v] with such art and skill that the impetuous waves can do it no harm, in so far as the form can affect it. For these shapes need to be laid out with ingenuity, not just haphazardly. For one type will have more strength if laid out in one manner rad1er than another, assuming that the shape is the same with the same capacity, the same quality of material, the same bodily form or corpulence- that is, the walls- and with the same angles. For all that, it will have more strength and value, because time will make a great difference between one kind and another, as I have stated and illustrated in the pentagon. So, although the figures have the same quantity and quality and material, there will be great difference between their situations.

As the same form will teach this, I shall not keep on expanding on myself but prove it with reasons, as it may be seen from the illustration at A and B. (Illustratt"on 406) Illustration 406 Sea

Land

E

The figure A has its angle B which is the angle facing the sea, and that is the angle which takes the brunt of the waves as they strike it. Sides C B and B D [!fol. 409r] (which is the other side), the water strikes in an uneven way as it comes toward the land obliquely, and so would not give them as much trouble as the other two sides CE, D F, since they lie straight toward the waves; but these can not be caused any harm, as the figure shows. The hexagon B lies in a different situation to hexagon A, which has angle B facing the sea, for B has its base or side G H facing the sea and is thereby much troubled and assailed by the waves as they come toward the land, striking it one after the other. This sĂ­de now has no defence, either from its design or its material, or its shape, nor yet from its site or place. For there are sorne things that are strong by reason of their shape, as well as their material or site. But this form can only be favoured by its material, and nothing else; so that material for material, figure A will always be worth more than B. Here the argument can be derived that in siting these figures, the two sides of shape B, that is H K and G I are not much troubled because they are struck obliquely by the [567]

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Illustration 407 Sea

Land

waves. And from K to M, and from I to L the walls do not receive much damage, as they are concealed from the sea- I mean from the waves- so this figure B is troubled on three sides, and figure A only on two, and at three angles, while figure Bis troubled at four angles which are struck by the waves. (Illustration 407)

[!fol. 409v] There is the same difference in the heptagon, or seven-sided figure, as there is in the pentagon and hexagon. It is true that this difference is stronger in sorne figures than others, as the sides are not so oblique; but more in the end as the figure has obtuse instead of acute angles, so the distance across will not be too large- I do not mean between P to Q, nor A and B, nor in the pentagon, but in figures whose angles wait for the waves, for in these the traverse from one to the other is very slight. The same is to be understood with all other possible figures, of eight, ten or twelve sides; in each case there will be the same difference according to the size and number of the angles, for the more there are, the more places in angles to seaward that can be affected (and the more that will not, as in figure Q).

So now we have given the reasons and causes why one shape has greater strength than another, and very clearly.

Now the truth of what we are discussing is made plain, on this subject of waternot all water, only the water of the sea, which has much greater strength than any other; the cause being the winds which give ir a continua! motion, so the first octagon A, having its base toward the sea [!fol. 410r] is regularly under attack from the waves while the other two bases B D , CE are better placed to resist (Illustration 408) the sea than to divert it. In this way: in a different position, like

A

Il/ustration 408

D

5 G

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the second octagon L M, its angle would face the sea, and divert the fiercest waves when the sea strikes it. L M and N O do that. So these four divert the water and the sea itself embraces and fortifies the construction, because it compresses it, and so strengthens it, so that we can say that it reinforces it. But this is not produced by the sea, but by the situation of the internal shape. The first one does the opposite, for when the water strikes it, it pushes it away, as if striving to break it clown by force, so the sea hits it full face: and has greater effect on it than on the second.

In the second case, half should be within the land- that is the base V X and its angles N P andO Q. Let it then be founded firmly in the land, as far as the middle of the bases. [!fol. 410v] But on account of its position, [/fol. 4llr] it has no strength in itself because the mighty furious waves can break it clown outside the two parts of Z D 8 . But because everything from Z downward, and likewise from D, is within the land, these sides can not be battered in any way, since the water within them is as though still. Even if it were to have sorne motion, it could not exert any force, partly because the extent of the motion is kept short and partly because the walls prevent the air or wind from having such fury as to drive the water with the Ă­mpetus it would have, were there nothing to block it.

So every harbour must be partly in the sea and partly in the land, and in this way will enjoy much greater security and stability than if it were entirely founded in the sea. Also when working in the sea there can be no repairs done as there are on dry land, [!fol. 4llv] where much better equipment can be used.

Toward the sea, (Illustration 409) the section marked A should be added, with a very high tower, to overlook a great extent of sea. Mis the harbour, six hundred paces wide, G is the promenade, FF the two chain towers, H the warehouses, I the customs house, and K is the colonnade. Many like the entries near the land, but in my opinion that is not good because of lack of depth there.

The mole is to have the following design in the grouncl and above grouncl, in the water ancl above water: [!fol. 412r] A is a parapet, seven palms high; B a level space for walking, twelve to sixteen palms wide; C is sorne steps; D (Illustration 410) is another walk of five palms; E the wall that goes clown to the water; F stones to tie up ships; G sorne rings for the same purpose; H is the glacis- that is the least clepth it can have, for the greater the clepth given to the mole, the better ancl more secure it will be.

The seconcl figure resembles the upper figure somewhat, although there are many differences. In it there is a parapet looking toward the sea; it is seven palms wide, anclas many high; Bis a step, two palms high by two wide; [!fol. 412v] a roadway twenty palms wicle; D four steps, six palms wide and as many high; E a walk six palms wicle; F five steps, eight palms wide; H is the wall with two moorings G; I the outer face or glacis. K and L are two vaults, filled with earth to save expense. The beginning of the glacis must be strong and have a good appearance.

N is a large pilaster for the vault, and is the beginning of the wall insicle the mole or harbour. The dimensions may be discovered from the numbers, which go up by fives ancl give all the measurements of this design. (Illustration 411)

e

The thircl figure is quite different from the others. A is a parapet with the upper part rounclecl; B a level space; e ten steps; Da level space which runs all rouncl- at intervals stairs go clown, ancl there are moorings; E is the harbour wall, s 'outside the two parts of Z D' ... probably D in the text is represented in the diagram by the Greek alpha.

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JllustratiOJt 409

Illust1'ation 41 O First figure W ater Base of the mole.

Foundation.

,, ._.

'l. S

1 •

"\S

.h.. ~nÑ·· . . .. .. . .. . ..J_n

+•

· - · •.

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I/lustration 411 Second figure

Illustration 412 Third figure

[!fol. 413r] as far as K; the vault F is filled with earth; the outer face ís G in the upper part, and K, and that concave curve 19 where the waves strike.

The compass or width of a harbour is to be very large and spacious, with plenty of depth for cargo vessels to go in and out freely. Close attention must be paid to the 9

'that concave curve I' ... the text has 'convexa', but this muse be a slip.

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traffic of the neighbourhood, to the líe of the place, and its situation, which is why sorne harbours have to be rnade larger than others. There are three kinds allustration 412) of harbours: sorne are called docks, others havens. They do differ in their construction, since docks are entirely dug out of the land next to the sea, [!fol. 413v] while havens are not enclosed like docks, but have only the one long wall, which gives protection to the vessels which líe at anchor there. These establishments should have sorne spring or river nearby, where sweet water can be drawn. Docks are notas large as harbours, and are dug near the shore, where the depth is good, and the entries free of rocks. They are to be dug deep enough for any vessel to enter about 20 or 25 feet. After they are dug, build good stone walls all around; and take note to put good iron in the walls, or else hoops or rings very thick and big enough to hold any vessel. It will also be necessary to have sorne stones, also very large and thick, set upright like columns, and fixed firmly in the wall with the iron fastenings or leaded hooks set firmly in them (if these should be of bronze or bell-metal, that would be better). Here we draw the shape of the dock or harbour to make it more intelligible; and so we indicate the inner and outer profile. [!fol. 414r] This design many will think far too wide, but Ido believe that it should be very plump, for that gives it more stability and security. A is the parapet with the glacis; B a spacious level area; the ships tie up at C; D is three steps; G the Illustration 413 Fourth figure

parapet or wall, and atE there are moorings. Staircase F (ltlustration 413) goes clown to the harbour; L is the beginning of curve M, which cannot be broken at all, because of the two circles or part-circles, one convex and the other concave, so that even though the waves may strike it, they will slip back. The two vaults K H are to save material, and leave this design much safer. That arch I is also empty, at least of mortar. These vaults are to be filled with earth, which if well tamped clown like a mud wall, will serve as well as masonry. [/fol. 414v] Arch I will be equally [572]

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Illustration 414

Fifth figure Water

devoid of mortar. Then, so that the building will be very securely constructed and very durable, a quarter circle reaches to the waves, at the height of the stair, M N. The stairs go clown under the boats, as that is more convenient for loading and unloading. (Illustration 414) By variation the mind is broadened: the more sorne matter is scrutinised or investigated, the more the searcher's judgement strives to become more refined in its enquiries- if he is one engaged in that profession. It is certainly a great satisfaction for the mind to see clifferent forms for a single effect. Somebody might ask [!fol. 415r] what is the reason I have made those arches E in the 'corona lisis', as Vitruvius Pollio calls it in his work 10 • ABare pilasters which support the whole of that wall. On the same subject, I have already said that it is necessary that the waves do not touch anything that will offer them resistance, and I now repeat that assertion yet again; it is preven that the waves will break more easily on the sides of those pilasters A, because they must end their raging there, and then fall back downwards, and so break the waves which follow them. All that could be disputed against me is at G: but that point is far from the waves, and B to O is safer because the waves do not strike so much there, since they are first checked at pilaster A. The outline ground-plan of this design is as follows, together with the elevation: at B there are to be vaults in the opposite direction to che others, in this section, made as indicated in the ground-plan. They too are filled with earth, as stated for the rest, tamped clown well as each floor is laid. See the figure on the next page.

The plan which follows shows the difference between the vaults or arches, bread at one end and narrow at the other. These vaults C are filled with earth. [!fol. 415v] B are pilasters between the vaults, the stairs E face into the harbour.

This figure too is on the next page. (Illustration 415) lO 'the «corona lisis» as Vitruvius Pollio calls it' ... the corona in fact was part of the cornice of che Vitruvian facade, so its meaning here is obscure.

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Volume V lliustration 415

Plan of the sixth figure

There is another plan, that of the sixth figure, which at each eighth forms a curve. This invention of a harbour wall is I believe very strong and everlasting, of great value and resistance, as each face is curved. For at these angles- those curves[!fol. 416r] the waves break one ancither, so that it is not susceptible to any harm, except at S. Mis the batter of the curve, N a level area above, in front of the parapet, for if anyone should want to employ great subtlety, he could make parapets with columns, so people can walk there and enjoy the view of the sea, secluded from all disturbance of the business of the harbour. O is the parapet, which runs all round; P a street; Q steps all the way round; R round staírs with a large landing to load and unload merchandise and so forth. (Illustration 416) The figures of harbours have been discussed elsewhere. Certainly any man who undertakes a job like this must have a clear and well founded judgement, keen understanding, anda vigorous mínd, [!fol. 416v] because it is not gíven to every man to carry out a work like this. He should have great experience of various matters, and have seen works of similar type in various places; he should have studied their íngenuíty, their secrets and their advantages- and also their flaws, where they are susceptible to damage. He should understand the strength of línes, their effects, and the reasons for their good points; where their strength líes, where weaknesses are bom, where the security and perpetuity of the work líes- I mean as regards the material, shape and site. (Illustration 417) As I would have him all this, [!fol. 417r] I say that he is to be not only a good architect, but a very good mathematician and an excellent philosopher. That is why I say that buildíngs like [574]

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Illustration 416

this ought not to be entrusted to every craftsman even if he does know how to work stones, for if that were so, anyone could be a genius. In works like these, note has to be taken of the winds, and what shape will be more secure, and where the harbour will be least injurecl by the sea, and where the waves will deposít least sand, for that is one of the most ímportant parts of thís whole subject. Most harbours that today are seen in ruins appear to have failed because so much Illustration 417

Sixth figure

o

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Volume V sand was deposited as to close their entries, and now they have been left high and dry, so choked with sand that it is quite impossible to make any use of them. And if one did want to take the trouble and undergo the expense of restoration it would cost so much, and besides in a little while they would be in the same state as before, beca use one day would deposít more than another. Then they would have to abandon the whole thing, because of the danger to vessels. So always, when a building is to be erected, do not be constrained to found it in one particular place.

When you can choose the place and have no concern for anything else, it is best for your choice to fall on a site among mountains, as may often be found.

With very little help, [!fol. 417v] it will turn out to have been built almost by its very nature. When a bay ís found, made by the sea, in the mountains, then the mountaíns embrace, shelter and protect a place líke that, and defend ít from the raging winds; as if they wanted to keep the wínds from touching it. Leaving its position aside, it is very safe and strong because of the mountain crags which will give you the convenience of havíng a lookout almost ready made, so you can see who ís coming in and going out. Sailors will be able to guide their ships there from the midst of the sea with a place so well marked. I leave aside the lower expense involved when such a place ís díscovered, for it can indeed be done incomparably cheaper, províded the place is justas we portray it, and has a great capacity, and great natural security, províded too that the rocks do not threaten to ruin it, that ít has a good safe approach by land as well as sea; and that it is convenient to bring merchandíse in and out; and room there to live, and sweet water [!fol. 418r]; and that the place can be made secure, but not be too far removed from towns, since those who make port there will have to be supplied with all they need, especially things to eat.

Our díscussíon about constructíng a harbour conforms to the opinion of the majoríty of those who engage in this art. Thís professíon belonged in ancient times to architects, but nowadays to those who are popularly called engíneers, or better, to those who have called themselves engineers11 . They have taken over this profession, claiming that the business of war and water works are one and the same thing. In this I see that many are deluded, and they also·delude many, specially princes, who order soldíers or quarrymen or stonemasons to erect such structures- the former because they are men of war, [!fol. 418v] and claim that war and water works are the same, and that the whole of architecture resides in them.

But I would rather say that that is a great abuse and a plain blunder; a man who wants to be a good engineer should be an architect and understand architecture and geometry so as to deal well wíth military matters, as well as knowing how to draft plans for them by hand. lt is impossible for anyone who does not know how w draw up a plan to be able to understand this subject- not even to deceive somebody else about it. He who knows how to draw knows how to draft plansa notorious error- yet there are very few who do understand this subject, since the man who does the draught does not understand the subject, and the man who orders the draught does not understand the draught. For if the draughtsman were to understand the subject he would understand the causes on which the subject is based- yet he can only draft properly if he understands what he has been ordered.

11 'those who have called themselves engineers' ... 'ingenieros'; elsewhere 'engíneer' translates the Spanish 'artífice', because 'ingenieros' are evidently to be understood here as milita1y engineers only.

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This is the source of so many mistakes in plans or draughts, when architects get others to do them; and afterwards when the mistakes that arise in this way are seen, they throw the blame on the worker or the transporter or the draughtsman, who failed to understand them and could never complete what was missing, although he was given his orders a hundred times. That way they take the opportunity to defend their own ignorance with a shield of malice, to shelter from the mistakes they have committed in the work they were ordered to perform. All the time they defend themselves by always throwing the blame on others, and so discharge themselves from their own mistakes, and lay them on somebody who never thought of any such thing. [/fol. 419r] All the science of these engineers lĂ­es only in talking big and much proclaiming of the mistakes that others have made: but their own they cover up with other men's clothes.

At other times it may happen that the job is given to sorne stonemason, who claims that he knows how to work stone and make a walllevel, and there is no need to know any more, as he can work wonderfully in masonry and ashlars, and besides he can make a cornice with a pigeon crop: and in that the whole of architecture is contained. And what is more- even more exquisite, he knows how to make a chape! with a tracery of fifteen keys- that does include everything. To give credit to such people, they do not need to know any more than how to talkthat is enough- he has done such and such a job, he built a church (badly put together), there you have the whole of architecture, here you have the best man of any in Spain. He would do better if he said, 'here you see the whole of architecture made into an epilogue, and laid out in a great thick bundle'. And hence it comes about that recommendation and ignorance are joined into one, and hence the barbaristn there is even in Spain in this matter of recommendation.

This I say as an eye witness, it is not just what I have heard from other people, I myself have found it coundess times. So I swear by the law of goodness that I used to get quite sick of hearing so.many heresies and blasphemies spoken in architecture, observing so many remarkable errors in this subject. So I say, what nobody would believe lightly or easily, [!fol. 419v] that I have seen aman who did not know how to make an adobe wall, but he wanted to talk about architecture- and the poor fellow did not know how to make a straight line, nor draw one. When a prince wants to entrust arduous matters of the greatest importance, he ought to assemble coundess architects and himself see how the modus faciendi is treated, and thereby he will eventually draw out the pure truth, and understand where the skill and intelligence lie; he will not rely on information from a knight who swore to God that he had heard sorne person recornmended, whose whole skill was in reality not good enough fo.r an apprentice. Nor arn I astonished that a letter of favour could deceive the knight, and the knight the Prince or the King- and that to the detriment of his honour, and that of the King himself, and of his Kingdoms too, as I have seen in the business of forts, that were very bad, and badly understood, and worse ordered. Certainly I have seen many bastions in different places, which were really just as if they had been made of mud- and I would make a better bastion out of mud than they with their artĂ­fice and design. Let nobody deceive himself: he who is not a good architect can never be a good engineer- and if he should be in one thing, he would not in different things. And if someone does know something it is only through having discussed it with architects. And that I can not endure. If a craftsman should praise somebody of that profession, either he is not believed or he is not listened to. So I see everything is the wrong way round. Nor have I found [577]

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in Vegetius De Re Militari12 architectural matters- and if he has any, they were taken from architects. [!fol. 420r] Although architectural matters may be found written in military works, for all that they are not so treated for the sake of military men. For military works are first constructed by builders before soldier, knight or gunner is involved: if the builders did not make them, the soldier would not use them. For the craftsman knows the effects that the instrument or machine is to have, much better than he who makes use of it.

