Ten Books on Architecture/Book 5

by Vitruvius

BOOK V

Introduction .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		129
The Forum and Basilica .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		131
The Treasury, Prison, and Senate House .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		137
The Theatre: its Site, Foundations, and Acoustics .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		137
Harmonics .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		139
Sounding Vessels in the Theatre .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		143
Plan of the Theatre .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		146
Greek Theatres .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		151
Acoustics of the Site of a Theatre .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		153
Colonnades and Walks .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		154
Baths .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		157
The Palaestra .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		159
Harbours, Breakwaters, and Shipyards .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .     .		162

BOOK V

Introduction

¹ Those who have filled books of unusually large size, Em­peror, in setting forth their intellectual ideas and doctrines, have thus made a very great and remarkable addition to the authority of their writings. I could wish that circumstances made this as permissible in the case of our subject, so that the authority of the present treatise might be increased by amplifications; but this is not so easy as it may be thought. Writing on architecture is not like history or poetry. History is captivating to the reader from its very nature; for it holds out the hope of various novel­ties. Poetry, with its measures and metrical feet, its refinement in the arrangement of words, and the delivery in verse of the sentiments expressed by the several characters to one another, delights the feelings of the reader, and leads him smoothly on to the very end of the work.

² But this cannot be the case with architectural treatises, be­cause those terms which originate in the peculiar needs of the art, give rise to obscurity of ideas from the unusual nature of the lan­guage. Hence, while the things themselves are not well known, and their names not in common use, if besides this the principles are described in a very diffuse fashion without any attempt at conciseness and explanation in a few pellucid sentences, such full­ness and amplitude of treatment will be only a hindrance, and will give the reader nothing but indefinite notions. Therefore, when I mention obscure terms, and the symmetrical proportions of members of buildings, I shall give brief explanations, so that they may be committed to memory; for thus expressed, the mind will be enabled to understand them the more easily.

³ Furthermore, since I have observed that our citizens are distracted with public affairs and private business, I have thought it best to write briefly, so that my readers, whose intervals of leisure are small, may be able to comprehend in a short time. Then again, Pythagoras and those who came after him in his school thought it proper to employ the principles of the cube in composing books on their doctrines, and, having determined that the cube consisted of 216^[1] lines, held that there should be no more than three cubes in any one treatise.

⁴ A cube is a body with sides all of equal breadth and their surfaces perfectly square. When thrown down, it stands firm and steady so long as it is untouched, no matter on which of its sides it has fallen, like the dice which players throw on the board. The Pythagoreans appear to have drawn their analogy from the cube, because the number of lines mentioned will be fixed firmly and steadily in the memory when they have once settled down, like a cube, upon a man's understanding. The Greek comic poets, also, divided their plays into parts by introducing a choral song, and by this partition on the principle of the cubes, they relieve the actor's speeches by such intermissions.

⁵ Since these rules, founded on the analogy of nature, were followed by our predecessors, and since I observe that I have to write on unusual subjects which many persons will find obscure, I have thought it best to write in short books, so that they may the more readily strike the understanding of the reader: for they will thus be easy to comprehend. I have also arranged them so that those in search of knowledge on a subject may not have to gather it from different places, but may find it in one complete treatment, with the various classes set forth each in a book by itself. Hence, Caesar, in the third and fourth books I gave the rules for temples; in this book I shall treat of the laying out of public places. I shall speak first of the proper arrangement of the forum, for in it the course of both public and private affairs is directed by the magistrates.

CHAPTER I

The Forum and Basilica

¹ The Greeks lay out their forums in the form of a square surrounded by very spacious double colonnades, adorn them with columns set rather closely together, and with entablatures of stone or marble, and construct walks above in the upper story. But in the cities of Italy the same method cannot be followed, for the reason that it is a custom handed down from our ancestors that gladiatorial shows should be given in the forum.

² Therefore let the intercolumniations round the show place be pretty wide; round about in the colonnades put the bankers' offices; and have balconies on the upper floor properly arranged so as to be convenient, and to bring in some public revenue.

From Gsell

FORUM AT TIMGAD

• A, Forum.
• B, Basilica.
• C, Curia.
• C', Official Building.
• D, Small Temple.
• E, Latrina.
• F, Atrium.

The size of a forum should be proportionate to the number of inhabitants, so that it may not be too small a space to be useful, nor look like a desert waste for lack of population. To determine its breadth, divide its length into three parts and assign two of them to the breadth. Its shape will then be oblong, and its ground plan conveniently suited to the conditions of shows.

³ The columns of the upper tier should be one fourth smaller than those of the lower, because, for the purpose of bearing the load, what is below ought to be stronger than what is above, and also, because we ought to imitate nature as seen in the case of things growing; for example, in round smooth-stemmed trees, like the fir, cypress, and pine, every one of which is rather thick just above the roots and then, as it goes on increasing in height, ta­pers off naturally and symmetrically in growing up to the top. Hence, if nature requires this in things growing, it is the right ar­rangement that what is above should be less in height and thick­ness than what is below.

⁴ Basilicas should be constructed on a site adjoining the forum and in the warmest possible quarter, so that in winter business men may gather in them without being troubled by the weather. In breadth they should be not less than one third nor more than one half of their length, unless the site is naturally such as to prevent this and to oblige an alteration in these pro­portions. If the length of the site is greater than necessary, Chal­cidian porches may be constructed at the ends, as in the Julia Aquiliana.