So to return to our subject, nowadays the líe of a knight is better believed than the pure truth of a craftsman, and a líe is affirmed for truth, and so belíeved, and accepted as such. This I say as an eye witness, having heard such things said countless times. By the law of good the man whom the knight recommended was not fit to be a mediocre architect's 'prentice boy. That comes of wanting todo a favour, to the prejudice of others. Four lines of favour are worth more than all the science of others. So they raise the príce 'ad tertium caelum' 13, and by the same token do the duty of a good friend; 'cecus cecum ducit, et ambo in foveam cadent'.

When undertakings like this are required, there ought to be a great search throughout the whole kingdom for people there- or in other kingdoms, and then bring them over for such a purpose. I see that a knight who has an ill horse sends for three or four farriers, for a horse worth a hundred ducats: and for a matter that will cost thirty thousand they rely on somebody such as I have portrayed above, who was never seen in a harbour, stillless understands its arrangement. Sorne I belíeve will understand me [/fol. 420v] and hold me for malícious, for telling the truth, but I call God to witness if I am lying in all this.

Certainly I have in this point somewhat overstepped the limits, more than I ought. So I return to the subject, although I have in various places dealt with the method of making harbours of various shapes, and together with that have given instructions with reasons illustrated to show how one shape is better in one position than another, even when the shape or plan is the same, without adding or removing anything. As I think it would not be inconvenient to recapitulate what was said on this subject, in a different order- only six or seven shapes can be used for a harbour. Of these the spherical figure is the principal one, and the source of all the others- I mean of all the polygonal figures- so the more they approximate to it, the greater perfection they possess. The second is the pentagon; the third the hexagon; the fourth is the seven-sided shape, the fifth is the octave which has eight equal sides, seventh (sic) is the nonagon with nine, then that of ten, the eighth is the onzave with eleven1\ ninth the one with twelve equal sides. Upon these figures many more can be made, proceeding 'usque ad infinitum' to make harbours. And I firmly maintain that no harbour has ever been seen with more than twelve sides[!fol. 421r] most are of eight- Ido not think any will be found to have been made with more. If you were to exceed twelve I would prefer to make it round than add any more sides, because it would then have greater capacity than any other figure, 12 'Vegetius De Re Militari'... a classic late Roman work on military strategy and tactics. Sixteenth century editions frequently have illustrations taken from much more recent works on siege warfare.

13 'ad tertium caelurn' ... literally 'to the tbird heaven'- like 'usque ad infinitum' (420v), this means, with wild exaggeration. 'Caecus caecum ducit' ... the blind lead the blind and both fall into a ditch...

14

'the onzave with eleven' ... from Spanish 'once', eleven. The 'octave' and the 'octahedron' are errors for 'octagon'- rather peculiar.

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but making such a large circle would be ,;ery difficult to achieve, more than most people suppose. As for those with angles, by means of a Doric square, once one angle is obtained the others may be taken, and so all will come very well upon one only. So only three comrnon ones, the circle, hexagon, and octahedron or octave; all the rest are fruitless.

The strength of a harbour can be achieved in three ways: first, by its shape, with the design giving it strength; second, by the material, which may be such that however much the waves may fight against it they can never damage it; and the third neither of these but the site, for sometimes a síte is found which is formed by nature. In that case even if the design is not good nor the material; by which is to be understood all the artificial part, put there by hwnan hands to such a purpose- the position is enough, when the harbour is protected by mountains so neither air nor winds will do it any harm, [!fol. 421v] nor yet will the waves be able to damage it. As I have already explained what design makes one wall stronger than another, there is nothing to detain us further in this subject, nor weary the reader any further.

Laying foundations in the sea is such a clifficult and arduous business, and there is so much that has to be considered, that I often despair when I think how a man sets out to struggle against that most powerful enemy, which nothing can resist, and which ever labours to conquer and overthrow its adversary. How much more so when we want to make a lügh building in the sea, which can stand firm and dry among the waves. That certainly does amaze me, specially as I understand that sorne years since His Majesty ordered a castle to be built in the sea below Tortosa 15I was astonished that there should be a man so bold as to venture on a job like that.

It is frightening enough to make a harbour which is to be linked to dry land, having everything ready to hand, but the undertaking still arouses fear and Trembling- and that is something which is done every day- so how much more if it is to be so far into the sea. Still, I have been thinking how this castle could be built, and I find that there are various ways it can be erected in the water.

Certainly it is cause for wonder- making some pieces of wall to surround a harbour is nothing at all by comparison, for there you begin on land and keep your link with ít and there is not so much work because it is entirely surrounded with lost stone until it is brought to the surface or tongue of the water. But when making a castle the walls to be made are very different. [!fol. 422r] Once again, · I maintain it is a very difficult business, but I would deny that it is impossible.

Rather I say that it can be done, but only with great difficulty and at excessive cost.

So this is what I have thought out over the course of a long period of time, to put it into effect. First, let a small wooden model be made, containing all the details which a fortress should have. After the model has been made, look at it, examine each detall many times. But do not rely on yourself, show ít to people learned and expert in this profession, and ask their opinions. Thís model is to be made of the right measurements; let them be palms, feet, paces, rods, varas as best 1' 'His Majesty ordered a castle to be built in the sea below Tortosa' ... Vigueras González says that the author meant either a castle planned by Charles V, or 'one of the castles which Philip II had constructed to defend the entry to Tortosa, or that of La Ampolla, to prevent the Barbary pirares from taking water there' (Vigueras González 1979, p. 156). García Diego conclu.des that the text must refer to plans to protect the mouth of the Ebro, a very sensitive point, in the later 1570s.

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suics the reckoning. After this consulcation, when any faults have been noted, leave it for a few days: and then study it again and inspect it anew. When you are quite sure that everything is as ít should be, then view the place where the foundation of the building is to be laíd, and measure the depth of the sea, from the bed to the surface. Then see what kind of ground there is, and if all is well, see where you are to lay your foundation, arrange a site to erect your building; [!fol. 422v] produce your inventions and construct machines to make a cofferdam so you can work and found the structure.

Mark out the circuit to be endosed with something that will show up- like fishermen who put a cork float where they have cast their nets, so they will be able to see where they are. If there is no cork to be had, use barreis or small casks, fastened with weighted ropes which will hold the barreis fast to the bottom.

In this way the circuit can be marked out, as each cask or pipe will stay in the same place. Having established the depth, start on your inventions for the construction. If the sea is not too deep for a very long piece of timber to reach the bottom, that would be excellent- drive in timbers two by two, (Illustration 418) each one having two grooves in it, on opposite sides. They are to be twelve palms apart, that is from Ato B and C; from B toE is to be six palms. In this space, [!fol. 423r] tie D toE with other beams, fastening one to the other, as was described when I spoke about the piers of stone bridges.

Illustration 418 ·This cross-beam ís to be tíed with che tímbers

A, B, C and the resc. These planks are to

point down

If there should happen to be sorne rock in the bed, which can not be penetrated as it is under the water, I have thought of a kínd of drill, with which it may be drilled through and sorne holes made, provided it is not too strong. Then throw in stone ballast from big barges. The stones are to be as large as possible, because the bigger they are the more resistance they will offer to the water, and the less it can move them. But if it is possible to drive in piles, let it be done in the way laíd clown for dams to dívert water. When driving the piles in, care should be taken not to form an angle. Be .it understood that a much greater area is to be taken than the model would indicate because as much space again should be induded as the structure will occupy. That ís because a building like this has to have excess room to sink clown and settle. If ít were possible to make a foundation, you would not need that kind of work so much, nor take such a circuit for it. The shape is given by the piles dríven in through the water: they are to be round, because that way the [580)

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Nineteenth Book waves will do thern less injury. If the sea-bed at that point is sandy, then drive in piles as I have saíd: but íf ít ís rocky, sorne other devíce will have to be used in forrn as follows: take sorne old hulks, or any other kind of vessel, and fill thern wíth the rnost rnassive stones that can be found. These vessels are to be pierced through: [!fol. 423v] so they can then be conveyed to the place; then unstop the holes and they will go to the bottorn. Place thern in order, as indicated, so they willlie 'on the bottorn as shown. The hulks or boats are (Illustratz"on 419) rnarked A, B the stones, C the second, the stones D. They are to be placed in a row as íf rnaking a wall. Lay down two or three layers of hulks, depending on whether they are large or srnall.

With chis invention the whole círcuit rnarked out shall be encornpassed.

Illustl'ation 419

A is the drill, B the wheel; the ball C is of lead. D is the iron bit, the crook E rnakes the drill rotate at G; it has a wooden shaft. This drill can be rnade in different ways, both the iron bit and everything else fitted to enable it to rotate ata very great speed, so it can bore through the stone [!fol. 424r] and hollow it out to cake the upright timbers. The hulks are gradually put in positíon to encornpass the whole circuit marked out. If you suppose that ernptying all the water it contains will be a rnatter of little difficulty or cost- don' t anybody think so ! It will cost a [581]

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great deal, and it will be a very slow job to finish emptying so much water. And once it is empty, you will need to excavate it in the middle, eventually it will cost an infinite amount, because it can never be so well enclosed that no water ever gets in- even assuming that an invention could be discovered to empty it. So, then fill up with stone ballast right to the surface of the water; then leve! it up with stone and lime until you can raise the walls.

Before we go any further, we need to conclude by explaining how each particular thing is to be laid. First, we shall deal with the timbers to be driven in once the whole circuit has been encompassed with two rows laid as indicated above, then planks laid sideways with a tight join- the rest only need to be sawn.

Join them to one another, until you reach the ground, and then fill with earth as we have said. Be it noted that the inside planks are laid first, and some barges are to be enclosed within, in order not to add work by having to put them in afterwards on top of the cofferdam. [!fol. 424v] The distance from one row to the other is to be at least twenty five palms. Four courses are to be laid down, and in the space between leave as much as will do for the foundation, and then as much again.

Illustration 420 Castle

Por you must not dig so close to the piles, as that may cause them to fall in. (lllustratz'on 420) To prevent that leave sorne space between each one. lt would be possible to copy one invention I saw, by aman who was making piers for a bridge. Because of the great amount of water that was seeping into his foundations, he laid unslaked lime mixed with the thick sand called gravel. [!fol. 425r] With this lime mixed into a powder he laid the base of his work. Thereby he did two things: one, he avoided the job of pumping out the water; and also, he did not [582]

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have to lose time in making his mortar, which he thus prevented from rendering the lime useless through excess of water. And so he brought hís work to perfection, at much less cost than he had thought. This then will serve as a dike and wall; with the skill of a good builder it will not cost so very much, nor will too much difficulty be found in its construction.

At the entrance of this harbour, two towers are to be so placed that a chain can be laid from one to the other, with another right in the mouth itself at A (the others are at B and C), to make it safer as ships go in and out- even if it does no more than exact the duties which merchants owe on their freight. .. but as this was discussed at length when we dealt with the parts of the harbour, let this just serve as a reminder. When harbours are dug out of the land they are made quite different from those made in the sea: because in the former case there is no need to make dikes or defences in order to work on them, since the water can not trouble you nor do any harm. But those made in the sea need great dikes and defences and inventions for their foundations, sorne of those whích have been discussed at length above- although there is indeed always sorne new invention found out, which can be added. So then, very large ones can be made, filled with stone and lime and set apart from each other until they can be raised above the water; and then erect arches from one pier to the next.

This invention of a harbour has an entry with bends at sorne distance from the harbour proper, [!fol. 425v] because there are great sand-banks all round the harbour, so it had to be made in that way to prevent shíps running aground as they carne in. This invention was of great importance and repute, and the work of a man who possessed great judgement and acute understanding, a very expert man he must have been, since he built at Ostia a harbour with such a successful and appropriate plan. (Illustration 421) Once that is done, other piers are to be founded opposite the first, and arched over likewise; and so carry on until the work is finished. The space left between the piers is to be filled in with ballast, [/fol. 426r] not laid in any order, but the stones must be very large to carry out their function better. Caissons which we have said are to be put in place to build the piers, are not to be placed any further apart than the distance between them. In this way the whole circuit of the harbour is enclosed, and the arches serve as a leve! wall around the harbour- for all are to be of the same height. With these defences the harbour will be protected from winds and storms, and no enernies will dare to come near it.

This next harbour, that of Baya16, is of circular shape; it is perfecdy round and founded in the sea; it is a very safe work and has at its entry defences against winds and against enemíes too. Por at the end of the mole there are two towers whích protect the entry and exit, although they were made more to give light by night than anything else. This harbour mole is very long, more than two hundred paces; the entry to the harbour at A is a hundred paces wide, at B and C it is a hundred paces and more. At D and E are the two towers, with their lanterns. F is the harbour 16 'the next harbour, that of Baya' ... perhaps Baiae, now Baia, in Ancient times a favourite seaside resort of wealthy Romans, not least on account of the thermal springs. There do not appear to be any remains of a port such as th.is, but given the frequent land movements in a notoriously seismic arca, ancient baths, or even a natural lagoon, may have been taken for a harbour in an area known to be near a major Roman naval base.

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Illustration 421

Port of Ostia in width 400 paces

mole which will be forty feet thick. The two towers will be eight paces in diameter, if their only function is to be light-houses, but if they are to form a bastion for the defence of the harbour, tower F will have to be made much wider than illustrated, in conformity with requirements.

Since the area indicated by B and C is very small, as it was only shown to explain the invention, [/fol. 426v] and since so little space is left for the protection of the harbour walls, although the number of paces are set clown from one end to the other- here I shall give no account of the method used in building the walls, (Illustration 422) as I have done so elsewhere- except for this piece of advice, that the walls ought to be made thicker and larger stones used where the sea most strikes the harbour-wall. If it be done on both sides of the walls, so much the better, although any kind of stone can be placed in the centre, even small fine stones- it does not matter since the sides are well fortified.

To make this invention of the wooden caissons, you will need to fit out two galleys as if you wanted to hold a tournament on foot at sea: have a floor of thick planks over thick beams [/fol. 427r] from one galley to the other; and if there should happen not to be much room lay three galleys together, make them fast and strong enough to hold these caissons. Drive in pointed posts with shoes at the ends.

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I/lustration 422 Steps all round the harbour, on the inside

Port of Baya

Then make two wooden frames to link the whole area to be encompassed. Each of these frames ís to be double, of the same size. Both go outside the posts, but one almost comes to reach the sea-bed, withín a vara and a half, while the other frame is to be fastened firmly to the top (Illustration 423) of the posts. Two more are made, to go on the ínside, smaller than the other two- the difference to be no more than the thickness of the posts. One frame is to be sunk or submerged to the level of what has been made to pass through to the sea-bed. The other is to be made fast to the flat upper surface on top, more or less. then long thick planks are to be attached to the sídes. On the bottom part toward the sea-bed, [!fol. 42 7v] a point should be made, to which is fastened a piece of iron so it can be driven ínto the sand. Keep laying these iron-clad planks, begínning at one end and so proceeding gradually until the whole circuit taken for such a pier has been completed. Then another is made on the ínside or on the outside, in the same manner, leaving a space between the frames of eight or ten palms breadth, which space atlustration 424) Illustration 423

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should be filled with clay or sorne other earth, right clown to the bed. That way the water outside can not get in. After tbis has been done, [!fol. 428r] many instruments should be installed to pump out the water in the middle; they might be force-pumps or screws or countless other instruments that exist for such a purpose. In addition, much stone, lime and sand should be made ready, and mortar made up; the stones need not be worked except for the joints. It is a job that may be done very rapidly with plenty of craftsmen and labourers. But this same subject will be found under piers of stone bridges, although they are not quite of the same kind, because the posts G and H are to go in between e and D, andE and F, andas the distance between frame e and frame D will be a greater quantity than the thĂ­ckness of posts A B, it will be necessary to use posts with each frame to hold it firm.

FINIS

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TWENTIETH BOOK Introduction Working under water Only the opening pages [!fol. 428v-439r] really deal with the task of the title, and they continue from the previous book, [426v-428r]. The idea of building in the sea sorne fortress that would protect a coast against an enemy was a longstanding ambition.