⁵ It is thought that the columns of basilicas ought to be as high as the side-aisles are broad; an aisle should be limited to one third of the breadth which the open space in the middle is to have. Let the columns of the upper tier be smaller than those of the lower, as written above. The screen, to be placed between the upper and the lower tiers of columns, ought to be, it is thought, one fourth lower than the columns of the upper tier, so that peo­ple walking in the upper story of the basilica may not be seen by the business men. The architraves, friezes, and cornices should

From Mau

FORUM AT POMPEII

• A, Forum.
• B, Basllica.
• C, Temple of Apollo.
• D, D', Market Buildings.
• E, Latrina.
• F, City Treasury.
• G, Memorial Arch.
• H, Temple of Jupiter.
• I, Arch of Tiberius.
• K, Macellum (provision market).
• L, Sanctuary of the City Lares.
• M, Temple of Vespasian.
• N, Building of Eumachia.
• O, Comitium.
• P, Office of the Duumvirs.
• Q, The City Council.
• R, Office of the Aediles.

be adjusted to the proportions of the columns, as we have stated in the third book.

From Durm

PLAN OF THE BASILICA AT POMPEII

⁶ But basilicas of the greatest dignity and beauty may also be constructed in the style of that one which I erected, and the build­ing of which I superintended at Fano. Its proportions and symmetrical relations were established as follows. In the middle, the main roof between the columns is 120 feet long and sixty feet wide. Its aisle round the space beneath the main roof and between the walls and the columns is twenty feet broad. The columns, of unbroken height, mea­suring with their capitals fifty feet, and being each five feet thick, have behind them pilasters, twenty feet high, two and one half feet broad, and one and one half feet thick, which support the beams on which is carried the upper flooring of the aisles. Above them are other pilas­ters, eighteen feet high, two feet broad, and a foot thick, which carry the beams supporting the principal raftering and the roof of the aisles, which is brought down lower than the main roof.

⁷ The spaces remaining between the beams supported by the pilasters and the columns, are left for windows between the intercolumniations. The columns are: on the breadth of the main roof at each end, four, including the corner columns at right and left; on the long side which is next to the forum, eight, including the same corner columns; on the other side, six, including the corner columns. This is because the

two middle columns on that side are omitted, in order not to obstruct the view of the pronaos of the temple of Augustus (which is built at the middle of the side wall of the basilica, facing the middle of the forum and the temple of Jupiter) and also the tribunal which is in the former temple, shaped as a hemicycle whose curvature is less than a semicircle.

⁸ The open side of this hemicycle is forty-six feet along the front, and its curvature inwards is fifteen feet, so that those who are standing before the magistrates may not be in the way of the business men in the basilica. Round about, above the columns, are placed the architraves, consisting of three two-foot timbers fastened together. These return from the columns which stand third on the inner side to the antae which project from the pronaos, and which touch the edges of the hemicycle at right and left.

⁹ Above the architraves and regularly dispersed on supports directly over the capitals, piers are placed, three feet high and four feet broad each way. Above them is placed the projecting cornice round about, made of two two-foot timbers. The tie­beams and struts, being placed above them, and directly over the shafts of the columns and the antae and walls of the pronaos, hold up one gable roof along the entire basilica, and another from the middle of it, over the pronaos of the temple.

¹⁰ Thus the gable tops run in two directions, like the letter T, and give a beautiful effect to the outside and inside of the main roof. Further, by the omission of an ornamental entablature and of a line of screens and a second tier of columns, troublesome labour is saved and the total cost greatly diminished. On the other hand, the carrying of the columns themselves in unbroken height directly up to the beams that support the main roof, seems to add an air of sumptuousness and dignity to the work.

CHAPTER II

The Treasury, Prison, and Senate House

¹ The treasury, prison, and senate house ought to adjoin the forum, but in such a way that their dimensions may be propor­tionate to those of the forum. Particularly, the senate house should be constructed with special regard to the importance of the town or city. If the building is square, let its height be fixed at one and one half times its breadth; but if it is to be oblong, add together its length and breadth and, having got the total, let half of it be devoted to the height up to the coffered ceiling.

² Further, the inside walls should be girdled, at a point half­way up their height, with coronae made of woodwork or of stucco. Without these, the voice of men engaged in discussion there will be carried up to the height above, and so be unintelli­gible to their listeners. But when the walls are girdled with cor­onae, the voice from below, being detained before rising and becoming lost in the air, will be intelligible to the ear.

CHAPTER III

The Theatre: its Site, Foundations, and Acoustics

¹ After the forum has been arranged, next, for the purpose of seeing plays or festivals of the immortal gods, a site as healthy as possible should be selected for the theatre, in accordance with what has been written in the first book, on the principles of health­fulness in the sites of cities. For when plays are given, the spec­tators, with their wives and children, sit through them spell­bound, and their bodies, motionless from enjoyment, have the pores open, into which blowing winds find their way. If these winds come from marshy districts or from other unwholesome quarters, they will introduce noxious exhalations into the sys­tem. Hence, such faults will be avoided if the site of the theatre is somewhat carefully selected.

² We must also beware that it has not a southern exposure. When the sun shines full upon the rounded part of it, the air, be­ing shut up in the curved enclosure and unable to circulate, stays there and becomes heated; and getting glowing hot it burns up, dries out, and impairs the fluids of the human body. For these reasons, sites which are unwholesome in such respects are to be avoided, and healthy sites selected.

³ The foundation walls will be an easier matter if they are on a hillside; but if they have to be laid on a plain or in a marshy place, solidity must be assured and substructures built in accordance with what has been written in the third book, on the foundations of temples. Above the foundation walls, the ascending rows of seats, from the substructures up, should be built of stone and marble materials.

⁴ The curved cross-aisles should be constructed in propor­tionate relation, it is thought, to the height of the theatre, but not higher than the footway of the passage is broad. If they are loftier, they will throw back the voice and drive it away from the upper portion, thus preventing the case-endings of words from reaching with distinct meaning the ears of those who are in the uppermost seats above the cross-aisles. In short, it should be so contrived that a line drawn from the lowest to the highest seat will touch the top edges and angles of all the seats. Thus the voice will meet with no obstruction.

⁵ The different entrances ought to be numerous and spacious, the upper not connected with the lower, but built in a continuous straight line from all parts of the house, without turnings, so that the people may not be crowded together when let out from shows, but may have separate exits from all parts without obstructions. Particular pains must also be taken that the site be not a "deaf" one, but one through which the voice can range with the greatest clearness. This can be brought about if a site is selected where there is no obstruction due to echo.

⁶ Voice is a flowing breath of air, perceptible to the hearing by contact. It moves in an endless number of circular rounds, like the innumerably increasing circular waves which appear when a stone is thrown into smooth water, and which keep on spread­ing indefinitely from the centre unless interrupted by narrow limits, or by some obstruction which prevents such waves from reaching their end in due formation. When they are interrupted by obstructions, the first waves, flowing back, break up the form­ation of those which follow.

⁷ In the same manner the voice executes its movements in concentric circles; but while in the case of water the circles move horizontally on a plane surface, the voice not only proceeds hori­zontally, but also ascends vertically by regular stages. Therefore, as in the case of the waves formed in the water, so it is in the case of the voice: the first wave, when there is no obstruction to inter­rupt it, does not break up the second or the following waves, but they all reach the ears of the lowest and highest spectators with­out an echo.

⁸ Hence the ancient architects, following in the footsteps of nature, perfected the ascending rows of seats in theatres from their investigations of the ascending voice, and, by means of the canonical theory of the mathematicians and that of the musicians, endeavoured to make every voice uttered on the stage come with greater clearness and sweetness to the ears of the audience. For just as musical instruments are brought to perfection of clearness in the sound of their strings by means of bronze plates or horn ἠχεἲα, so the ancients devised methods of increasing the power of the voice in theatres through the application of harmonics.

CHAPTER IV

Harmonics

¹ Harmonics is an obscure and difficult branch of musical science, especially for those who do not know Greek. If we de­sire to treat of it, we must use Greek words, because some of them have no Latin equivalents. Hence, I will explain it as clearly as I can from the writings of Aristoxenus, append his scheme, and define the boundaries of the notes, so that with somewhat care­ful attention anybody may be able to understand it pretty easily.

² The voice, in its changes of position when shifting pitch, becomes sometimes high, sometimes low, and its movements are of two kinds, in one of which its progress is continuous, in the other by intervals. The continuous voice does not become sta­tionary at the "boundaries" or at any definite place, and so the extremities of its progress are not apparent, but the fact that there are differences of pitch is apparent, as in our ordinary speech in sol, lux, flos, vox; for in these cases we cannot tell at what pitch the voice begins, nor at what pitch it leaves off, but the fact that it becomes low from high and high from low is ap­parent to the ear. In its progress by intervals the opposite is the case. For here, when the pitch shifts, the voice, by change of position, stations itself on one pitch, then on another, and, as it frequently repeats this alternating process, it appears to the senses to become stationary, as happens in singing when we pro­duce a variation of the mode by changing the pitch of the voice. And so, since it moves by intervals, the points at which it begins and where it leaves off are obviously apparent in the boundaries of the notes, but the intermediate points escape notice and are obscure, owing to the intervals.

³ There are three classes of modes: first, that which the Greeks term the enharmonic; second, the chromatic; third, the dia­tonic. The enharmonic mode is an artistic conception, and there­fore execution in it has a specially severe dignity and distinction. The chromatic, with its delicate subtlety and with the "crowd­ing" of its notes, gives a sweeter kind of pleasure. In the dia­tonic, the distance between the intervals is easier to understand, because it is natural. These three classes differ in their arrange­ment of the tetrachord. In the enharmonic, the tetrachord con­sists of two tones and two "dieses." A diesis is a quarter tone; hence in a semitone there are included two dieses. In the chro­matic there are two semitones arranged in succession, and the third interval is a tone and a half. In the diatonic, there are two consecutive tones, and the third interval of a semitone com­pletes the tetrachord. Hence, in the three classes, the tetrachords are equally composed of two tones and a semitone, but when they are regarded separately according to the terms of each class, they differ in the arrangement of their intervals.

⁴ Now then, these intervals of tones and semitones of the tetrachord are a division introduced by nature in the case of the voice, and she has defined their limits by measures according to the magnitude of the intervals, and determined their character­istics in certain different ways. These natural laws are followed by the skilled workmen who fashion musical instruments, in bringing them to the perfection of their proper concords.

⁵ In each class there are eighteen notes, termed in Greek φθόγγοι, of which eight in all the three classes are constant and fixed, while the other ten, not being tuned to the same pitch, are variable. The fixed notes are those which, being placed between the moveable, make up the unity of the tetrachord, and remain unaltered in their boundaries according to the different classes. Their names are proslambanomenos, hypate hypaton, hypate meson, mese, nete synhemmenon, paramese, nete diezeugmenon, nete hyperbolaeon. The moveable notes are those which, being arranged in the tetrachord between the immoveable, change from place to place according to the different classes. They are called

parhypate hypaton, lichanos hypaton, parhypate meson, lichanos meson, trite synhemmenon, paranete synhemmenon, trite die­zeugmenon, paranete diezeugmenon, trite hyperbolaeon, para­nete hyperbolaeon.

⁶ These notes, from being moveable, take on different quali­ties; for they may stand at different intervals and increasing dis­tances. Thus, parhypate, which in the enharmonic is at the inter­val of half a semitone from hypate, has a semitone interval when transferred to the chromatic. What is called lichanos in the en­harmonic is at the interval of a semitone from hypate; but when shifted to the chromatic, it goes two semitones away; and in the diatonic it is at an interval of three semitones from hypate. Hence the ten notes produce three different kinds of modes on account of their changes of position in the classes.