Italian engineers of the fifteenth century put forward their suggestions, e.g. Taccola (Taccola 1972, pp. 100-1) and Francesco di Giorgio (Francesco di Giorgio 1967, I 33-4, tav. 15). In practice it was never very practical; it would always be easier to buíld on a headland or small offshore island. Only a century after our text were attempts made to erect light-houses on reefs as a warning. So this passage is rather an exercise of imagination, based on works for harbour moles, than a serious plan. He begins then with the caissons which are to be sunk, as foundation and to serve as cofferdams for this castle in the sea; and as an alternative, hulks filled with stone and rubble. The suucture is to be protected during erection by a palisade of piling, so evidently not in very deep water. A drill- rather like an outsize bit-and-brace- is to be used to break through any rocks [423v]; anda stone guard on the píles should keep them straight [429]. Most of this section is devoted to the caissons which will form the base of the structure, as well as its defence against the sea; variations are depicted, as usual, differing only in shape.

Once that is done, building the superstructure can start. The descriptions of each stage do show a knowledge of sea-bed conditions, such as the movement of sand and mud, and like Book 19 confirm that the author had sorne experience, although he does not seem to be very aware of underwater currents.

Diving As building under the sea means that men must go under the water, a new section deals with diving gear [434v-431r]. However this fascinating passage is notas original as the author implies, contrasting his idea with the old Roman Vegetius. In fact, much of what follows (435r on) is adapted from Book II of Niccoló Tartaglia's 'Travagliata Inventione', his 'Troublesome Inventíon' of 1551.

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lndeed most of the illustrations are taken from Tartaglia too, with minor alterations, usually suggested in Tartaglia's text in any case. In other places, the author takes up ideas from 'The Troublesome Invention' and develops them in detail, with illustrations not in the original. Thus, where Tartaglia propases a copper diving-bell shaped like a wine-barrel, here we have one which is like an elongated barrel, and then a copper sphere with glass windows, curiously reminiscent of the bathyspheres used in deep sea exploration this century. But a big glass sphere, in which aman could sit like a goldfish in a bowl, which Tartaglia supposed would not be beyond the capacity of the Murano glassworks, is not shown here; it was perhaps too fantastic.

In the Renaissance there was no question of going under water to any great depth. Diving bells and diving suits were only used to venture a few feet under the surface to investigare a defective pile or weakened pier, or attach a cable. The best contemporary account of a particularly venturesome descent is Francesco Marchi's, when he went clown to look at the sunken ships ofLake Nemi in 1535; a less detailed report tells us of a diving-bell in the Tagus at Toledo in 1538.

Tartaglia was aware of the problems created by water pressure on a diver, and was one of the fust to relate this to Archimedean hydrostatics. This is also explained here. Neither our author nor Tartaglia seem to worry much about how the diver could breathe; here che diving helmet is not even to have a watertight fit, apparently. Alchough ignorant of che function of respiration, people clid realise that the same air could not be breathed in and out over and over again, and accepted that air would somehow be 'corrupted'.

So it is strange that no pipe to the surface is shown, even though it appears in the pseudo-Vegetian pictures.

Design of Ships Considering the importance of shipbuilding in a Spain expanding across the Atlantic and even across the Pacific at the time, this is a short and deriva ti ve passage [43 7r-440r]; again freely adapted from Alberti (X.l 2) , omitting little but the weird comparison of a ship to a water elephant. Alberti was the fust to try and raise the Roman ship in Lake Nemi, although he could salvage only a few pieces. What we have here are general principies, although well expressed.

However, the caulking recipes are not in Alberti nor are the fearsome devices for defending a ship when attacked, nor those to block a harbour mouth with a wreck-' a well established practice.

Dredgers Dredgers reappear again; the grab and scraper do not cliffer much from earlier versions in Book 18. The wheel dredger is perhaps adapted from the noria, so as to scoop mud instead of water. It seems that machinery like this was used, but the great wheel cliameter needed for any but the shallowest of canals or harbours meant they could not easily compete with the mud-mill with a ladder-chain, developed in the Netherlands in the late sixteenth century; wheel dredgers were also more likely to spill back the sludge or clog their gears, for loading as depicted here [444v] must have been a tricky business.

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Salvage Since the Venetians were known as experts at raising wrecks, it is not surprising to find this section too leans heavily on the first «Ragionamento» appended to Tartaglia's 'Travagliata Inventione'. The system of 'camels', first flooded then pumped out . gradually to lift a wreck hydrostatically, may perhaps originare with him. Older methods included fishing it up with anchors ernbedded in the hull, or a rope noose, both shown here. Accounts of a Venetian's unsuccessful attempt to raise the 'Mary Rose' just off the English coast in 1545 do not mention pumps, which would be essential for Tartaglia's technique; the first good repmt of a trial of the hydrostatic method, also from the Venetian lagoon, dates from 1560 and so may have been inspired by Tartaglia; although that too did not work (Keller 1971). The author seems more aware than T artaglia how quickly silt will bury a wreck, but the main concern at the time was the danger to shipping from wreckage just below the surface; otherwise it was more important to salvage the cannon than the ship.

Underwater Illumination Here roo the author drew on the 'Travagliata Inventione', the Fifth 'Declaration' of Tartaglia's Supplement. The first recipe comes from this passage [451r], while .the other two may be inspired by a military technology book of the early sixteenth century, Battista della Valle's 'Vallo' (1524), These recipes do seem ro assume that a mixture of the most inflammable substances known will burn away without any air at all.

Canal Locks This section [453v-456v] may look rather out of place, as if the subject belongs much earlier, when the author dealt with navigable canals, in Book 6. Perhaps it is placed here because Alberti talks of locks asan aspect of marine engineering (X.12), to be used when flushing out a harbour. The oldest forro of gate was the verticallift of a single leaf (here A and B, 455v-456v). Pound-locks with gates swinging open certainly existed in places in Germany and Holland long before; Alberti's method would seem ro lose much of the width of the pound for the passage of boats. In Alberti the axle about which the single leaf pívots is to one side; here there are two gates, but the axles are central in their respective leaves. All this might look clumsy, even dangerous, but when the Dutch-Portuguese artist Francisco da Holanda was travelling in Italy in the 1530s he sketched something similar on the canalised Brenta between Venice and Padua. In the two-leaf gates shown here [456], the two sides close together flush.

Perhaps it was Leonardo da Vinci who introduced mitre-gates, with a small wicket gate in one to control the movement of water in and out; as appears later in the plate in Zonca's «Novo Teatro di Machine ed Edificü».

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Slipway A slipway or incline to join two waterways across a narrow strip of land: this too appears in the sketchbook of Francisco da Holanda, and in Zonca's book, in both cases based on an incline which enabled goods and passengers on the Brenta to cross over to the Venetian Lagoon at Ca' Fusina. The only difference between their illustrations and what is shown here is a shelter over the track, while Zonca also proposed a double track, with proper curbs. The use of the name 'horse' for the trolley here does imply that this is something the author has seen working. If at Ca' Fusina, then much of Book 20 would be inspired by technologies established in the Republic of Venice.

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To make de/ences /or harbours, so that fleets cannot enter there

any thlngs can be applied to construction ín water: take sorne stones, like large mill-stones, in which a hole is made big enough for a pointed post to go through; if there is a ground ínto which it may be driven, it can be armed with a good shoe, which clasps four pieces of wood so that the stone does not come away from the post as it goes down ínto the water. When the post is driven home, the stone will remaín above the bed, and will not Illustration 425 hamper it from penetratíng (Illustration 425) the ground. This invention could be used for wooden bridges, to keep their piers straight.

It does not matter if the stone e is not round, it will be good anyway as long as it is large enough. The shoe is B, the post A.

M

To see how much error there may be, and how far the work can be spoiled by carelessness, [!fol. 429r] however slight, when the post does not stand upright, it is plaín that the rod A B is upright, and is not ínclined ín any direcúon. Rod D is erected ín the same ground E, but is somewhat ínclined at E toward D. This is quite a small ínclinaúon as will be appreciated, half the square G; yet ín the region of e it looks impossibly far apart.

That is, out of sixty units of height which rod A B contaíns, it does not íncline more than one from rod D. Yet at the top of rod ít ínclines twelve times as much as ít does at E G . In this way you will realise how much it deviates from its position by a small ínclination, as can be understood from the illustration.

e

e

e

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11/ustration 426

It seems to me that there is often occasion to construct in water with old vessels, but there are seldom enough hulks or old ships to be found as may encompass a harbour, or take in an area big enough to make a cascle. So I have thought up another invention, much better than ships or hulks. It is to make some things like chests, which are to be as long as a beam, or more, and the same width. Make a frame of beams, (Illustration 426) not paying too much attention to the shape so muchas to the design. These arks will serve as hulks in this place. They should be capable of holding a great quantity of stone; [!fol. 429v] and if it were reguired to position the stone in the hulks like a wall, it could be done, so long as the ground was suitable for making holes. Then fit a lid on them to close them. These chests can be joined to one another until the whole circuit of the enclosure has been completed; these chests, for so we will call them, can be made as high as walls would be. Mount them in the same place upon one another, and as I say fill them with stones.

Iltustration 42 7

While they are being lowered to the bed have a man by each of the holes to unstop them so that this frame can all go down together at the same time. Por if it is all going down together it will not shift, even if the bed is not level, which will be very different from the previous type. (Illustrattón 427) This is the chest used as a hulk, with its holes A and B. Piece C fastens the two pieces of hulk D; and the same with the two ends of G, H K. That will do for the circuit of the area. [/fol. 430r] Hit is required to fill in the whole, it will be necessary to throw in many chests, all full of stones, sorne loose and sorne fitted tight. Do not forget the holes so they can go to the bottom with their stone. Por this purpose keep plenty of timber, sawn and unsawn, and great quantities of stone and lime, and sand and countless other things, such as nails, cordage, panniers, osier baskets, wooden and iron shovels, spades, picks, iron crowbars and mallets, wooden basins or tubs, large and small of every kind, plenty of planks, quarter-timbers, and countless necessary things (Illustration 428), slings, pails and hods: for so much else will be needed to make a machine like the one illustrated.

To construct ita frame must be made all in one piece like this, P. A are nailed planks, [!fol. 430v] B the stones inside the chests. Por a purpose like this the machine has to be joined to form one piece, fastened firmly at each comer. It could be made in various ways, with chests different from those sketched here. (Illustration 429) [592]

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Illustration 428

Two kinds of chests are shown here. H is the space in the middle, K the stones in the square chests or hulks I- although they could never lie in the position they are sketched, in no wise, because it is irnpossible so to place them that they should be joined tighdy together [!fol. 431r] without any spaces between them, specially when there are two rows together líke this. Still, sorne single chests could be made, with one side broad and the other narrow, as at I and L. Figure M is quite different in the shape of íts chests: the fírst must be filled with large stones, (Illustratz"on 430) which are also good for the second and third rank of each type (although in this sketch there are only two). The joins need to be well made so the chests can be filled with stone; they then need to be caulked and lined wíth pitch, otherwise they will be no good, because before long they will go to the bottom. The middle will be filled with stones wíthout chests, since the stone thrown down there will be able to pile up. If there ís fine stone in the middle ít will Illustration 429

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Volume V Illustration 430

settle by itself much better and with greater security than thick stones, [!fol. 431v] since there is less empty space. Often people rely too much on big stones, for when they forma top-heavy load they overturn very easily, much more than small stones would do. A man may well think that as the stone is large and heavy, any weight can be loaded on to it. But if once there is a load on it, it overturns straightaway, and it will cause great damage. Once the heap of stone rubble has been raised, to reach the surface of the water, level it off, and fill in with lime and sand, to even up the base and flatten it. When it is quite flat, a base of paste should be thrown over it, tamped clown well as they do with adobe walls when they are being smoothed over. This pasty mortar should be at least eight palms in height, or six anyway.

After it is dry, stones should be laid and walls and bulwarks made in the shape best suited for such a purpose. Very large stones should be Jaid all round the construction where the waves may strike, attached to one another by iron or bronze clamps, well leaded, as I said about bridges and harbours. Much ingenuity must be used; where the waves strike regularly, there make use of a convex line, or of the corona lisis of Vitruvius, which is N. The base is M, that mortar which I said had to be tamped clown like the adobes O. The stones are P.

[!fol. 432r] These chests will certainly last for a long time in the water before they are consumed or rotten, but they must be caulked. I should like to make the point that a body in the water, however deep it may be, takes no wear, because the water does not (Illustration 431) attack nor move it from the place where it was positioned the first time it was submerged in sea water. It never moves, but rather is loaded with sand and mud; and this we learn from experience, for we see that Illustration 431

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whenever a vessd is wrecked in the sea, much hard work is needed to recover it because of the amount of mud with which it is laden. So an object in the water bears no weight- granted that it may have as great a quantity of water above it as you can imagine, but that does it no harm nor does it affect it. Now water is what affects a construction, but when all this material has been put into position, it will make no more movement thereafter.

The third kind of bed is when it is muddy; that is more difficult, as then there is no base available for the things that have to rest upon the bed, so you will need to find sorne invention to enable you to build on it, something quite different from those preceding; and it is this: [!fol. 432v] take the depth of the water in the place where the structure is to be erected, and having observed that quantity, make a wooden frame, in pieces to take in the whole circuit, laying it gradually, as if it were required to make a wall all of wood, with the boards at least four fingers in thickness- it is to be thirty palms wide or more. This framework must be caulked well and lined with pitch, so that no water can get in anywhere. After it has been laid clown, place in it thick stones roughly positioned or worked in such a way that they can be laid on the bed and along the sides. Put them in position with their metal hooks or clamps, and so continue: in the middle lay fine masonry, and at intervals lay as stretchers sorne long stones to cross the wall made by the chests or framework.

But before you think of putting anything in position the frame should first be conveyed to the place where it is to be lowered. There proceed evenly with the positioning, put the wall in place until it reaches almost to the top of the frame.

Once it is in position it is lowered nor does it cease filling in because only when none of the wood remains to be filled, will it go to the bottom. The reason is that a ship will contain as much water as the weight it supports on the water, which is as much weight as can be contained in its volume. That done, raise the frame again, as was done the first time, and put it in position again, taking care to make the frame firm at certain places with the same stones, [!fol. 433r] so raising it as much as its girth is extended, because otherwise nothing will be done. Note should be taken when the frame of this construction is a man's height above the water, position it very promptly so it may be lowered evenly on to the bed. If the frame has been properly bound with ties, even if the bed is not as levd as it should be, for all that it will not fail to lĂ­e straight because of the great weight over it, particularly if the bed is of mud, for that willlie evenly. When all the circuit has been made very firm, make and complete the building intended. As I have stated dsewhere, fill in whatever space is left empty with stones and earth. Yet even if all was well thought out, it will be a business of very great expense; and you must have a clear judgement and a livdy understanding for anything so difficult as this business of water.

The forro of the frame as it was discussed: A is the outer part, (lllustration 432) B the inner, C the two cross-members. In this way it can be made up in sections and then joined together. [!fol. 433v] The method of joining up the beams will be found in the book on wooden bridges- that is, how they are to be coupled to one . another. If the wood is put clown green it willlast much longer without spoiling because it preserves its natural moisture. When it has to be lowered to the sea-bed the depth of the water should be taken first. Besides that, first send clown a good swimmer to see what kind of bed there is. So this device can be built through the water, with great courage, and it will perform the function required. If there should happen to be some obstacle in the place where it is to be put, you can move it aside or shift it, so the device willlie better.

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11/ustration 432

The construction can be made with another kind of frame. The pointed posts

will go in like C. The beams A B FE are joined at GH; they are much longer, (lllustration 433) overlapping more than five palms, so they can be nailed together at K L. O M N O are members with points on the bottom, on which iron shoes are mounted so they will penetrate the earth. Any kind of instrument can be joined up in this way. [!fol. 434r] Note must be taken to have someone with considerable experience of that stone, for the salt of the sea consumes sorne particular kinds of stone, where the waves strike continually against them.

When this construction has been put in position, many instrurnents must afterwards be installed to pump out the water: various kinds such as may be found in the section on stone bridges. After this, shafts can be dug, as deep as possible, away from the enclosure, and in them erect large pilasters sixteen feet thick, which are to be made in the manner illustrated for the pilasters of aqueducts.

With this procedure, it will be possible to carry out intentions like those of our lord the King at the shoals of Tortosa.

Once the pillars have been raised, the spaces between them can be arched over, or vaults constructed of sorne thick material- but doing it this way will mean hard work and much expense, and much danger too. If it should happen when a job like this has to be done that no stone of the proper kind is to be found- but there is available a black sand which in Italy Ă­s called pozzolana, which kneaded with lime hardens in such a way as to form a very strong stone- then this material can be laid in moulds and made into stones of the shape required.

Illustration 433

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[!fol. 434v] To lay things in water, you should have sorne swimmers who are very skillul under water, so that when something is to go to the bottom, you may k.now whether it is going well or not on the sea-bed; and they can signal to us any snags there may be clown there, not to guide them below, but to signal to us in which direction it would be best to lead the construction. There is also an instrument to enable a man to stay under water, and certainly I do not believe it would be off the subject to set forth the method of making an instrument for this purpose. It is true that Vegetius has one in De Re Militari1, but it lacks all ingenuity.

For with this instrument of his, made of leather, he wants a soldier ro cross a river under water; but it could not be used in the sea. This device is to make a leather costume, that is doublet and hose, with a cap all of dressed cow's leather. Then he will put on the mouth-piece of the helmet a pipe, likewise of leather, to be no greater calibre than one inch, or a little over. It must be very long, and can be pulled along in the way it is done with decoys for quails. At the top there is to be a cork float to support the Illustration 434 leather above water. And he wants men to cross a river with this invention. [!fol. 435r] With this pipe one can indeed breathe in and out.

But the instrument which I wish to illustrate here is quite different, for with this e device a man can stay under water half a day or even a whole day without coming to D any harm, eating and drinking under water. A is the instrwnent. It is a glass bubble at least three palms in diameter, pierced at e, (Illustration 434) so anyone who wants to go under water can put his head inside. B D E is the frame, a wooden construction to which the glass ball is fixed in position.

In the base is placed a lead plate weighing at least a quintal, which is G; it must be fitted on securely so that it can not fall off. Then attach cork floats to keep it above the water. With a very little weight it will be able to go clown to the sea-bed, and once the weight is removed [!fol. 435v] it can rise again above the water, so it has to be very finely adjusted to go up and clown. At the side of the instrument a winch L K is fitted; 1 'it is true that Vegetius has one in De Re Militari' ... this must be the pict~r~al app_endix to t~e 1532 and later editions; the description fits the illustrati_on on p.180 of that edm?n qutte well. Ltke other woodcuts in that book, it probably came from a fifteenth century manuscnpt.

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Illustration 435

then take a cord of best hemp, not too thick, and hang from it a lead ball, weighing ene arroba.

When the man wishes to go down to the bottom of the sea to find something, the lead ball I is placed in the water. Then he turns the winch and winds up the cord to which ball I is attached, and so the instrument goes down until it reaches the sea-bed. Then he looks at whatever he wants, and when he wants to go up again he releases the cord; in this way the instrument will rise by itself just by e slackening the cord. The ball A can be made of rotmd holes will have to be made all round it, then but 435) bronze, (Illustration with glass windows set in the holes large enough to look through into the sea in order to find whatever has been lost. A is the ball, B the windows, C the hole through which the head is inserted. It can be made another way, from a cask like those for wine; it should be well hooped and have that same lead plate fitted to the base, with the cork floats around it, as I said of the previous one, [!fol. 436r] but in this case the base of the barrel has to be pierced with a hole large enough for a man to get through: the same with the lead plate, which should also be pierced. Inside a seat is fitted, and on one side put the winch to take in the cord. All around square holes are to be made, in which are placed glass windows to look at the sea.

When this instrument is placed in the water, it should be in an upright position, not inclining in any direction. Those floats need to be put round it, with the cords to attach them to the machine in such a way that they can not work loose from it.

Instead of cork floats a great many gourds could be employed, large ones that contain a cantare of water in each, or more. A is the cask, H the glass windows, I the lead plate, K the hole for the man, L the gourds, M the sea, N the winch, O the lead ball.

This invention may be made another way, as a very large copper ball with holes in it, in which windows can be inserted in conformity with what was said of the other inventions. Or it can be made in yet another manner, so the man who is to go into the device can eat and drink and even have a light inside. It will be necessary to make a large square wooden chest, having all those parts that have been described; [!fol. 436v] for lack of cork floats or gourds it could use stuffed wineskins, but then they should be caulked on the outside, because water would spoil the leather. Care must be taken to keep the weight in the right proportion in everything; and likewise whatever is to lift the weight upwards. Ollustration 436) Ships, it is clear, are like mobile houses; they are sea dwellings in which men live upon the waters and in them carry out all their activities. Vessels and ships could also be called beasts of burden as they take cargoes to various places; we could then say that harbours [!fol. 437r] are the dwellings of these vessels and serve them like stables for animals, to rest as if in a sea dwelling. Others hold a contrary opinion, that ships are travelling fortresses. But leaving all this aside, with ships and galleys two things alone will save our material and will be the salvation and victory of the captains of fleets at sea. The first thing consists in making the ship in such a way that it does not roll, and the second in fortifying harbours so that you have sorne base if you are to attack, or if you are yourself attacked, for ships are so ordered that they carry you and your companions. The other thing is that you can [598]

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I!lustration 436

wage war straightaway so long as you are in no danger of perishing through the vessel herself.

Sorne dangers originate in the ships themselves, while others manifest themselves on them. The troubles not caused by the ships themselves are furious winds which make rough the impetuous waves of the sea, or drive them aground on sorne sand-bank, or smash them agaínst hard rocks. All these can be avoíded with long experíence of the sea, wíth knowledge of places and winds, and so with good judgement these accidents can be provided for befare they happen. But the dangers which originate in the vessel herself derive from her shape or because of the decay of the timbers.

To cure things like that, [!fol. 437v] make provision that the timber is good, and will not split or decay, nor be too heavy nor so fragile that ít breaks at the least blow. These things are most important: the nails and cramps to be of bronze or copper, because iron thíngs decay, and are ímmedíately consumed by the rust which the sea causes. That may be understood from the ship which Trajan had built, and put on the lake of Ariccia2; which sank and stayed submerged in the water one thousand and three hundred years; and then a few years ago it was drawn up- and the timber-work, pine and cypress, had lasted wíthout spoiling all that while. The ship was of thís kind: on the outside she was made of double planks, one upon the other, and then caulked with pitch and sulphur. Afterwards she had been covered wíth linen cloth and caulkecl over, and then covered with leacl plates cast like organ pipes. Everything was coverecl with these lead plates nailecl clown well, wíth the joínts of the plates well solclered. The nails with which they were fastenecl were of bronze or latten.

Those who were the ínventors of shíps took their form from fish; but upsicle clown, wíth the belly on top ancl the backbone unclerneath. Ancl they dícl the same with the fish's heacl, for the head they macle the tail of the shíp, [!fol. 438r] ancl what is tail in the fish they macle head in the shíp. So everythíng was reversecl; for 2 'the lake of Aricda' ... the text has 'lago de Recia'; this is Lake Nemi. Although Alberti uses the old Latin name, Bartoli translates as 'lago di Riccia', from the little town of Ariccia near the lake.

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Volume V what is -tail in the fish is the rudder and helrn of the ship, what are fins for the fish serve as oars for the galley. Vessels are of two kinds : sorne to transport cargo, and the others to move or run fast. Long vessels are the best for fighting; these are the galleys which overtake and retreat at a great speed. Short vessels are handier and better controlled with the rudder than galleys. Ships to carry merchandise are to be no longer than three times what they are in width- nor shorter as illustrated here.

I leave aside the castles that stand at poop and prow, for they go in the air and do not touch the water; I am only to be understood as meaning that part of the ship which goes in the water. Galleys, being vessels of war, are longer than galleons; they are to be in length nine times their width, as is here indicated by the numbers, although it does seem very long, simply through not having any decoration. The galley is B. To recount all the details of the galley or ship would be a very wordy business: the most noteworthy are; the keel, the stern, the prow, the sides, the mast, the yards, the rudder, the sails, [!fol. 438v] the anchors, the cables, rigging and Illustration 431

countless other things which belong to ships and galleys. Here we shall conclude that the ship will bear weight equal to thc weight of the water it could contain.

The keel of the ship (Illustratz'on 43 7) is made in curved lines, like a bent arm; the wider the keel the more cargo the ship will carry. When the keel is narrow, the ship will travel faster, but it should be filled with ballast or sea sand so the ship does not roll. The wider the keel in relation to its depth, the better will it serve for sailing. [!fol. 439r] But if the ship is to sail through a very deep sea, the keel should be narrow and drawn in; then, the more she sails and the deeper the sea, the safer she will be. Let the ship be very high at the sides, and the prow and stern high, so the ship can break the waves. However vessels made like that are much harassed by the wind. The more a vessel has her bows pointed, and the higher they rise, the lighter she will be to sail. The more slender the stern the straighter the ship will go [600]

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and the lighter the ship will hold herself. The backboards and bulwarks of a ship must be very sturdy and strong.

No vessel has more than one rudder. Yet I say that the more she carries the safer she will go- but more sluggishly. With more rudders she rolls less with the wind, but is held back, because with each rudder there is a braking of the waterand that is why they do not put more than one rudder on a ship, for speed's sake.

Let the masts be as long as the ship; and let them be fitted with main sails, crow's nests, foresails, and countless other things. for ships to last, let them be made of good timber, well nailed and caulked- use a good quantity of sulphur, for that lubricares her on her way, and so there is no need to careen her so carefully.

Caulking a ship preserves her from decay and keeps the water from getting in. [!fol. 439v] It takes ten pounds of pitch, a hundred of brown sulphur which is cheaper, all melted together; and the ship caulked with the mixture. Bitumen is much smoother and protects timber better than pitch alone, and stops the ship worm getting into the wood. Sulphur is very thick, and smoother and stronger than tallow or pitch, and it lasts longer, because the sun does not soften it; that is a new secret to preserve ships better.

To puta ship in trim many things need to be provided; oars, anchors, cordage, cables, pulleys, capstans, pumps, points of vessels, towers, boats, ladders, crow's nests, masts, sails, timbers, boards to hang from the sides, points, picks, masts to serve instead of towers, the masts from which to hang main sails and topsails.

The ship illustrated has three rudders, A, B, C. The crow's nests are used to look out for enemies, and defend yourself. The masts serve instead of bridges; the Ancients used to use machines which they called homs3 , which served for war; now they are put on the stern, prow and sides. On the masts they put rocks, sacks, cords and rapes for defence of the ship; they serve as a palisade all round it; [/fol. 440r] to prevent the enemy getting up, laya rope net over the ship; andas for the ship's deck, which is made of planks, sow it with iron points- which is the work of a moment- so the enemy will be nailed if they try to leap over. (Itlustratz'on 438) Illustration 438

>'machines which they called horns' ... i.e. 'cuernos'; which may be the ancient 'Corvus', as 'poínts' (above) may be the «rastra» or rams of ancíent warships.

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I//ustration 439

Here is another inventíon. Make a deck of planks round the ship, where the enemy can get up, and once they are up, with one blow of a hammer, the whole thing collapses -and the enemy fall on the iron poínts, and there die an evil death.

This ínvention ís A; (Illustration 439) [!fol. 440v] B C the planks, DE the beams on whích the planks rest; G the post on which the hammer blow is given, it has free play at that point.

T o defend a harbour from enemies, send sorne old vessels to the bottom outsíde the entry: because íf the enemy come with saíls spread to try and break the harbour chain, they will first bump agaínst the vessels placed there for defence. H they should happen to budge the machine with their great ímpetus, they can not break the chain. The iron points on this machine will pierce any such vessels; it can not be set in motion, as ít is made fast with so many anchors. The machíne is constructed like a shield laid up, for the head whích faces toward the harbour ís to be as broad as the harbour entry. The machine is made of whole beams, in conformíty to the manner we sketch it here. Fírstly, it is necessary to take many casks, mounted on a frame like a shield, well nailed to one another, so as to support the frame A with the casks. Six rows of them are laid down to cover the width of the harbour. They are made fast with beams to keep them together. Make as many as may be needed, and kept steady with anchors and other weights. [!fol. 441r] This will be a valuable means of protection. Above the frame D, a deck must be laid, of somethíng simple, like wattles. Then cover it with earth so the enemy do not burn the machine, and construct thick wooden towers on a grand scale around the círcumference; fasten them well with anchors so they will be fírm enough to resist the furious waves.

(Illustration 440) D o it in such a way that the enemy can not see the towers. The machíne is constructed like a semi-círcle on the side where it will be struck by any ships which try to make a forcible entry into the harbour.

This is the machine to be laid on the frame A. As for layíng the barreis, that could be made in various ways; ít ís enough to give one, [!fol. 441v] for any man (Illustration 441) who has good judgement can invent many others. E is the íron points, which must be very long and thick". D is the machíne, E are posts to which are fixed the íron points F. G are protective ribs for defence of the timbers with the points, made crosswise, in order to offer greater resistance to any object that stri.kes them. The one on top goes like so: in order to resist the fury of the waves 4

The fírst 'E' in the text must refer to F in the drawing: 'G' to the outer protective frame.

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better, and have less need of anchors on the outside. This will be a very effective method of defending the harbour. You can obstruct the entry to the enemy in another way, [!fol. 442r] with old vessels full of stones and earth, and so sent to the bottom- so the enemy can not get in, unless at great cost to him, because he will not be able to move them on account of their great weight, if they are placed in good order and position. The way they are to be sent to the bottom will be found in the place where we discuss how to found a castle in the water. The illustration following shows what I have said. A B C D are the sunken ships or Illustration 441

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Chain of the harbour

barks; and that is enough to show our purpose. allustration 442) The [!fol. 442v] ships which block the entry should be laid in order, all together with their prows toward the enemy, touching one another, and there submerged.

As a rnethod has been given for defending a harbour so that enemies do not hann it, a method should also be given for how to clean a harbour, even though it has been set down elsewhere how to rernove rnud and every kind of filth in a site where the foundations of bridges are laid, with sorne instruments for it.

Another piece will be found under harbours too. But I have decided to have another fresh discussíon of it and set down sorne more instruments allustration 443) to show how they can be used, as I have already demonstrated how the grab removes it and empties it, but not how it is itself to be opened and emptied. A is the grab5 , B the rope, wound round lantern E. Rope e winds round lantern D, and so it opens. You can make it open another way, by inserting a peg in the drum of lantern D when you want the grab to open. It will be so connected that the rapes B ande go together, [!fol. 443r] and turn with the peg G. The rings are to go on the sides at H. There is another machine which can be employed to clean out a harbour. It is a wheel mounted on a barge, or on two as may be convenient. The wheel ís to be of such sort that it can go up and down according (Illustration 444) as the water is high or low; ít empties into a hopper fitted insíde a barge, and when the hopper ís full it is carried outside the harbour to be emptíed. And so they proceed by stages s 'A is the grab' ... 'la bolsa', literally a bag or purse.

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until they have finished cleaning out the harbour. This wheel is three palms in circumference, enclosed with boards on both sides, and has round ít boxes like waterwheel buckets. But these boxes will be open on the outsíde, and the dívisions between each one will be curved. B is the paddles to collect the mud, enclosed on both sides as at C. The wheel A ís to be very robust, [!fol. 443v] because it has to cany a great weight, and endure heavy duty; the arms D are to b e strong too, for the same reason. E is the axle of the wheel with free play at the gudgeon, F. The wheel is lowered at A; part G is raised to pour out the mud in part A. There is a lantern in the axle E moved by wheel M. Two men operate i.t from within the wheel, moving it with their feet on those bars N. The wheels are raised and lowered according to the level of the harbour. These two axles (Illustration 445) O E are fastened firmly to those two posts Q Q, to which the transom P is fixed. This is braced by R R; although each peg Q has two struts at the sides, they are without letters to avoid confusing anybody who looks at it. [!fol. 444r] The method of raising the wheels looks very difficult, but really it is very easy, because the bed of the harbour is not even or flat, so the wheel can take up the mud. Anyone who considers the matter well, will see that it can perform its function properly. Put iron plates on the sides of those curved paddles, so they will not wear out as they turn. This wheel is four palms wide, the paddles B are two palms high. The number of men will b e according to the size of the wheels. The barges are lashed together for this purpose, in two or more places. At the sides of the two little barges, those balks Q at the front should have fairly deep grooves where gudgeons of the wheels will go. In the side of each one they (Illustration 446) have boles, [!fol. 444v] so that they can ride up and clown; iron pegs pass through the boles to support the iron gudgeons-

Illustration 444

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although they must líe on something else wooden, not on iron. U pon the four balks there are to be four wooden pulleys with free play, through which pass the ropes to raise the wheels in turn, and hold them in a suitable position.

In order not to confuse the reader's comprehension of this matter, I have decided to set out piece by piece the parts which are to go together. Thus, the two pieces (Illustration 447) Q are uprights, and on them are mounted the two pulleys X, where the ropes pass with their two hooks X. These ropes are wound round the two pieces V (whose axle is T), with free play at Z. At each end there are spokes to turn the axle T. [!fol. 445r] In the balks Q there is a groove R, in which go the gudgeons of the two wheels, although the ropes are laid the opposite way round, the hooks come on the side of the groove R, to take up the gudgeons, in order to Illustration 446

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lllustration 447

raise them. I have here set down most of the letters which go with the other form of this invention for the better understanding of this subject: the hopper in the barge receives the mud which the wheel e pours into it. Its buckets are A. And with this device a harbour will be cleaned.

Asto the preceding figure which has this mark, it is cliscussed up to where that same mark stands, and it ought to have been inserted in this space, but by mistake it was put in earlier on, and so it must be taken into account that it should be here in the course of the subject matter and its figures.