⁷ There are five tetrachords: first, the lowest, termed in Greek ὕπατον; second, the middle, called μέσον; third, the conjunct, termed συνημμένον, fourth, the disjunct, named διεξευγμένον; the fifth, which is the highest, is termed in Greek ὑπερβόλαιον. The concords, termed in Greek συμφωνίαι, of which human modulation will natur­ally admit, are six in number: the fourth, the fifth, the octave, the octave and fourth, the octave and fifth, and the double octave.

⁸ Their names are therefore due to numerical value; for when the voice becomes stationary on some one note, and then, shift­ing its pitch, changes its position and passes to the limit of the fourth note from that one, we use the term "fourth"; when it passes to the fifth, the term is "fifth."^[2]

⁹ For there can be no consonancies either in the case of the notes of stringed instruments or of the singing voice, between two intervals or between three or six or seven; but, as written above, it is only the harmonies of the fourth, the fifth, and so on up to the double octave, that have boundaries naturally corres­ponding to those of the voice: and these concords are produced by the union of the notes.

CHAPTER V

Sounding Vessels in the Theatre

¹ In accordance with the foregoing investigations on mathe­matical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up to the double octave. Then, having constructed niches in between the seats of the theatre, let the vessels be arranged in them, in accordance with musical laws, in such a way that they nowhere touch the wall, but have a clear space all round them and room over their tops. They should be set upside down, and be supported on the side facing the stage by wedges not less than half a foot high. Opposite each niche, aper­tures should be left in the surface of the seat next below, two feet long and half a foot deep.

² The arrangement of these vessels, with reference to the situations in which they should be placed, may be described as follows. If the theatre be of no great size, mark out a horizontal range halfway up, and in it construct thirteen arched niches with twelve equal spaces between them, so that of the above mentioned "echea" those which give the note nete hyperbolaeon may be placed first on each side, in the niches which are at the extreme ends; next to the ends and a fourth below in pitch, the note nete diezeugmenon; third, paramese, a fourth below; fourth, nete synhemmenon; fifth, mese, a fourth below; sixth, hypate meson, a fourth below; and in the middle and another fourth below, one vessel giving the note hypate hypaton.

³ On this principle of arrangement, the voice, uttered from the stage as from a centre, and spreading and striking against the cavities of the different vessels, as it comes in contact with them, will be increased in clearness of sound, and will wake an harmonious note in unison with itself.

But if the theatre be rather large, let its height be divided into four parts, so that three horizontal ranges of niches may be marked out and constructed: one for the enharmonic, an­other for the chromatic, and the third for the diatonic system. Beginning with the bottom range, let the arrangement be as de­scribed above in the case of a smaller theatre, but on the enhar­monic system.

⁴ In the middle range, place first at the extreme ends the vessels which give the note of the chromatic hyperbolaeon; next

to them, those which give the chromatic diezeugmenon, a fourth below; third, the chromatic synhemmenon; fourth, the chromatic meson, a fourth below; fifth, the chromatic hypaton, a fourth below; sixth, the paramese, for this is both the concord of the fifth to the chromatic hyperbolaeon, and the concord^[3] of the chro­matic synhemmenon.

⁵ No vessel is to be placed in the middle, for the reason that there is no other note in the chromatic system that forms a natural concord of sound. In the highest division and range of niches, place at the extreme ends vessels fashioned so as to give the note of the diatonic hyperbolaeon; next, the diatonic diezeugmenon, a fourth below; third, the diatonic synhemmenon; fourth, the diatonic meson, a fourth below; fifth, the diatonic hypaton, a fourth below; sixth, the proslambanomenos, a fourth below; in the middle, the note mese, for this is both the octave to proslambanomenos, and the concord of the fifth to the diatonic hypaton.

⁶ Whoever wishes to carry out these principles with ease, has only to consult the scheme at the end of this book, drawn up in accordance with the laws of music. It was left by Aristoxenus, who with great ability and labour classified and arranged in it the different modes. In accordance with it, and by giving heed to these theories, one can easily bring a theatre to perfection, from the point of view of the nature of the voice, so as to give pleasure to the audience.

⁷ Somebody will perhaps say that many theatres are built every year in Rome, and that in them no attention at all is paid to these principles; but he will be in error, from the fact that all our public theatres made of wood contain a great deal of board­ing, which must be resonant. This may be observed from the behaviour of those who sing to the lyre, who, when they wish to sing in a higher key, turn towards the folding doors on the stage, and thus by their aid are reinforced with a sound in har­mony with the voice. But when theatres are built of solid ma­terials like masonry, stone, or marble, which cannot be resonant, then the principles of the "echea" must be applied.

⁸ If, however, it is asked in what theatre these vessels have been employed, we cannot point to any in Rome itself, but only to those in the districts of Italy and in a good many Greek states. We have also the evidence of Lucius Mummius, who, after de­stroying the theatre in Corinth, brought its bronze vessels to Rome, and made a dedicatory offering at the temple of Luna with the money obtained from the sale of them. Besides, many skilful architects, in constructing theatres in small towns, have, for lack of means, taken large jars made of clay, but similarly reso­nant, and have produced very advantageous results by arranging them on the principles described.

CHAPTER VI

Plan of the Theatre

¹ The plan of the theatre itself is to be constructed as follows. Having fixed upon the principal centre, draw a line of circum­ference equivalent to what is to be the perimeter at the bottom, and in it inscribe four equilateral triangles, at equal distances apart and touching the boundary line of the circle, as the as­trologers do in a figure of the twelve signs of the zodiac, when they are making computations from the musical harmony of the stars. Taking that one of these triangles whose side is nearest to the scaena, let the front of the scaena be determined by the line where that side cuts off a segment of the circle (A–B), and draw, through the centre, a parallel line (C–D) set off from that posi­tion, to separate the platform of the stage from the space of the orchestra.