NOTE:

Mud can be removed from a harbour with another instrument, in some places called a dredge and used by farmers to level their lands. It is easy to make, as it involver little ingenuĂ­ty. It is used in Germany [!fol. 445v] and various other places; in the winter-time, when there is ice, boys have the custom of taking an instrument like this, and sliding over the ice; besides, in mountainous regions they take exercise in it, to escape idleness they go up one slope and down another- this instrument is no cliHerent from that except that it has no iron straps like the one employed in carrying earth from one place to another, and it has a somewhat di.fferent shape, in that the rear part is wider. (Illustration 448) AtA there is to be an iron piece to take the upper and lower parts, nailed to them both; and B is the top part. At e the mud is collected, D is to empty it, with a lead weight inside to keep it on the ground. The two rings E F at I K have two partners attached to another ring H L, all four being attached at one point so as to lift the dredge once it is full.

M G are two more rings [!fol. 446r] which keep it sweeping the ground until it has filled up, and then empty it in the way we shall explain. R is the crane, with free play at Q; the mast holds the pulley N (Illustration 449) throught which the rape passes; the jib S has a strut T. The frame Q has four legs made fast to the barge on the left hand side. The heel P raises the scraper, and draws in forward. eare must be taken in placing the rapes so that in the winch O where both are taken in, they are laid opposed to one another, so that when one draws the scraper the other Ă­s [607]

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____ ......s.......

slackened. The crane can turn in any clirection to empty the scraper into a hopper fitted on that barge, so it can be removed outside the harbour. So two barges will be needed with their hoppers in order that when one is gone to clischarge, the other is filling up. The two barges are to be attached to each other [!fol. 446v], and a deck goes from one barge to the other in order to transfer the wheel. Two or three men are to move it, pulling and lifting.

As we have discussed various buildings founded in the sea, and coundess other instruments, it would be well if we were to deal with how a ship that has sunk in the sea can be drawn up when it does not seem safe to pass over her. Now it is such a difficult thing to draw her up from under water, because it has to be done with very thick cables, so they can take hold of the ship; the cables should be thick enough to resist the heaviness of the weight. If the ship should happen to be so Illustration 449

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Twentieth Book placed that the cables can not gird her, all the work will go for nothing, because she will be full of sand or stones or sludge, as she has been under water for a long time. For this sorne artifice must needs be used. Let us take the case that the sunken ship was of a thousand tuns or casks of wine, then to move this ship we shall take two ships which are equal to that: let each contaín a thousand tuns burden. Empty all the fíttings so that only the essential hull ís left, and when all has been taken away and the port boles shut, they must be caulked or lined well with pitch so that no water can get in them. Then fasten them together [/fol. 447r] with beams at a distance that may be judged to equal the breadth of the ship under the water- but let it always be somewhat more rather than less- and lay very thick beams across from ene to the other, so as to project outside the ship as drawn here.

These are ABC, holding the ship D. The ropes G hold the ship as if she were swathed orina sling. E and F are the two ships, which are to be pierced in the bottom in two or three places so they (lllustration 450) can fill with water. Then close them well so they do not go to the bottom- and bring in various instruments to empty the water from the two ships. When a small quantity has been removed, draw it up now from one side now from the other and so keep raising her from each side in turn, [!fol. 447v] little by little, until you have brought her up to the surface. The ships are to be laid stern to stern and prow to prow; the beams to be very stout because they will have to support a very great weight.

The method of girding the ship with cables is as follows. (Illustration 451) The noose A is crossed, and the more it is pulled the tighter it becomes, since it crosses at F. On account of the two rings B C through which pass the two ends it is a very strong noose. Here stout iron hooks will be fitted, as it will never be possible to find so many anchors. The hooks are inserted in a dífferent way from anchors, since they will buttress the ship. The more the noose is closed, the more they ensure that it does not come away and cease to swathe the ship, which is behind the noose G. [!fol. 448r] The flukes of the anchors would prevent the Illustration 450

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Illustration 451

noose G pulling in the ship, so that the cable G needs to be attached to the anchors M. The loop ends at H which is the ring through which end K passes, then through the ring or shackle I, and the end of the cable L which tightens noose G. Then take ten or twelve anchors and make them fast to the beams, lashed by the shank with the cable. A is the anchor, B the fluke, C the knot, M N the hooks; they take up the noose O. A deck of planks should be built (Illustration 452) on the barges after they have been filled with sand, water or stone. And so in this manner the sunken ship will be drawn up very easily, and can be conveyed somewhere else where she can be dried out.

Illustration 452

H no ships should happen to be available as big as the sunken one, take four ships together, for with them she may be drawn up. If no ships are to be found, take eight of the ordinary sort of barges, provided they are of capadty twice that of the ship to be salvaged; if eight are not enough, take twelve, [!fol. 448v] provided that six of them equal the ship in capacity. Those who would understand this machine should take note that when the ship is detached from the sea bed, she does not then contain more water than the ships or barges used to draw her up; little by little keep drawing her up until she comes above the water. That is easy to do with capstans or winches. Once she is on the surface, empty the water from [610]

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the hulk and the device (because she will carry a great weight) so she can be removed with greater ease. The following illustration shows how much human understanding can do, since with God's help, we do not lack the industry to devise machines to our purpose. So, if we lack heavy ships for this function, we shalllay our hands on fishing smacks. Note should be taken how much weight each smack can carry by itself: let us take the case where the sunken ship carried two thousand cayzes of wheat, the reckoning made, the smacks have to carry a weight of four thousand. So each ene will need a capacity of 334 cayzes weight; and then the ship under water will be drawn up easily. The smacks are to be so arranged that they all have the points of their prows toward the sunken wreck, sorne on ene side and sorne on the other. [!fol. 449r] Por this task it is very important that the cables should be numerous and stout, with the ends tying atA B (the prows of the smacks are C D), so that the weight will be equal everywhere. It is also desirable to double the ropes if possible because the more folds are given to the ropes the less weight they will cause the cable.

Illustration of what has been discussed. (Illustrattón 453) There is another invention too, to raise the ship, without anchors, nor even hooks. A is the smack, BC the beams which cross over the smack, [!fol. 449v] E I the beams which go alongside the smack where cables F H are laid to envelop the ship G. The beam D is ene of those that go between the smacks, to keep them all level and at the (Illustration 454) same distance. At L N the ends of cables K M are attached, and after attaching the ship's sling, give ita turn. Then attach the two ends again at L M. Let them be as taut as the noose can be as it goes next to the beginning O . It then passes under S, at P; then passes again over Q, and at R [611]

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passes under V; at S passes over P, and at T passes under O, and then over V. The other end is X. When a ship has been sunk for a long time, and the cargo she carried has scayed within her, and is various merchandise, [!fol. 450r] all of nature much Iighter than water, Ă­t is to be supposed that owing to che length of time the ship has been under water she will be full of mud or sludge- for which I will avoid giving the reason for the moment- although it has been stated that bodies by their nature less heavy or weighty than water are raised more easily from the sea bed, than things of their nature heavier or weightier than water: on these more force must be applied than on any other kind. But if the bodies and the material be of equal proportion to the weight, that will be quite convenient- which is not the case with those heavier than water; so the heavier a thing is the more it prevails over light bodies.

The illustration of things heavier or lighter than water, I here explain at A B. A is lighter than water. Bis equal to water. e is heavier than water. D is much weightier than e, and for this reason, that it is very much heavier than water, it sinks to the bottom, whereas if it were not so much heavier, it would stay up like B or C. (Illustration 455) As I have so far dealt with the material that concerns drawing up things that are submerged beneath the water, and have set clown the procedure [!fol. 450v] for filling and emptying these ships or smacks, it does seem to me that it will be a great deal of hard work. Many pulleys with their rapes will be needed, to fill them, with Illustration 455 Water Water Water

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the winches or capstans, adding pulleys ro the anchor cables; with this invention she can be raised by placing the ships or barges in a line, as was stated in the figure with the twelve barges. The noose to embrace or gird the ship should first be attached to the anchors or hooks, which are themselves very thick; and so lower them around the ship. That done with all possible care, pull on the two ends of the cable noose, and if there be only the one, a very strong iron ring must be attached.

Then pass the other end of the cable through that ring, and so make a noose with it. That will keep it very fírm so that ít can not work loose; then make it fast with the same anchor cable, at the same place. But the depth of the water should be no more than the length of the ship; if the depth should happen to be much more than that, the ropes are to be laid wíth the greater care and strength, anda deck of thick planks built over these vessels. Thís deck is to be very wíde and spacious, to províde a base for the winches or capstans [/fol. 451r] for raísing the shíp. And so she will be raised now from one síde now from the other, until you feel that she is detached from the bed: and so little by little she will rise to the surface.

I believe it would be well to give instructions on the way to find something lost in the sea, however deep it may be, and even keep a light to look for any object lost under water, provided it is in water and not in sludge. So then, take a wooden pail, or one of iron, which has an iron handle- and if the vessel be of copper so much the better, provided it is ten cubits in height. Then take two pieces of thick rope, turn the cauldron or iron pail upside clown, and cross the ropes at the mouth, so they will make a cross at the base of the pail also. Then, wíth these rwo pieces of rope make a loop, from which another long rope can be attached. Then hang the pail wíth the mouth clown and the base up. A weight should then be suspended from the handle of the pail, enough to make it go clown into the water without turning over. Put in the rope cross and a píece of pipe, to hold a candle attached to the handle of the pail and the rope cross, tied at both sides as may be seen from the example. Then put in the candle, [!fol. 451v] lit so that its flame goes toward the bottom of the pail. (Illustraúon 456) A is the pail, B the base, C the mouth, D the handle, E the weight, to be of lead; the ropes are G G G G, forming a cross at the base A, H the loop, I the cord to be suspended, F the pipe in which is the lit candle K: and this is the invention to carry a light under water. It can be fítted in various ways, which I leave out as they are not very irnportant; I only want to give instructions on one very easy way. K ís the pail, L L L L the hooks to which are attached those four pieces of cord V V V V, fastened ro the ring M. N ís the cord from which the pail is suspended, K the wooden handle passing through the two holes X X at R. The iron part P holds a tang whích passes through the handle R at S, where the candle Q goes. O is the weíght to carry it under water; [/fol. 452r] this weight is suspended from the handle R; T is the cord. So it is all very easy to do.

When something lost or sunk in the sea has to be found, a device will be needed to make more light. They then take a big copper cauldron, polished till it shines, and put in it a lump of taper wax, which will cause much greater light and claríty.

Even if the vessel is of wood, so long as it has an iron or copper plate fixed to the base, it will be well [!fol. 452v]

If the ship should happen to be so deep that she can not be seen owing to the obscurity of the water, another artifice of the fue they call artificial may be used.

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Illustration 456

Take nine ounces of saltpetre, six ounces of sulphur, six ounces of very clear transparent Greek pitch or cocala, three ounces of refined camphor and one ounce of mastic; pound up each ingredient by itself, but not too much, then put it all in a glazed vessel until it is well mixed; then take three pounds of common gunpowder and four ounces of petral oil, and mix it all very well; then test wi.th a feather to see if the material is loase or stiff; if loase add powder, if stiff, oil.

Put all this material in a linen cloth, as wide as it is long, and thick, tie it very tight with a cord, with many turns. Then pour sulphur in a vessel, and pour it, well dissolved into a bag. Leave the bag to absorb the sulphur until it is so saturated that it forms a crust on the outside. To this attach an iron or copper wire with a big weight of lead or sorne other material; this is to extend five palms, and to have a loop or hitch which a long cord may be attached so it can go as far clown into the water as may be required. Before putting the device in the water, a hole is drilled through the middle of the bag, at the point where it has the lead weight.

Stuff the hole with a little powder and light the device where you are going to look for the lose object. That way the man will go clown fust in the great clarity of the light and will find what he wants. The light is to be kept hanging over the man all the time, in arder that the black smoke should not obstruct his view, since the water will become very black, and the fish will be frightened off and flee away in great terror, without doing the man any harm, and so let him take away whatever he wants. A is the ball, (Illustratíon 457) fastened with an iron wire at B; C is the loop or hitch, D the cord. E is the counterweight to take it to the bottom, G the hole that gives the light.

There is another kind of artificial fire used for making light, and as an engine of war. [!fol. 453r] Take a cloth of hemp or burlap and make a little sack or purse, [614]

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one palm in width, and fill it with coarse powder, then tie it well as it is drawn here.

Make a hole, just the one if it be to light, but several if it is to burn, put sorne little sticks through the holes in such a way that the longer part projects outside, wnip in the purse the material that follows: take five ounces of refined saltpetre, seven of sulphur, three of pine resin, two of camphor, two of turpentine, five ounces of fine gunpowder, half an ounce of vitriol, three of petrel oil, one ow1ce of linseed oil, one of the finest brandy. First grind the material until it forms a thick powder, then it is put in a vessel to boĂ­l, all mixed up with the oils and the water, and when all is boiled and well mixed, it is put in the hemp ball made like a purse. Fold it over several times until it has covered the compound well and forms a thick crust over all. When the ball is dry, remove the little sticks and stuff the holes \VĂ?th powder for setting light to the ball. When you want to cast it, fasten an iron wire round it, and attach a weight so that it will go to the bottom. The iron wire will have to be very long [!fol. 453v] so that the cord that keeps the ball suspended in the water will not get burnt.

The same can be done in the darkest abyss. Take five parts of coarse powder, three of refined saltpetre, one part of sulphur, a half of colophony, pitch or pine resin, a half of camphor, one and a half of turpentine, a half of Roman vitriol or of copperas- not to be ground too fine- it is to be ground by itself and then mix it with one and a half parts of petrol oil, one part linseed oil and one part of brandy, and all well mixed together. Put it in a vessel to incorporate properly.

Then put half the powder into the bag so that this mixture will form a crust; keep putting more cloths on to form extra coats, and then lay more sulphur over them. l t will then serve for the required purpose as the following illustration shows. (Illustration 458) Sometimes it happens that navigable rivers, because of their water being employed for irrigation or other things to the benefit of the local people-, as it might be to make sorne conduit- demand of us great ingenuity and industry [!fol. 454r] in order to keep doing what we want of them. For if their water is taken off to make conduits with sluices, if the water is never to fail, these sluices may be the cause why no barge can go up or down the river, which is a great inconvenience to the towns that can not supply themselves with merchandise as they used to. To retain this benefit I thought it would be a good idea to make this invention. In the lowest part of the rivera wooden structure is to be made, that is a pound-lock made of thick posts crowded close together; two gates are left so they can be opened and shut, as may be seen in the illustration we shall sketch. Let a square enclosure be made big [615]

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Illustration 458 To emit light Lead

enough to contain two barges within it, the drop square too; and high enough to extend above the head of water when it is required that it be lowered. Let the construction be very firm and secure, so that it can bear the great weight of the water it will hold with it. When barges want to go up that leap, they must enter the structure; then shut the gates of the endosure, until the water reaches the top, level wíth the water upstream. The same thing ís done when the barge wants to go clown. Note that the barge does not leave the locks before all the water has gone out, because otherwise it could suffer serious damage. The structure can be made of stooe, [/fol. 454v] and would then be less liable to decay than if it were of wood; but there is greater expense of stores and workmen, nor can it be repaired so easily as wood. (Illustration 459) The strength of this structure líes in making it properly secure. T o show how the sluices or gates open and close: let the locks be rectangular6, forty palms in width, sixty in length, and of the following shape. Build a structure, cover the gates A B, on which you may fit a device to raise them. The device has a wooden screw made of holm-oak, elm, service or sorb. The screw has a lantern Illustration 459.

6

'let the locks be rectangular' ... in the text 'cuadrado'.

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[!fol. 455r] with its gate or nut through which passes the spindle or thread of the screw; it is to be placed on the gates in accordance with the instructions I shall gíve. A is the water corning clown into the locks- B that inside them. e is the barge, D E the sluice-gates, F the shores which serve to support it, and entirely surround it; there are to be severa! of these, close together and sorne shorter than others so as to give stronger support. The sluice gates are raised with the winches A; they may also be raised with a screw and lantern. There are then four ways of raising them: A is the first, B the second, e the third, D the fourth. Illustrations are provided of all four, to show the dífference between them.

This sluice or gate opens quite dífferently from the others. In the middle it has an axle which turns on two iron gudgeons, and is narrower at the bottom than on top. This sluice-gate turns very rapidly, because the .. ~( Illustration 460 lower part becomes heavier; this gate may be higher than the others since it opens in the rniddle ~- · e (Illustration 460). e is the sluice-gate. The gate D opens in another way; it turns on a pívot like the T 1 '!' rest, but with a central gudgeon: with which 11 .' it empties faster than any of the others invention ~~...

11 i1 [!fol. 455v]. It is as follows: the two parts should turn in (Illustration 461) opposite directions but f'p r.y '>,. both open toward the water. atlustration 462) The ~ part H I turns into the current and has its jambs; 1 1 they too open in different ways, for they have to join in the middle at K L. It opens with chains fl and winches which draw it inward and so the ~; of the locks open. The following sluice-gates 1 <z. the first, A, with the gates raised by is invention .. ' / a winch. B is the second where they are raised by that screw that goes into gate G, which is then raised and lowered very simply as lantern H is turned by two men.

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1

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¡

There is another invention which can b e used to raíse and lower a fall of water.