² The platform has to be made deeper than that of the Greeks, because all our artists perform on the stage, while the orchestra contains the places reserved for the seats of senators. The height of this platform must be not more than five feet, in order that those who sit in the orchestra may be able to see the per­formances of all the actors. The sections (cunei) for spectators in the theatre should be so divided, that the angles of the triangles which run about the circumference of the circle may give the direction for the flights of steps between the sections, as far as up to the first curved cross-aisle. Above this, the upper sections are to be laid out, midway between (the lower sections), with alter­nating passage-ways.

³ The angles at the bottom, which give the directions for the flights of steps, will be seven in number (C, E, F, G, H, I, D); the other five angles will determine the arrangement of the scene: thus, the angle in the middle ought to have the "royal door" (K) opposite to it; the angles to the right and left (L, M) will desig­nate the position of the doors for guest chambers; and the two

THE ROMAN THEATRE ACCORDING TO VITRUVIUS

outermost angles (A, B) will point to the passages in the wings. The steps for the spectators' places, where the seats are arranged, should be not less than a foot and a palm in height, nor more than a foot and six fingers; their depth should be fixed at not more than two and a half feet, nor less than two feet.

⁴ The roof of the colonnade to be built at the top of the rows of seats, should lie level with the top of the "scaena," for the rea­son that the voice will then rise with equal power until it reaches the highest rows of seats and the roof. If the roof is not so high, in proportion as it is lower, it will check the voice at the point which the sound first reaches.

⁵ Take one sixth of the diameter of the orchestra between the lowest steps, and let the lower seats at the ends on both sides be cut away to a height of that dimension so as to leave en­trances (O, P). At the point where this cutting away occurs, fix the soffits of the passages. Thus their vaulting will be sufficiently high.

⁶ The length of the "scaena" ought to be double the diameter of the orchestra. The height of the podium, starting from the level of the stage, is, including the corona and cymatium, one twelfth of the diameter of the orchestra. Above the podium, the columns, including their capitals and bases, should have a height of one quarter of the same diameter, and the architraves and ornaments of the columns should be one fifth of their height. The parapet above, including its cyma and corona, is one half the height of the parapet below. Let the columns above this parapet be one fourth less in height than the columns below, and the architraves and ornaments of these columns one fifth of their height. If the "scaena" is to have three stories, let the upper­most parapet be half the height of the intermediate one, the columns at the top one fourth less high than the intermediate, and the architraves and coronae of these columns one fifth of their height as before.

⁷ It is not possible, however, that in all theatres these rules of symmetry should answer all conditions and purposes, but the

From Durm

THE THEATRE AT ASPENDUS

architect ought to consider to what extent he must follow the principle of symmetry, and to what extent it may be modified to suit the nature of the site or the size of the work. There are, of course, some things which, for utility's sake, must be made of the same size in a small theatre, and a large one: such as the steps, curved cross-aisles, their parapets, the passages, stair­ways, stages, tribunals, and any other things which occur that make it necessary to give up symmetry so as not to interfere with utility. Again, if in the course of the work any of the material fall short, such as marble, timber, or anything else that is provided, it will not be amiss to make a slight reduction or addition, provided that it is done without going too far, but with intelligence. This will be possible, if the architect is a man of practical experience and, besides, not destitute of clever­ness and skill.

⁸ The "scaena" itself displays the following scheme. In the centre are double doors decorated like those of a royal palace. At the right and left are the doors of the guest chambers. Beyond are spaces provided for decoration — places that the Greeks call περιάκτοι, because in these places are triangular pieces of machinery (Δ, Δ) which revolve, each having three decorated faces. When the play is to be changed, or when gods enter to the accompaniment of sudden claps of thunder, these may be re­volved and present a face differently decorated. Beyond these places are the projecting wings which afford entrances to the stage, one from the forum, the other from abroad.

⁹ There are three kinds of scenes, one called the tragic, second, the comic, third, the satyric. Their decorations are different and unlike each other in scheme. Tragic scenes are delineated with columns, pediments, statues, and other objects suited to kings; comic scenes exhibit private dwellings, with balconies and views representing rows of windows, after the manner of ordinary dwellings; satyric scenes are decorated with trees, caverns, moun­tains, and other rustic objects delineated in landscape style.

CHAPTER VII

Greek Theatres

¹ In the theatres of the Greeks, these same rules of construc­tion are not to be followed in all respects. First, in the circle at the bottom where the Roman has four triangles, the Greek has three squares with their angles touching the line of circumfer­ence. The square whose side is nearest to the "scaena," and cuts off a segment of the circle, determines by this line the limits of the "proscaenium" (A, B). Parallel to this line and tangent to the outer circumference of the segment, a line is drawn which fixes the front of the "scaena" (C–D). Through the centre of the orchestra and parallel to the direction of the "proscaenium," a line is laid off, and centres are marked where it cuts the circum­ference to the right and left (E, F) at the ends of the half-circle. Then, with the compasses fixed at the right, an arc is described from the horizontal distance at the left to the left hand side of the "proscaenium" (F, G); again with the centre at the left end, an arc is described from the horizontal distance at the right to the right hand side of the "proscaenium" (E, H).