It is quite different from locks, although harder work, because you can keep on raising it little by little. [!fol. 456r] It will have to be considered how much head of water there is, in order to allow the ríse and fall, although the lift will anyway be somewhat more laboríous than in the locks, where it goes easíer because there is no detention of the water, beyond having a head of water which keeps raísing a boat until it reaches a suitable place. This gate to raise barges and rafts must be very long and wide. (Illustration 463) E is the head of water which falls twenty or thirty feet, so it can raise and lower barges. A B the gate, beginning ate D. G H is the weir [!fol. 456v] to raise the water F; I K is the end of it. The structure is of timber. Although this one is built in the rniddle of the river, it could as well be made at the sides, and that way it would be done at less expense. If the ground should be of rock, it must be pierced with sorne instrument to ensure that the timbers are made firm, and quite safe; shores are placed on both sides. Attention should be paid to the posts, whích should be pointed, very firm and planted well, for herein líes all the strength of the machine, at the two ends I H ande D . Thus with the builder's good care, the device will stay secure.

The gates of the locks in the fourth method are as follows. A B meet at G, with free play on the pivots H I; the two ends e D stril<e the jambs E F, and [617)

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Illustration 461

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Xl.

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1r Itlustration 462

1f that is how they open and close; the barges are to pass through G, no other way. allustratz"on 464)

T o join two rivers separated by about a hundred p aces or so, [!fol. 457r] from which would result great benefits to the neighbouring towns, since they would thereby be supplied with plenty of merchandise and provisions for the support of the local population. With God 's favour I shall give the procedure as to how this may be done, so that a ship can pass easily from one river to the other without unloading. T o this end, the banks of the two rivers should be levelled and an easy passage made clown to the water without any obstructions, and two winches installed, according to the dimensions of the barge; which when the device works will be drawn up with little labour, and conveyed to the other side. Todo this more easily, look for the narrowest place between the two rivers. There will be a house there, where the man who is to take charge of the device may live and keep anything else that may b e necessary. When the ground is poor, it must be boarded over so the b arges can cross better with the winches, making two lines of boards along the sides of the track which the boat is to take when they haul it over to the other side: or else, drive in round stumps twenty four palms in width on both sides of the track. Board in the whole with thick planks, the posts to be eight [618]

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Twentieth Book

Illustration 463

I/lustration 464

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D

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palms apart from one another. Lay down rollers between the posts, and thick planks on top so the barge will go over them: and thus it may be carried across without any damage or deafening noise.

There is another invention for this purpose, which is a low wheded wooden carriage; [!fol. 457v] there are to be four wheels, with two axles, all in one piece and bound with iron hoops, with four rings nailed on to the ends of the carriage: it is drawn by winches. The posts are driven only three palms into the ground, in order not to obstruct the passage of the barges. See the following illustration; from A B the distance between the two rivers may be known, and so the passage for the barges. (Illustration 465) The invention of the rollers, with the conveyance of the barges is as follows:

[!fol. 458r] when a barge is to pass from one river to the other, the goods it contains are emptied and conveyed with the winches- that is, before the barge is [619]

fUNDACIĂ&#x201C;J\ JĂźA)(ELO TURRlAl\0

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Illustration 465

carríed across, the goods are conveyed by various devices, that is, with a four-wheeled carríage which is quite small and different from the one that carries the barge.

Convey the barge itself from one river to the other with winches or capstans, two or three according to the distance between the two rivers. Employ pulleys with thick ropes- the more pulleys the better it will be, for the weight will be lighter, and the more folds there are in the ropes, the better, for the weight is more divided; they are put in various parts of the work. Conveying the barge clown the incline will be very easy: it will be necessary to let the ropes go slack (Illustration 466) and turn the capstan backward, since the barge will go clown to pan L almost by itself, although ít will need sorne help to keep it going clown gradually so it reaches the other river. If the rivers should not happen to be so elose together, it could be done where there is a river next to the sea, and the invention employed there. It is true that someone might say [!fol. 458v] that ít Illustration 466 Roadway

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Itlustration 467

would be much better, much less labour and expense, to make a canal to join the rivers, and let the barges cross there. I reply, that that is so, but it might be that the river in question was needed by the local people for sorne irrigation works, or to supply milis and fulling stocks- and also that if one river were lower than the other, the trench would have to be very low, and the water of the one would be conveyed into the other. So in this matter, attentíon should be paid to the advantage and profit of the local people, not to take away from them as much as they are going to receive.

This is the method of the carríage to convey the goods from the barges: the carriage to convey the barge is to be made in another way. The wheels are to go under the carriage they call the 'horse' on account of the load that it carries. The carriage to convey the allustration 467) boat is quite different from this one in its construction, as it is to be much bigger, and the ends are slanting or bevelled.

Illustration 468

[621]

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The 'horse' to carry the barge from one river to the other must be very wide and long. [!fol. 459r] It is as follows: A A and B B are iron straps, with hooks on which to put rings to pull the carriage along, in both directions. E E are the four wheels which are to have iron cramps nailed to them. H I are to be sloping so the barge can get up. This carriage or 'horse' can be made another way, to give free play under the wheels, and so it will go very comfortably.

FINIS

[622]

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TWENTY-FIRST BOOK Introduction Despite the sudden ending, this book does have an air of conclusion about it, winding up with a míscellany of odd copies. The bulk does consist indeed of divisions of water, and of land when changes in a river bed leave islands behind; the water-clocks too could be regarded as divisions of time by the movement of water.

There are three main sections to show the utility of geometry in the allotment of water and land. Whether the intention is to ensure equal access toa source of water, fair shares of the islands for all with property on the strand, or fair shares of the water from a conduit, geometrical reasoning will always come in handy. The complex legislation that regulated the output of irrigation conduits in the 'huertas' of Aragon, and che many conflicts that arose from disputes over the distribution of water are described by Glick (Glick, 1970); divisors like the cutwaters shown in these diagrams survive in many places in the region.

No doubt the author had experience as a surveyor, and perhaps as arbitrator in these cases. Evidently he appreciated why there would be greater velocity in the centre of the channels, and noted the effects of friction along side walls, and against partitions and cutwaters. In all tbis he inserts related problems, like measuring the width of a river by cord, without use of instruments [459-460v]; or applies a geometrical solution to the proportions between sections of varying orífices for leats supplying milis.

However, the 'libro' begins with sorne crude water-clocks [459v-462v]. At least two are derived from Battista della Valle's 'Vallo' (1524), Book I, ch. XXV-XXVI, pp. 17-9.

Our author has not looked elsewhere for ingenious or accurate clepsydras; these are intentionally rough and ready, to mark the night watches for a camp, as Delia Valle explains, or serve a military engineer in open country. But the third dock is not from 'Vallo', and must be one of the first designs to incorporate a waterwheel's revolution to measure the passage of time.

Near the end, a few more interpolated thoughts: first, an insulated room. Alberti says a little about this (X.16), and Vitruvius (VII.4.5) recommends Greek winter quarters (<<hibernacula>>) giving instructions that resemble those offered here, although there are differences which suggest a contemporary adaptation of this ancient practice.

Then, a division by water; in effect measurement of specific weights, on Archimedian principies, possibly inspired by Tartaglia- rather incidental here, and rather unclearthe alternative technique even more so. The 'bronze vessel' is, as appears from the sketch of a boy's head, meant to be an aeolipile- an ingenious notion, briefl.y described [623]

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by Vitruvius (!.6.2), which caught the fancy of the Renaissance, so that a number were made, of which a few survive. But there should be an inlet tap, and a narrow outlet pipe; and water should go into the aeolipile to boíl, thus emitting a jet of steam; the aeolipile does not go in the water (but Vítruvíus himself is ambiguous about this).

At the end we return to clivisíons of water in irrigatíon channels; to show how the posítion of síde branches in relaúon to the main channel affects the current (as inclicated by flow lines) and so the volume of water that enters them: and finish abruptly with a conduit sectíon calculatíon ...

[624]

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Which deals with the division of waters, o/ islands and other matters o/ water In margin: 'an~ water-clocks

T n·

he way to make a dock with water to indicate the hours of day and night. . . b emg ts may b e d one at little expense, spect"ally when sorne structure ts made in open country where there ís no habitation, for the proper ordering of the workers. T o make this dock, a wooden vessel should be constructed with a capacity of six cantaros of water; it could be made out of a barre! by removing one end; or a little piece of wood, for any wood whatsoever is good for this purpose. A small hole is made in the base of the vessel, or near it, and in the middle fix a rod firmly; it is to be square, and higher than the vessel. Then fill the vessel with water, and see with a quadrant how many hours it takes for all the water to empty through that little hole, which willlast quite a long time. Let us take the case that the emptying lasts the whole of one natural day, that is from daybreak until nightfall, you will realise that the process has lasted so and so many hours. Knowing that, take the whole height {/fol. 460r] and divide it up into the hours from moming till night, and when the whole distance has been divided ínto equal spaces, start to mark off one, two, three and so on until you have marked off all the spaces. Then take a píece of cork and drive a thin íron wire through ít long enough to reach all the hours, as an indicator. So, as the water goes down, the cork will keep going clown too, and the íron wíre will indicate the hours. The wire ís bent at the top, so it will touch the rod on which the hours are marked by numbers. The point of the wíre is made like a bead. If the vessel ís made with sufficient capacity to last the whole day and níght, it will be seen more distinctly how many hours there are in the night. Anyone willing to take the trouble could easily find out when ít is noon and when mídnight. This can be known by fitting the cork well so that ít does not move from its place to mark the hours; then take a tiny iron wire, shape ít like a square handle, dríve it through a cork, so that it enters the rod in the middle of thís handle. In thís way it can not come apart from the rod. Another vessel collects the water which pours out, in order to return it to the original vessel. The operation of the vessel is to be seen drawn on the following page. A is the vessel, B the rod, C D the water, E is the one which receíves the water. [!fol. 460v] Half h ours and quarter hours can also be marked. The water [625)

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Volume V I//ustration 469

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discharges at G. After having filled the vessel with water, mark off on the rod where the water reaches, and from there take the distance and divide it into equal spaces with their numbers. More care would be required if anyone wanted to know at what time day broke or night fell, or when it was noon or rnidnight. (Illustration 469) Another kind of water-dock can be constructed with counterweights. It is m ade in this fashion. T ake two square wooden laths and fas ten them both to a base. They are to be two palms apart, and eight palms in height. At the top two round hales of equal síze are made, and then insert a round piece whích reaches from one lath to the other, well centred so it can have free play in the holes. Then take a vessel of water and attach it with a cord, and weigh the vessel with the water, and take another [!fol. 461r] of lead of equal weight. Then make of this twelve equal parts and attach them to the cord to which d1e vessel is tied, and give two turns of the cord to the turned rod. Let the vessel and the counterweights be equal on both sides. In the vessel holding the water there is to be a tiny hole, very thin or narrow, so that the water may last twelve hours. So, as the water empties, it goes up by reason of the counterweights which raise it. The counterweights are to reach the ground, and as the vessel goes up the counterweights come down. In this way the counterweíghts will have no more force than they need, and no more weight will stay in the air than ís in the vessel. (lllustration 470) When the vessel has finíshed emptying, the counterweights are lying upon the ground, except for the counterweight of the empty vessel ítself. The whole space that the vessel has been raised befare it was empty is taken and divided into twelve equal sections furnished with their numbers, counting from the bottom. In the base of the vessel there is to be an index-hand to mark the hours, driven firmly in. [!fol. 461v] It is of the shape illustrated: A is the water vessel, B the cord, D the round rod, C the turns given to the cord on the shaft; E the counterweights, G one leg which has the numbers of the hours, P ís the other one. Another vessel could be put underneath to catch the water pouring out of vessel A. Another dock can be made, which is quite different from those preceding.

Take a vessel of any type whatsoever and make a very small hole in the base, through which the water it contains can pour out. In front of it, put a wheel, [626]

fUNDACIÓ?\ JüA)IELO TURR!Al\0

Twenty-First Book

Il/ustration 470

like a millwheel, where the water can strike it and make it turn. Let each revolution be one hour.

The axle of the wheel is to be mounted on sorne stable object. Through the wheel a wooden pin is to be thrust, gíving on to another bucket of the wheel on which the hours are indicated. On the circumference of this wheel, there ís to be a bucket which knocks against the pin fíxed in the water wheel. So each hour a turn is given to the hour-wheel, which has the hours marked by numbers. In the foot of the vessel from which the water pours there will be an index-hand, to mark the hours, and the turns each wheel has given.

This dock is more d.if:6.cult than the previous ones, because the spaces on the wheel have to be measured so asto be exactly one hour, and here líes the difficulty, for as to the rest of it, the fashion of it ís a brief business. See the illustration for better comprehension of what has been said. A is the vessel from which the water pours; [!fol. 462r] wheel B turns upon H. The water strikes atE, e is the hour-wheel. The bucket of wheel B is F, that of wheel e is G. D is the index-hand to mark the hours. From this the whole fashion of this dock can be understood; the two wheels are to be on a level, and the hours marked on the other side so asto be seen without any obstruction. (lllustration 471) It sometimes happens that a field of triangular shape, in which there is a spring or well or water-tank, has to be divided into two parts; and each side claims that the spring is to fall to his part; and it is in such a position that it can not be divided, nor can they both share it. For a solution let us take the case where the spring arises at one end, orto one side, and not in the middle. To divide the field with the spring: [!fol. 462v] let us suppose that such a field is a triangle whose shape is as follows . It will be divided in this way; that is, side Be into two equal parts, which will be at D. Then draw a line from D toA; the spring will be G: from G another line is drawn to A, and this done a parallelline is drawn from D to E, and another from G toE; this line will be the one that divides the triangle equally.

This is not perfect: half of this triangle is from E to A, and from E to G; and from [627]

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Illustration 471

E to e and from e to G is the other half of the triangle. The lines from the points are of no value beyond dividing the triangle- apart from dividing the field there is no need of them. Supposing someone does not believe that it is properly divided into two parts, let them reduce the pair to four and then they will see the truth.

Although this is a matter of geometry, as it is a division of water, I have set it clown. (Illustration 472) Illustration 472

A

Another case presents itself: there is a property belonging to two men, which has a well in a comer of the triangle. This property has two equal sides, for it has one right angle and two acute. The well or spring is in an acute angle. At the time they wanted to divide the properly, each party claĂ­med that the well was to fall to his share, because of the irrigation. I say that it is an easy matter to rescue them from this confusion and let each one share the water without entering the other's portien. The triangle is as follows: [!fol. 463rl A is the right angle, B and e the acute ones. The greater side of the triangle eB is divided into two equal parts, which will be at D. D raw from D a line to A, then divide A B into two equal parts at E, and the same with AC. Draw a line from E to e, and another from F to B, so that the spring is in the angle C. H alf of the triangle is E A F e and the other half is e B D E. Thus the triangle and the spring are divided equally, as the figure demonstrates. Just the one line going from D to e would have been enough to divide it equally, but all those lines were made so that the truth might be recognised. (lllustration 473) [628]

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I/tustration 473 Spring

tc-----..---~:.___ _ _ _ _ _ B

If it were required to make sorne

divísion of water to serve a particular aim, using a third of the whole of sorne quantity of water it will not be every peasant or stonemason who would know how to divide it, {m}ess he were a geometer, and quite clever at making these divísions, so that only the water he has measured will pass.

Let us take the case that the measure is a perfect square, and from this square a circle is to be made which shall be as high as the square; and within the circle we are to form a triangle whose sides are equal to the sides of the square. [!fol. 463v] e (Illustration 474) Draw a line from one angle of the triangle to the mid-point of the circle, that is its centre; this line is one ~ide of the square, that is a third of rhe big square ABe D.To make this division properly, it will be necessary to make a square stone whose volume is neither more nor less than the square ABe D. Then make another square of the dimensions of the third; these two squares are not to be laid off next to one another, but the smaller is to be further forward. The reason is that the large one carries much more water. This invention could be arranged in another way, with the small square somewhat further back, as shown below.

So the square A B D is three times larger than square E F G H. M is one side of the large square, and also one side of the triangle, whose sides should therefore be as large as those of the square. Then take and draw a line from the mid-point of the triangle to one angle: this line is one side of the small square, the third of the large square. To recognise the truth of this, let the side M of the large square be divided into six, [!fol. 464r] so that in all there will be 36 parts; take twelve of these litde squares and form a square, and it will be seen that it comes out exactly if it be done with care; the square M is three thirds, and square T is one third of the three.

e

I say that of these two conduits one is M (Illustration 4 75) which is three thirds and N is a conduit which carries one third of that whole quantity. In the form with Illustration 474

A A~------------------,

~------------------~ D

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Illustration 4 75

side O it will carry more than a third; the reason is that unless the conduit were narrower by as muchas N, it would not receive more water by as much as one third of the quantity of the conduit M. But in as much as the conduit ís wider at O than at N, ít receives much more water, because much more water accumulates so as to exert much more force than it would were ít not wider than conduít N.