² As a result of this plan with three centres, the Greeks have a roomier orchestra, and a "scaena" set further back, as well as a stage of less depth. They call this the λογεῖον, for the reason that there the tragic and comic actors perform on the stage, while other artists give their performances in the entire orchestra; hence, from this fact they are given in Greek the distinct names "Scenic" and "Thymelic." The height of this "logeum" ought to be not less than ten feet nor more than twelve. Let the ascend­ing flights of steps between the wedges of seats, as far up as the first curved cross-aisle, be laid out on lines directly opposite to the angles of the squares. Above the cross-aisle, let other flights be laid out in the middle between the first; and at the top, as often as there is a new cross-aisle, the number of flights of steps is always increased to the same extent.

CHAPTER VIII

Acoustics of the Site of a Theatre

¹ All this having been settled with the greatest pains and skill, we must see to it, with still greater care, that a site has been selected where the voice has a gentle fall, and is not driven back with a recoil so as to convey an indistinct meaning to the ear. There are some places which from their very nature interfere with the course of the voice, as for instance the dissonant, which are termed in Greek κατηχοῦντες; the circumsonant, which with them are named περίηχοῦντες; again the resonant, which are termed ἀυτηχοῦντες; and the consonant, which they call συνηχοῦντες. The dissonant are those places in which the first sound uttered that is carried up high, strikes against solid bodies above, and, being driven back, checks as it sinks to the bottom the rise of the succeeding sound.

² The circumsonant are those in which the voice spreads all round, and then is forced into the middle, where it dissolves, the case-endings are not heard, and it dies away there in sounds of indistinct meaning. The resonant are those in which it comes into contact with some solid substance and recoils, thus producing an echo, and making the terminations of cases sound double. The consonant are those in which it is supported from below, increases as it goes up, and reaches the ears in words which are distinct and clear in tone. Hence, if there has been careful attention in the selection of the site, the effect of the voice will, through this precaution, be perfectly suited to the purposes of a theatre.

The drawings of the plans may be distinguished from each other by this difference, that theatres designed from squares are meant to be used by Greeks, while Roman theatres are designed from equilateral triangles. Whoever is willing to follow these directions will be able to construct perfectly correct theatres.

CHAPTER IX

Colonnades and Walks

¹ Colonnades must be constructed behind the scaena, so that when sudden showers interrupt plays, the people may have somewhere to retire from the theatre, and so that there may be room for the preparation of all the outfit of the stage. Such places, for instance, are the colonnades of Pompey, and also, in Athens, the colonnades of Eumenes and the fane of Father Bacchus; also, as you leave the theatre, the music hall which Themistocles surrounded with stone columns, and roofed with the yards and masts of ships captured from the Persians. It was burned during the war with Mithridates, and afterwards restored by King Ariobarzanes. At Smyrna there is the Stratoni­ceum, at Tralles, a colonnade on each side of the scaena above the race course, and in other cities which have had careful archi­tects there are colonnades and walks about the theatres.

² The approved way of building them requires that they should be double, and have Doric columns on the outside, with the architraves and their ornaments finished according to the law of modular proportion. The approved depth for them re­quires that the depth, from the lower part of the outermost columns to the columns in the middle, and from the middle columns to the wall enclosing the walk under the colonnade, should be equal to the height of the outer columns. Let the middle columns be one fifth higher than the outer columns, and designed in the Ionic or Corinthian style.

³ The columns will not be subject to the same rules of sym­metry and proportion which I prescribed in the case of sanctu­aries; for the dignity which ought to be their quality in temples of the gods is one thing, but their elegance in colonnades and other public works is quite another. Hence, if the columns are to be of the Doric order, let their height, including the capital, be measured off into fifteen parts. Of these parts, let one be fixed upon to form the module, and in accordance with this module the whole work is to be developed. Let the thickness of the columns at the bottom be two modules; an intercolumniation, five and a half modules; the height of a column, excluding the capital, fourteen modules; the capital, one module in height and two and one sixth modules in breadth. Let the modular propor­tions of the rest of the work be carried out as written in the fourth book in the case of temples.

⁴ But if the columns are to be Ionic, let the shaft, excluding base and capital, be divided into eight and one half parts, and let one of these be assigned to the thickness of a column. Let the base, including the plinth, be fixed at half the thickness, and let the proportions of the capital be as shown in the third book. If the column is to be Corinthian, let its shaft and base be pro­portioned as in the Ionic, but its capital, as has been written in the fourth book. In the stylobates, let the increase made there by means of the "scamilli impares" be taken from the description written above in the third book. Let the architraves, coronae, and all the rest be developed, in proportion to the columns, from what has been written in the foregoing books.

⁵ The space in the middle, between the colonnades and open to the sky, ought to be embellished with green things; for walking in the open air is very healthy, particularly for the eyes, since the refined and rarefied air that comes from green things, finding its way in because of the physical exercise, gives a clean-cut image, and, by clearing away the gross humours from the eyes, leaves the sight keen and the image distinct. Besides, as the body gets warm with exercise in walking, this air, by sucking out the humours from the frame, diminishes their superabundance, and disperses and thus reduces that superfluity which is more than the body can bear.

⁶ That this is so may be seen from the fact that misty vapours never arise from springs of water which are under cover, nor even from watery marshes which are underground; but in un­covered places which are open to the sky, when the rising sun begins to act upon the world with its heat, it brings out the vapour from damp and watery spots, and rolls it in masses up­wards. Therefore, if it appears that in places open to the sky the more noxious humours are sucked out of the body by the air, as they obviously are from the earth in the form of mists, I think there is no doubt that cities should be provided with the room­iest and most ornamented walks, laid out under the free and open sky.

⁷ That they may be always dry and not muddy, the following is to be done. Let them be dug down and cleared out to the lowest possible depth. At the right and left construct covered drains, and in their walls, which are directed towards the walks, lay earthen pipes with their lower ends inclined into the drams. Hav­ing finished these, fill up the place with charcoal, and then strew sand over the walks and level them off. Hence, on account of the porous nature of the charcoal and the insertion of the pipes into the drains, quantities of water will be conducted away, and the walks will thus be rendered perfectly dry and without moisture.