In the dívision of waters great care should be taken, because there are many deceptions in enlarging and deepening fOnduits. It may happen that water is being conveyed between two towns and in a certain place sorne of it has to be taken [!fol. 464v] over the rest. I say that if the first shall have a wider conduit it will carry more water even if it is divided into equal parts. After the conduit is deepened by three palms it will carry much more water than others because of the great head which attracts more water. I say then that the conduit N will be more advantageous the further back the stone wíth the hole is placed to measure the third, for its conduit grows wíder as far as its hole: it has one third more water, partly because the conduit is wider and so holds more water, partly because the hole is placed . further back. This provides the advantage that there is a much greater quantity of water to enter through the hole, and the water which accumulates at that point exerts a much greater force than it would if there were just enough to pass through the hole. Whenever water is to be divided, walls should always be built at the sides of the conduits. I say then that square N attracts so much more water because it conveys much more: if the two boles are to be stopped up the two thirds are to be separated each by itself and the water would exceed what it would contain by the squares of each one third by itself, what it contains in one square alone; and for this reason the third is set somewhat further back.

The method of dividing waters is a very difficult business. In case a water has to be divided into two parts, and sorne have to convey two parts of three while others get the other third, a square should be constructed of the whole quantity of water. The water that will pass through that square is then to be dívided into three properly equal parts. [!fol. 465r] When it is required to divide the quantity of water, as stated, let it be done like this- as I shall set clown an example here: having made a square ABe D, take the centres of the four sides of the square, which will be E F G H. Make a cross in that same square, and having dívided the square into four equal parts, draw lines from E to F, from F to G, from G to H, from H to F. The square formed in the middle of square A B e D will be a thirdthe large square will be twíce as big as the small one, for it is four and the small one two, and the third of síx is two, which is what we are seeking. (Illustration 476) These matters may not seem to demand any great dexterity, yet well consídered, they involve greater ingenuity than many suppose, but as it does not cost anything, [630]

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Iliustration 476

. . - - - - - - -- - . f

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G

it does not interest people. If water was sold as other liquids are, I fmnly maintain d1at wise roen would apply the greatest careto it. Take the case that a conduit is to be clivided into iliree equal parts, two of which are drawn off at the side, and the other to emerge in the centre. The conduit is A, those into which it is divided are BCD, such that B and D are drawn off at the side, and the central one is C. I say then that all iliree are equal in width, [/fol. 465v] but there will always be a slight clifference, and conduit C will always convey more water than B or D. The reason is that the water travels in a straight path; and besides it holds a greater quantity of water in the centre than at the sides, along the banks. That we plainly see, for every conduit carries a greater load of sludge at the sides than in the centre, since the water moves at a greater speed in the centre. It is also plain that when anything runs along and makes impact with something, the cause of the impact gives it sorne check or stop; and anything that is checked can not travel at the same velocity that it could before. Now the water as it travels makes impact with the sides of the conduit. Those two conduits come out of the sides of the big conduit, and as the water strikes the sĂ­des it Ă­s somewhat stopped, and does not travel at so great a velocity, as in the centre conduit. I say then that conduit C will always carry off the advantage. (Illustratz'on 477) Illustration 477

A

This is better

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Itlustration 478

[!fol. 456r] Here sorne types of conduit outlets 1 are set down, to show the difference between them. Thus in this figure walls are placed which enter conduit A; they are part of the deception, for if it were done without them there could be no deception. E is the conduit, F G H the divisions. I say that in order (lllustration 478) that there should be no deception, the inlets of the two conduits at the sides should begin to open much higher up, that is at I K. If those two angles I K were to begin much lower, on the line F G H, G would always have the advantage, but if the conduit begins to widen higher up, in the manner of conduit G, there will not be any difference between it and conduits F H. If it be done any other way, as in conduit A, there will be deception. I shall set down here below several figures of divisions. When the divisions are equal, and each one carries its own equal portian, I say that conduit F will undergo less harm than G, and conduit H will carry much more water than G. This may be observed because condtút H is much lower {/fol. 456v] than either of the two F G, so that they do not receive as much water as it does. The reason is that water is borne by the lowest conduit most. Someone will tell me that in the division of conduit A, I said that e receives much more water than either of the other two, but now I say that H, which is the lowest, receives most. The reason for this is that as the water is borne to the lowest- thís is to be w1derstood of when the conduits have equal beds- so the further back the mouth of the one conduit is put, the more water ít will receive in comparison with the other two. Thís subject can be understood from the path travelled by the water, for making ímpact in various places ít always undergoes sorne check in its path. So if its path stays free, the water has greater force there than elsewhere, that is why it receives more water- and G receives more than F- for the causes stated above.

To divide a conduit of water into two equal parts, first make two walls on the two sides of the conduit, at least twelve palms long in the place where it is required to make the divisíon, from the cutwater onward. Then build the cutwater in the middle of the conduit- and let it come to a point- and in the base lay two slabs, one piece to each conduit, and line the base with slabs in front of and behind the cutwater. I would wish the slabs to be laid on the cutwater sideways, so that it can not be undermined [!fol. 457r] when lined right down to the base. The walls of the conduit are A, B the lining, the cutwater: the water is to be divided at D, where the slabs D D are laid. In this way there can be no deception. Now at four or five palms from the cutwater a slab ís laid in the manner indicated here; E ís that stone.

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'Here sorne types of conduits' ... note that here the pagination is repeated.

[632]

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Illustration 479

A

A

D ~

t

In such a place there will be great deception because the water will make an impact upon the slab, and turn back. The form of it is as follows. (lllustration 479) Illustration 480

In allotting water, the whole quantity of the greatest of water that comes into the conduit should be amount A taken, and its height and width measured. Let us take the case, where the water is ten palms wide by four B deep, and it is all to be reduced to square palms, so four times ten make forty, divíded into two is 20 square palms to each conduit, which is five palms wide and four deep to each conduít. If it should so happen that there have got to be two squares in the conduit- I mean two holes through which the two streams of water are to pass- each one is to have its hole conform to the measurement in palms whích we stated. Now let us say that sorne make their hole five palms wide by four deep, [!fol. 457v] others want it six wide by three and a third deep. Many are of the opinion that there will be a deception here, not because sorne palms are more or less than others, but because the conduits are not so full of water all the time as to fill the measure of the five wide by four deep. As the water does not have sufficíent depth to fill the entire conduit, and the other has a wider hole, even though it is not so deep, a greater quantity of water is contailled in it than in the other. (Illustration 480) Thus, square A is the whole quantity of the water in conduit G; and it is required to divide it into two equal parts, B, the half of square A. With this arrangement the two squares can be divided equally, having the same capacity, but not the same shape.

It is plain to see that there is no difference in the quantity- I mean that when a small amount of water enters conduit G, the hole or square B will swallow much more water than A. This is something any peasant can understand, however stupid he may be. (Illustration 481) [!fol. 458r] So it is with the passage of water through a vessel: more will pass through one that is wide but not deep than through one that is square, because water normally spreads out wide before it rises up. That is why although each of the vessels has the same circumference as the other, yet for all that B will not fail to contain more than A. Someone could tell me that what can not go wide goes up, [633]

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Illustration 481

A

yet I s·ay, all heavy things go down more easily than light ones, and for that reason it can be imagined that the heavier a thing is, the slower it travels. And I see that water does the same thing: much more weight accumulates at A, since it has a greater depth of water, than passes through B, whereby we see that the more water spreads out wide, the less weight remains on the rest that is underneath. For that reason much more water travels through the lower part B than through A, as one water piles up more on another. I well know that people will tell me that water travels with greater force when there is a greater quantity than when there is little.

But I say that when water is free and does not make any impact with anything, then when it does make impact with something which checks it, it has the more force.

And much more water collects then, than when it finds no resistance, because its own weight stops it from travelling at the same velocity as it would have, were there no check.

It is required to divide a water into two equal parts, but sorne wish their water to pass through a square hole while others want a hole of triangular shape. The division should be made in such a way that there is no deception in any part. [!fol. 458v] One of two things must be done, either divide the square into a triangle, or the triangle into a square. Let us take the case that the triangle is to be divided, reducing it to a square, it is a certain rule that every equilateral and equiangular triangle is the half of a square, the sides of the square being of the same dimensions as the sides of the triangle, which should be made conformable to the sides of the square. Or divide the triangle into a perfect square; it is done in this way: take one side of the triangle and divide it into three equal parts, then out of those three take two of the portions, and the square that will be formed will be equal in area to the triangular A B C. The square is DE F O. (Illustration 482) This is the division of the triangle to a square, which is precisely the same quantity as the triangle. The same division can be made from square to triangle; the triangle is equilateral and equiangular as the figure demonstrates.

Illustration 482 .l>

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Ittustration 483

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a To know how to measure enough water for a mili, they usually make a round stone which is a palm anda half in height, [!fol. 459r] or diameter, and the water which goes through that hole will be the required amount. But that is no article of faith, since others tell me that measuring water for a mili is done with a hole in a stone one and a half palms high· by two palms wide- and only that measure, the capacity of that hole is enough for a mili. So I say that the mean of such waters requires to be measured- but they must be of equal sides and not otherwise. A mill may be made to go with little water, while another with much more does not go. That is caused by the power and force one water brings while another is gentle and has no force. The case is much altered too by the position of the wheels. This is to be understood of a mili with a race, and of no other kind. I say then that the true measure of a mili of water is two palms high by two wide, although I have seen a very large conduit of water through a hole that would be only the height of two playing cards. But the true measure gf a mili of water is as stated, provided it has a race. (Illustration 483) The three measures sketched are all for a water mili, [!fol. 459v] if you wish to confirm which of these is the largest, so each mancan choose the one that seems best in his judgement. But I say that I see a great distance between them because circle A is not more than five palms in circumference, square B is seven palms and square C eight palms.

If there were occasion to divide sorne water into two equal parts, but in the division each party wanted to have bis measure distinguished from the others, thinking he would benefít more from the water so, form a perfect square of two and a half palms each side. That divided up comes out at one hundred square quarter palms. For the other, forro a parallelogram, which is a square, but wider than it is high; it is one and a quarter palms high and three and three quarters long.

Then the circumference of this is equal to square A. (Illustration 484) For A is ten each side, four times ten makes forty, and in the parallelogram B, which is five quarters high and fifteen long, [!fol. 460r] two sides are thirty, and the other ten, which makes forty in all. These two squares may be equal in circumference, but as for their capacity they are quite different by one fourth part. For counting the quarter palms of the perfect square they make one hundred. By counting those of the parallelogram they are five times fifteen which is seventy five. And seventy five falls short of a hundred by twenty five, which is a deception of one fourth as is plain to see in the iliustration- although many people would not believe it without seeing the figures. But I wanted to undeceive them all with a warning that would help them succeed in any partition. If it is required that the parallelogram be of the same capacity, the squares should be twenty. Then five times twenty makes a hundred, and so the two capacities conform to one another.

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Il/ustration 484

A to

o

\

11

' J

S to

11

~

1)

If by chance it should happen as it often does that from one large conduit a branch is to be drawn which will be one seventh of the whole, it can not be done without geometrical calculation. A square should be formed of the whole capacity of the water having 49 divisions. Take seven of these and forma perfect square.

But since seven parts are difficult to reduce to a perfect square, let it hold precisely 25- for seven times 25 makes 175. But as it is troublesome to reduce a square to 175 we should look for another easier and truer way. Form a square any way that you like, which to your judgement will be one seventh, [!fol. 460v] and when that is done draw a long line &om the bottom of that square, take the compass and measure along that line another seven equal spaces. That done, take the compass again and look for the centre of the eight squares, and draw a semi-circle. Then produce a line through the interior, through D B, to touch the cĂ­rcumference of the semi-circle. This line will be one side of a square E G H I, which will be seven times larger than the small one: the large square becomes a parallelogram D B K L, which is reduced to a perfect square as can be understood from the figure.

(Illustration 485) Illustration 485

G

A ~----d----~----~--~~~--~------~----~--~\ L

1

1

' ~---~~H~--~----~--~1~~--------------------~K

Unexpected things often happen; as, that a portion of water is to be taken from sorne conduit or river, and has to b e a ninth part of that water. The same rule should be used as was given for the last case, even though the quantity is different.

Todo this, the whole quantity of water should be reduced toa perfect square; divide into nine equal parts, and each will then be 36. So in all there will be 324 [636]

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parts. But this method ís very lengthy and even this large square may be divided into nine portions more ingeniously: [!fol. 461r] do it in the same way as the square from which a seventh was extracted, by the interior square, for with this rule any portian whatsoever can be extracted. And that is enough of this subject.

I think this subject of dividing water has been discussed at sorne length, and now another subject presents itself before us. Often, and indeed you could even say normally, large rivers in their floods create islands in the middle- or sometimes more to one side. There is commonly argument over them, specially in questions where interests are involved, so that it has become necessary to lay clown laws about them, in matters of property; and so to give and set boundaries distinguished by geometrical calculation which will give each party his own in conformity with what is right. As this is a matter of water, I have set out here a few illustrations, although it is more a matter of law than of geometry- but beca use of the divisions of the lines it can not be done without rules of geometry. Also as this business regularly causes wrangling over these islands which arise in rivers, a procedure should be given for their division. I see that those who border the river on both sides claim that this island is theirs; it originated in front of their property, and so it is theirs by right. So, to take away occasion for quarrels and discord, thís island should be divided.

Here I shall set clown the way to do so, with a figure for easier comprehension of what is being discussed. Let us suppose that on one side of the river, A, there are Juan, Martín and Gonsalo, and one the other side B, there are Francisco, Alonso and Andres. In front of these properties, on both sides, there is a strand of the river [!fol. 461v] before you reach the river itself, which needs to be divided to prevent litigation between the neighbours. T o divide this island yo u should start from the properties on one side and measure off until you reach those on the other side. Do not pay any attention to the river bank. Having observed this distance, its centre must be marked; then draw from ita line through the island. lt is then to be divided into portions according to each party's frontage. So on bank A where there are four properties, P edro, J uan, Martín and Gonsalo, lines must be drawn to touch the line M drawn through the island. These lines should form right angles with line M. atlustration 486) Those on the other side of the river, B, are Francisco, Alonso, Andres: in the same manner, [/fol. 462r] lines should be drawn from their properties to reach line M. Even if the lines from the edges of the properties would come out inclined, they should be drawn straight from the bank, where they front on to the strand, so as to form a right angle with the line M. Por if the lines were to be drawn just as the edges of the properties come out, it would be to the great prejudice of sorne and to the advantage of others. The division of this island may be plainly seen: Pedro gets no bigger portion than C, Juan gets D, Martin E, Gonsalo F, andas for the others on the other side, Francisco gets G, Alonso H, and Andres l. In this division there is no concern to have equal portions, one gets more and another less, according as it falls out for each.

In this partition the whole width of the river should be taken, in such a way as to pass through the centre of the island. T o do this fairly, a cord should be taken, as long as may reach from one side to the other; then drive a stake in on one side, carry the cord over to the other side and drive another stake in there. Attach a pulley, pass the cord through it and pull it as hard as you can. Make marks on the cord as it crosses the river, as it might be to indicate varas or feet- although varas [637]

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Illustration 486

are better for counting than any other measure. These marks on the cord are to be like those which peasants make when they plant vines, passing little scraps of coloured cloth along the cord, and so counting the varas on the cord from one side to the other. Having observed the distance, [!fol. 462v] mark out on the island the middle of this distance between the properties. Let us take the case where there are four hundred varas between the two sets of lands to the mid-point; mark where that comes on the island, and having done so divide it up between the properties, as demonstrated in the previous illustration. Once the mĂ­d-point of the distance across the river has been found, two stakes should then be aligned at the ends of the island. Draw another cord, see to it with a set square that the cords form a right angle. That done, this right angle divides it correctly. I would like to advise you of one thing which could cause great deception in the cross- the cord must not cross the river at a slant, for much depends on its crossing the river straight.

(Illustration 487) Begin at any point required. Let us say that it begins at side A, [!fol. 463r] starting with Pedro, and drawing lines to the centre; it does not matter at all if you begin in the middle or at the ends, nor on which side- what matters most is carrying out the division carefully. Let no-one deceive himself by paying attention to the edges of the properties, for that would be a notable deceit.

Fields are not all straight lines, indeed sorne will be as peculiar as can be, but for all that pay no attention to these lines, either of their edges or their ends, but only to where they front on to the strand. Measure from there, and draw lines parallel to the line of the cord drawn through the island: only by this procedure can the island be properly divided into various parts.