⁸ Furthermore, our ancestors in establishing these works provided cities with storehouses for an indispensable material. The fact is that in sieges everything else is easier to procure than is wood. Salt can easily be brought in beforehand; corn can be got together quickly by the State or by individuals, and if it gives out, the defence may be maintained on cabbage, meat, or beans; water can be had by digging wells, or when there are sudden falls of rain, by collecting it from the tiles. But a stock of wood, which is absolutely necessary for cooking food, is a difficult and trouble­some thing to provide; for it is slow to gather and a good deal is consumed.

⁹ On such occasions, therefore, these walks are thrown open, and a definite allowance granted to each inhabitant according to tribes. Thus these uncovered walks insure two excellent things: first, health in time of peace; secondly, safety in time of war. Hence, walks that are developed on these principles, and built

Photo Booklyn Institute

THE TEPIDARIUM OF THE STABIAN BATHS AT POMPEII

Photo Booklyn Institute

APODYTERIUM FOR WOMEN IN THE STABIAN BATHS AT POMPEII

not only behind the "scaena" of theatres, but also at the temples of all the gods, will be capable of being of great use to cities.

As it appears that we have given an adequate account of them, next will follow descriptions of the arrangements of baths.

CHAPTER X

Baths

¹ In the first place, the warmest possible situation must be selected; that is, one which faces away from the north and north­east. The rooms for the hot and tepid baths should be lighted from the southwest, or, if the nature of the situation prevents this, at all events from the south, because the set time for bathing is principally from midday to evening. We must also see to it that the hot bath rooms in the women's and men's departments adjoin each other, and are situated in the same quarter; for thus it will be possible that the same furnace should serve both of them and their fittings. Three bronze cauldrons are to be set over the fur­nace, one for hot, another for tepid, and the third for cold water, placed in such positions that the amount of water which flows out of the hot water cauldron may be replaced from that for tepid water, and in the same way the cauldron for tepid water may be supplied from that for cold. The arrangement must allow the semi­cylinders for the bath basins to be heated from the same furnace.

² The hanging floors of the hot bath rooms are to be con­structed as follows. First the surface of the ground should be laid with tiles a foot and a half square, sloping towards the furnace in such a way that, if a ball is thrown in, it cannot stop inside but must return of itself to the furnace room; thus the heat of the fire will more readily spread under the hanging flooring. Upon them, pillars made of eight-inch bricks are built, and set at such a dis­tance apart that two-foot tiles may be used to cover them. These pillars should be two feet in height, laid with clay mixed with hair, and covered on top with the two-foot tiles which support the floor.

³ The vaulted ceilings will be more serviceable if built of ma­sonry; but if they are of framework, they should have tile work on the under side, to be constructed as follows. Let iron bars or arcs be made, and hang them to the framework by means of iron hooks set as close together as possible; and let these bars or arcs be placed at such distances apart that each pair of them may support and carry an unflanged tile. Thus the entire vaulting will be

THE STABIAN BATHS AT POMPEII

• S,S. Shops.
• B. Private Baths.
• A-T. Men's Bath.
• A′-T′. Women's Baths.
• E.E′. Entrances.
• A,A′. Apodytoria.
• F. Frigidarium.
• T,T′. Tepidarium.
• C,C′. Caldarium.
• K,K,K. Kettles in furnace room.
• P. Piscina.

completely supported on iron. These vaults should have the joints on their upper side daubed with clay mixed with hair, and their under side, facing the floor, should first be plastered with pounded tile mixed with lime, and then covered with polished stucco in relief or smooth. Vaults in hot bath rooms will be more serviceable if they are doubled; for then the moisture from the heat will not be able to spoil the timber in the framework, but will merely circulate between the two vaults.

⁴ The size of the baths must depend upon the number of the population. The rooms should be thus proportioned: let their breadth be one third of their length, excluding the niches for the washbowl and the bath basin. The washbowl ought without fail to be placed under a window, so that the shadows of those who stand round it may not obstruct the light. Niches for washbowls must be made so roomy that when the first comers have taken their places, the others who are waiting round may have proper standing room. The bath basin should be not less than six feet broad from the wall to the edge, the lower step and the "cushion" taking up two feet of this space.

⁵ The Laconicum and other sweating baths must adjoin the tepid room, and their height to the bottom of the curved dome should be equal to their width. Let an aperture be left in the middle of the dome with a bronze disc hanging from it by chains. By raising and lowering it, the temperature of the sweating bath can be regulated. The chamber itself ought, as it seems, to be circular, so that the force of the fire and heat may spread evenly from the centre all round the circumference.

CHAPTER XI

The Palaestra

¹ Next, although the building of palaestrae is not usual in Italy, I think it best to set forth the traditional way, and to show how they are constructed among the Greeks. The square or oblong peristyle in a palaestra should be so formed that the circuit of it makes a walk of two stadia, a distance which the Greeks call the δίαυλος. Let three of its colonnades be single, but let the fourth, which is on the south side, be double, so that when there is bad weather accompanied by wind, the drops of rain may not be able to reach the interior.

² In the three colonnades construct roomy recesses (A) with seats in them, where philosophers, rhetoricians, and others who delight in learning may sit and converse. In the double colonnade let the rooms be arranged thus: the young men's hall (B) in the middle; this is a very spacious recess (exedra) with seats in it, and it should be one third longer than it is broad. At the right, the bag room (C); then next, the dust room (D); beyond the dust room, at the corner of the colonnade, the cold washing room (E), which the Greeks call λουτρόν. At the left of the young men's hall is the anointing room (F); then, next to the anointing room, the cold bath room (G), and beyond that a passage into the furnace room (H) at the corner of the colonnade. Next, but inside and on a line with the cold bath room, put the vaulted sweating bath (I), its length twice its breadth, and having at the ends on one side a Laconicum (K), proportioned in the same manner as above de­scribed, and opposite the Laconicum the warm washing room (L). Inside a palaestra, the peristyle ought to be laid out as described above.

³ But on the outside, let three colonnades be arranged, one as you leave the peristyle and two at the right and left, with run­ning-tracks in them. That one of them which faces the north should be a double colonnade of very ample breadth, while the other should be single, and so constructed that on the sides next the walls and the side along the columns it may have edges, serving as paths, of not less than ten feet, with the space between them sunken, so that steps are necessary in going down from the edges a foot and a half to the plane, which plane should be not less than twelve feet wide. Thus people walking round on the edges will not be interfered with by the anointed who are exercising.

⁴ This kind of colonnade is called among the Greeks ξυστὅς because athletes during the winter season exercise in covered running tracks. Next to this "xystus" and to the double colonnade

should be laid out the uncovered walks which the Greeks term παραδρομίδες and our people "xysta," into which, in fair weather during the winter, the athletes come out from the "xys­tus" for exercise. The "xysta" ought to be so constructed that there may be plantations between the two colonnades, or groves of plane trees, with walks laid out in them among the trees and resting places there, made of "opus signinum." Behind the "xys­tus" a stadium, so designed that great numbers of people may have plenty of room to look on at the contests between the athletes.

I have now described all that seemed necessary for the proper arrangement of things within the city walls.

CHAPTER XII

Harbours, Breakwaters, and Shipyards

¹ The subject of the usefulness of harbours is one which I must not omit, but must explain by what means ships are shel­tered in them from storms. If their situation has natural advan­tages, with projecting capes or promontories which curve or return inwards by their natural conformation, such harbours are ob­viously of the greatest service. Round them, of course, colon­nades or shipyards must be built, or passages from the colon­nades to the business quarters, and towers must be set up on both sides, from which chains can be drawn across by machinery.

² But if we have a situation without natural advantages, and unfit to shelter ships from storms, it is obvious that we must pro­ceed as follows. If there is no river in the neighbourhood, but if there can be a roadstead on one side, then, let the advances be made from the other side by means of walls or embankments, and let the enclosing harbour be thus formed. Walls which are to be under water should be constructed as follows. Take the powder which comes from the country extending from Cumae to the promontory of Minerva, and mix it in the mortar trough in the proportion of two to one.

³ Then, in the place previously determined, a cofferdam, with its sides formed of oaken stakes with ties between them, is to be driven down into the water and firmly propped there; then, the lower surface inside, under the water, must be levelled off and dredged, working from beams laid across; and finally, concrete from the mortar trough — the stuff having been mixed as pre­scribed above — must be heaped up until the empty space which was within the cofferdam is filled up by the wall. This, however, is possessed as a gift of nature by such places as have been de­scribed above.

But if by reason of currents or the assaults of the open sea the props cannot hold the cofferdam together, then, let a platform of the greatest possible strength be constructed, beginning on the ground itself or on a substructure; and let the platform be con­structed with a level surface for less than half its extent, while the rest, which is close to the beach, slopes down and out.

⁴ Then, on the water's edge and at the sides of the platform, let marginal walls be constructed, about one and one half feet thick and brought up to a level with the surface above mentioned; next, let the sloping part be filled in with sand and levelled off with the marginal wall and the surface of the platform. Then, upon this level surface construct a block as large as is required, and when it is finished, leave it for not less than two months to dry. Then, cut away the marginal wall which supports the sand. Thus, the sand will be undermined by the waves, and this will cause the block to fall into the sea. By this method, repeated as often as necessary, an advance into the water can be made.

⁵ But in places where this powder is not found, the following method must be employed. A cofferdam with double sides, com­posed of charred stakes fastened together with ties, should be con­structed in the appointed place, and clay in wicker baskets made of swamp rushes should be packed in among the props. After this has been well packed down and filled in as closely as possible, set up your water-screws, wheels, and drums, and let the space now bounded by the enclosure be emptied and dried. Then, dig out the bottom within the enclosure. If it proves to be of earth, it must be cleared out and dried till you come to solid bottom and for a space wider than the wall which is to be built upon it, and then filled in with masonry consisting of rubble, lime, and sand.

⁶ But if the place proves to be soft, the bottom must be staked with piles made of charred alder or olive wood, and then filled in with charcoal as has been prescribed in the case of the foundations of theatres and the city wall. Finally, build the wall of dimension stone, with the bond stones as long as pos­sible, so that particularly the stones in the middle may be held together by the joints. Then, fill the inside of the wall with broken stone or masonry. It will thus be possible for even a tower to be built upon it.

⁷ When all this is finished, the general rule for shipyards will be to build them facing the north. Southern exposures from their heat produce rot, the wood worm, ship worms, and all sorts of other destructive creatures, and strengthen and keep them alive. And these buildings must by no means be constructed of wood, for fear of fire. As for their size, no definite limit need be set, but they must be built to suit the largest type of ship, so that if even larger ships are hauled up, they may find plenty of room there.

I have described in this book the construction and completion of all that I could remember as necessary for general use in the public places of cities. In the following book I shall consider private houses, their conveniences, and symmetrical proportions.

1. Codd. CC. & L.
2. The remainder of this section is omitted from the translation as being an obvious interpolation.
3. Codd. diatessaron, which is impossible, paramese being the concord of the fourth to the chromatic meson, and identical with the chromatic synhemmenon.