To understand my intentĂ­ons, when I talk of the lines of the edges of the fieldsthey could be divided like this: let lines be drawn as if to form a right angk with [638]

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Illustration 487

cord P Q. Let us say that the edges of Pedro's property have oblique Unes. If we had to draw up the division to conform with these lines, they would end up by taking in almost the whole island, and the others would not reach the island by a long way. But let a figure be constructed so that you can understand the difference between the two. Let us take the case where the two sides of Pedro's property are A B and D, if they are extended to reach the line of the cord P Q, they will take in the whole island. If Martin's property had to be used for the division by the lines of its sides, it would hardly even reach the river. So sorne will get excess and others will go short. The figure is as follows. (Illustration 488)

e

[!fol. 463v] What has been stated can now be seen from the Unes. If we had to divide according to the lines of the edges of the fields, Pedro's land would take in almost the whole island, because of lines A B L and e D E: if a line from L were extended to the island, it would take it all, but his portion can not be more than what is indicated by the lines that touch the cord P Q- that is 1, 2, 3, 4. On the other hand Martín would not receive any portion at all, because F G H I K do not reach the line PQ; and that would be an obvious cheat, if somebody with frontage on the river did not get any portion. Hence the deception which would be caused by measuring in this way is plain to see. So let his portion be 5, 6, 7, 8, which is the whole width of hís land on that bank: justas Pedro's lands can receive no more, [!fol. 464r] so Martin's can not receíve less, than his frontage along the river. But the way more falls to one side than the other is to be understood in general, with every kind of line that can occur with the edges of fields. Besides that, in case somebody's lands do not come so far forward as the others, yet so long as there are no other lands in front of his, for all that he does not go without receiving his portion, like the rest, as the figure demonstrates. (lllustration 489) [639)

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Volurne V I/lustration 488 Field ...

Ponion

It is plain to see that Lucius does not go without his portian, just like Aelius, Glaucus and Lentulus, although he is much further back [!fol. 464v] than any of them, while Andronius hardly receives any, although he is much further forward than Lentulus. So, although someone's frontage on che river should be well back, Iltustration 489

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Twenty-First Book we must not fail to give him his portien, since he does front on it, so all the same the reclaimable waste does not stop being his. If he fails to work it, that will be because the land is no good, or because when the river rises water líes on it, or he wants it to remain a brake for firewood or a meadow for pasture. So he may then leave it through neglect, just not taking the trouble to grub ít up or remove the weeds- just as it is, it can stay workable from many aspects. 1his divisíon is to be understood as applying to both banks of a river.

Besides, great care should be taken in measuring these things, since sorne rívers happen to have very large strands on both banks, although they often form such beaches unequally. For while thís leaves sorne on one bank, they take sorne away on the other. I have very seldom seen rívers leave strands on botl.J sides unless ít were in the summer, because then the water fails and the rivers climinish and so leave plenty of strand on both banks. So when making these lines or partitions of islands it will be necessary to take care to measure from the widest part of the banks; even in the case that the lands do not reach the old banks, you ought not for that to fail to draw your lines from them to the middle, as demonstrated; let us insert a figure for greater intelligibility.

[!fol. 465r] A straíght line should be drawn (Illustratzón 490) crossing all the lands or ends of properties which front on to the beach of the river- granted that one may be further towards the river and others further back, for all that it must Illustration 490

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Illustration 491

not fail to reach the centre of the island, as can be seen in the figure above. You must know how to be discreet in this business of partitions, but all the same doubts can be born in every situation. If a property has no frontage on to the beach, but is wide away from the river and narrow toward it, as in A in the figure, then if it has to be divided in conformíty with the lines of the property it would not receive any portian of the island. For as it went straight to the middle of the island, it would not contain any part of it, since the lines come to a point, to form a triangle which does not reach the centre by a long stretch. For that reason parallellines must be drawn as stated elsewhere. With the figure of property A whose sides come to a point, as at B, [!fol. 465v] in arder for the two lines e D (Illustration 491) to reach the island the strand will have to be regarded as if it were the island and lines E and D G must be so drawn that it manages to receive sorne; it can be done no other way.

To show us that in the one subject various problems may arise in the same case, it commonly happens that rivers make large bends on both banks, [!fol. 466r] and an island is created in the middle between them. It is to be divided to conform with the bends in the river: the same method holds here as with the rest except in the rniddle of the island. That is, from the frontages of each man parallellines are to be drawn from each property to reach the middle of the island: (Illustration 492) but there another device must be used; it is not divided by a straight line, but in conformíty with the sinuous lines or bends on both banks. The reason is that the river bed does not vary, and as the island is in the middle and there is no change on the banks, the division must be made in such a way that the two lines which meet at the rniddle of the island are equal, [!fol. 466v] even though they do not form right angles on the island, but come out almost like curved rhombs. These curves are of the manner indicated in the illustration. So you must divide from the banks to the middle of the island in parallellines, so that neither side can be caused any loss, since you can not take away from sorne nor give to others. As the river does not vary its position, and can not take away from anyone nor give to anyone, obviously they are to receive land in conformity with the point where they reach the rniddle- because we assume that as in the other cases here too we will make partition according to the distance from where we leave to the mid-line of the whole width. Likewise even though the entries are further back, they are not to

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D

have any less. Even if the land does go in bends, it does not obtain more, for both will receive more or less according to the distance of the mid-line of the island from them. But all reach the middle of the width of the river, so it is right that division be made in conformity with the banks of the river. And let that be enough of that.

If in a river there are many íslands, large and small, as the following illustration shows, I say that there is to be no difference in thís division either. It is to be divided like island M, in the same way [!fol. 467r] without adding anything or taking anything away. Island A is the only one that belongs only to those on that side because it does not extend to the middle of the river; likewise ísland B ís nearer to bank M than bank N, and does not extend to the middle of the river. For that reason those on side N have no part in it. But both sides share island C, whích is in the middle- so long as it is in the middle, for if it were more to one side, ít would belong to those to whom it was nearest: island D whích is nearer bank N than bank M will belong to those on side N as the figure shows. (Illustration 493) When all the divisions have been drawn- that is E F G H for those from side M- E obtains island A for himself alone, as well as a very little of island C. G too receives a little of island C, H only receives island B, for he does not get any of island C. L receives a little of island C and half island D, O receives half island D. [!fol. 467v] Hereby the division may be seen with each one's portien, just in the forms that he obtains it, for E gets his share in two parts, and L too; that is because they have a bread frontage.

If we have occasion to make an apartment which is to be occupied in regular use- sorne person of quality is to make his residence there for most of the day, and he wants this apartment to be cool and moist in summer, and warm and dry in winter- it might be done in the following manner. The ground is to be excavated [643)

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Il!tt.rtration 493

toa depth of two feet, evenly, and then a bed of matweed should be laid, four fingers in thickness or height, through the whole of the excavation. Then lay a bed of charcoal, fine in the beginning and afterwards coarse. Settle it as stonemasons do stones, with a wooden mallet, levelling it well; then lay over the charcoal a bed of lime and pieces of ground brick, which serve in place of sand. This bed is to be half a foot high. Then give another portian of lime and iron scoria to be used as sand, and polish this bed well. Although rnany will imagine that it will be cold, yet I may say that it is going to be much wanner- for many reasons, firstly because of the matweed which is warm and absorbs the moisture into itself, secondly because of the charcoal which does not let the moisture come up from the ground. The scoria is warm, the lime is warm, and the brick is dry too, even though it is not warm, and the scoria keeps the warmth of the straw, for if it reaches something · warm, it becomes warm itself, and if something cool, it is fresh. What they did in the temple of Apollo at Ephesus2 holds even better, for charcoal was laid all over the ground befare putting in the foundations [!fol. 468r] or building anything at all, so that anyone could walk bare foot in winter without feeling cold. This has been set clown because moisture concerns water more than anything else.

T o know how to measure a figure by water, be it of marble or metal or any other salid body, in square palms or cubic feet as we might say: I wish to know how to measure a figure in square feet or palms, to know what it contains in bulk after it has been made, that is how many feet of volume it has. Now whether we are dealing with stone or metal, a rectangular wooden vessel should be constructed, like an elongated square; it should be, we might say six palms high by ten long by five high, so as to contain the figure or figures inside it. This vessel is to be lined with pitch so that no water can get out, because if that should happen, nothing could be done and it would be worthless. Having put water in the vessel, palms, half palms and minutes should be marked off on one side of the vessel from the base up to the top. Then put the figure in, so that water pours out as its space is occupied by the figure, and once that is done the figure is to be taken out, leaving the water to run off over the vessel. Then see how much the water in the vessel has 2 'in the temple of Apollo at Ephesus' ... the famous temple at Ephesus was dedicated to ArtemisDiana, not Apollo. This reference is unclear: Vitruvius mentions laying down beds of charcoal in the foundations but does not explain it as insulation.

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dimínished: see how many palms and minutes the figure has made the water pour out, and then multiply the whole palms, and see how many minutes there are in all.

Since four thousand and ninety síx minutes make a whole cubic palm, thereby it may be understood to be sixteen minutes wide, high and long. With this procedure it will be seen how many cubic palms there are in such a figure, if it were agreed that for each cubic palm a certain quantity should be allowed. There is no way to know this except with this procedure.

[!fol. 468v] Yet it could be known another way, by weight, by taking a piece of marble and making a cubic palm of it. Weigh it and having seen its weight transfer it to the figure- as if we might say that the piece of marble which was one palm weighed five arrobas nine pounds three ounces, and then the figure might weigh ninety arrobas fifteen pounds four ounces, reducing to cubic palms according to the arrobas it weighs, that is twenty one and one sixth cubic palms, and one and a half pounds per arroba: but let us say that twenty five reales equalled the palm, it would amount in all to fifty two pounds eighteen solidi and eleven denarii.

Illustration 494

Lighting a fire with water would seem quite contrary to most men's judgement. Make a bronze vessel of two pieces soldered together well, and in it a tiny little hole is made. The vessel is placed near the fire to heat; it is put in a vessel of water so that the water will heat up and boíl. Then this bronze vessel converts all that water to exhalation, and the exhalation is converted into air so vehement that it will burn any block of wood that is on the fire, because of the great amount of air which the vessel throws off. (lllustration 494)

[!fol. 469r] The division of waters is a very difficult matter, knowing how to apply the method of dividing conduits when two or three junctions are taken off.

Let us take the case where they are taken off at the side: A is the large conduit, the divisions, which are all equal, are B D C. Ollustration 495) The middle conduit is C. Illustration 495

I say that more water will go by C than by the other two; even though all three are equal in breadth and depth.

However it is obvious that water travels in a straight line, and besides, in conduits there is always more breadth in the middle than at the sides. In addition, more water will enter at D than at B because the wall E is thicker than F. For as water makes impact with a broad body, that checks it more, so it does not travel so freely.

The conduit G is divided into three equal parts; it may be asked, through which of the three divisions the greatest quantity of water will pass? At [645]

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Iilustration 496

the point where the letters L M N are, it will travel equally, [/fol. 469v] but on reaching H I or K, I say that much more water will enter K than either of the other two because the water travels in more compact quantity at K as its cutwater is further back. So it normally attracts much more work to part K. This can be seen because it is always deeper further along. But many other reasons could be given for this. (Illustration 496) On dividing conduit A into three equal parts, B e D, it is asked in which of the three most water will enter. There is a difference, even though B is as broad and as deep as e, and D too. There is no inequality in the volume, but there is in the position, and so much less water will enter B than D, and more will enter e than either B or D. The cause is plain to see from the figure: because there is much greater breadth from point E to F than in the other two, and also because their Illustration 497

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mouths are further back, and because comer G is higher up than F. If this large conduit A is divíded into three equal parts, [!fol. 470r] all íts water is B e D. It is asked in whích will eilter the greatest volume of water? Plainly, more will enter e than either of the others, and more will enter B than D, because the water enters straíght at the cutwater F; for the same reason e has a much longer cutwater than D, and so the water is guided into e more than D, as may be understood from the figure. (lllustration 497)

Illustration 498

It is asked which of these conduíts has the most advantage. The main conduit is A E; B e D are the divisions. I say then that as much water passes through E as through B, or even somewhat more, although in no great quantity, although they are of the same width. [/fol. 470v] And more will enter D than e- although many will suppose the contrary, but truly, more will enter D than e, because as the water comes to stríke F with sorne impact, it is guided toward G (Illustration 498) more than e, and as there is no comer to be tumed, it then travels toward D more freely than to C. (Illustration 499) Thís division shows clearly how much larger a portion of water conduit

e

will receive than either of the others because it is in the middle of conduit A, (Illustration 500) and still more because of the way the water encounters bay E,

which has greater force to guide it into e than into the other two. More will enter B than D, because water turns back upstream with a very ill will even though the volume is not greater, but in the end there is a cross-over in it, even though all of them are equal- how much more difference would there be if they were unequaland all the more deceptíon.

Illustration 499

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lliustration 500

In this one there is the same difference as in the other above, although it works differently in the middle more will enter e, as it is in the middle: much more water will enter B than D, as the water is guided straighter into B than anywhere else, as

e is further back than the other two.

As I have begun to demonstrate the different effects of cutwaters, and since in diverse places diverse situaúons arise for men to deal with, and specially in matters of water there are great divisions- by way of information on this subject, I ask whích of these three divisions B D (as they are equal in breadth and depth) will receive the greatest quanúty of water? Most will confess it to be B, as it is closer to A, which is the major channel for the quantity of water, but for that reason it may seem more probable that has more, then B and that receives more water than D. Let us now take the case where the whole Illustration 501 quantity of A is to be divided into three equal parts, [!fol. 471v] and once that is done there will be no deception. (lllustration 501) It will be seen what porúon each one has in the quantity of A- quite plainly D has a much larger portien of the breadth than e, and B (Illustration 502) too does not have as big a portien as D. That is demonstrated by the two lines E and F of their cutwaters, all the more as the water comes with such great dispatch as not to be detained by the angles of the cutwaters as it enters its conduit; and because to D it travels in a much straighter line than in the others.

e

e

e

All these plans of conduits may look like a load of jargon with my setting clown so many different kinds, yet there is always sorne peculiarity to illustrate. A is the main conduit, and the others are B e D E: it is well known that much more water [648]

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, !.

will go to e than B [!fol. 472r] and a much smaller quantity will go toE than D. That is obvious because for D it is necessary that the water turn a comer, and besides as it stri.kes the wall of E it must need flow straight, and so strike the wall G, which guides it through into the conduít E with a·strong current, much more than ít can do for D. Besides, it will be seen how much of conduít e is occupied by the line which comes from comer G; and so too with the effect of the line from corner H, whích does not block it, but rather guídes a greater quantity of water into it than into D.

(Illustration 503) The same thing produces contrary effects; this is because the water in the maín conduit travels f01ward while conduít B turns it back; (lllustration 504) and so we recognise that a greater quantity will go to e and D than to B, as is clearly shown by the figure.

This invention of a conduit is quite difficult to understand; however from conduit A the water travels wíth much vigour into B, while from conduit E it travels no better in e than in D: see the illustration on the following page.

[!fol. 472v] (Illustration 505) From conduit A, ít is quite obvious into which of the three conduits the greatest quantity of water goes, as between B, e and D. It is to be noted that in B and C it enters almost equally, in this invention there is no great difference between them, although more does still enter e because the water travels in a straight line, which it does not do in the other two. It is true too that more goes into B than into D.

Illustration 503

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Volume V

Iltustration 504

Illustration 505

Illustration 506.

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Twenty-First Book When a division is made of two waters [!fol. 473r] (Illustration 506) which are taken by measure, I ask if there could be any deception in making the vessels or stones through which the water is made to pass, for they are all made with the same circumference.

Let us cake the case where I have to make a stone with a square hole, tw.o and a half palms to each side, which is ten palms' círcumference in all if it is a perfect square. Then I make another rectangle; two sides are three and a quarter palms and che other two are one and a half, which is the height. So six and a half are the two sides, and the other two of one an d a half make three palms, that is six and a half and three, which is nine and a half. So there is a difference of half a palm even though the two circumferences are equaP, yet in the rectangle there is a cheat of half a palm.

> 'so there is a difference of half a palm, even though the circumferences are equal' ... actually the half palm difference is in the perimeters (here _termed 'c;írcumferences', 'circunferencias'); the difference in area, which is presumably the pomt here, IS greater.

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TABLE OF WEIGHTS AND MEASURES USED IN THE 'TWENTY-ONE BOOKS' (according to the standards of Aragon)

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1

Length 12 dedos (fingers) = 1 palmo 4 palmos (palms) = 1 vara 1 vara = 83,59 cm Sometimes an alternative Castilian system is used; 12 pulgadas (inches) =1 pie (foot) 3 pies (feet)= 1 vara However in passages derived from Ancient sources; 125 paces = 1 stade (in Aragon 125 pasos geometras = 1 estadio= 174,15 metros) The Roman foot too could be divided into 12 inches or 16 digiti (fingers)

Weight 36 libras (pounds) = 1 arroba (12,60 k.ilograms) 4 arrobas = 1 quintal 1 quintal = 50,40 kg

Volume 12 celemines: 1 fanega 12 fanegas = 1 cahiz (in the Veintiun Libros, 'cayz') 1 cahiz (cayz) =666 litres Two other measures of volume are; Almud = 1,87 litres (lh bushel approx.)

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The Twenty-One Books of Engineering and Machines of Juanelo Turriano

Cantara could vary from 10 -16litres- supposedly the quantity contained in a wme-ยกar.

Other more approximate rule of thumb measures are also used; Jeme=distance between extended tips of thumb and index finger (roughly 18 cm.)

Muela=the quant.ity of water that will drive one mill-wheel, which could be treated as a measure of the quantity of water in a conduit.

Real =quantity of water that will flow through a pipe, whose circumference is that of a real (a silver coin).

Both of these are in effect measures of fluid velocity. The former perhaps = 260 litres a second; the latter is estimated at about 3 ~ cubic metres a day.

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