13. These proportionate enlargements are made in the thickness of columns on account of the different heights to which the eye has to climb. For the eye is always in search of beauty, and if we do not gratify its desire for pleasure by a proportionate enlargement in these measures, and thus make compensation for ocular deception, a clumsy and awkward appearance will be presented to the beholder. With regard to the enlargement made at the middle of columns, which among the Greeks is called [Greek: entasis], at the end of the book a figure and calculation will be subjoined, showing how an agreeable and appropriate effect may be produced by it.

CHAPTER IV

THE FOUNDATIONS AND SUBSTRUCTURES OF TEMPLES

1. The foundations of these works should be dug out of the solid ground, if it can be found, and carried down into solid ground as far as the magnitude of the work shall seem to require, and the whole substructure should be as solid as it can possibly be laid. Above ground, let walls be laid under the columns, thicker by one half than the columns are to be, so that the lower may be stronger than the higher. Hence they are called "stereobates"; for they take the load. And the projections of the bases should not extend beyond this solid foundation. The wall-thickness is similarly to be preserved above ground likewise, and the intervals between these walls should be vaulted over, or filled with earth rammed down hard, to keep the walls well apart.

[Ill.u.s.tration: THE ENTASIS OF COLUMNS

1. The entasis as given by Fra Giocondo in the edition of 1511.

2. The entasis from the temple of Mars Ultor in Rome compared with Vignola's rule for entasis.]

2. If, however, solid ground cannot be found, but the place proves to be nothing but a heap of loose earth to the very bottom, or a marsh, then it must be dug up and cleared out and set with piles made of charred alder or olive wood or oak, and these must be driven down by machinery, very closely together like bridge-piles, and the intervals between them filled in with charcoal, and finally the foundations are to be laid on them in the most solid form of construction. The foundations having been brought up to the level, the stylobates are next to be put in place.

3. The columns are then to be distributed over the stylobates in the manner above described: close together in the pycnostyle; in the systyle, diastyle, or eustyle, as they are described and arranged above.

In araeostyle temples one is free to arrange them as far apart as one likes. Still, in peripterals, the columns should be so placed that there are twice as many intercolumniations on the sides as there are in front; for thus the length of the work will be twice its breadth. Those who make the number of columns double, seem to be in error, because then the length seems to be one intercolumniation longer than it ought to be.

4. The steps in front must be arranged so that there shall always be an odd number of them; for thus the right foot, with which one mounts the first step, will also be the first to reach the level of the temple itself. The rise of such steps should, I think, be limited to not more than ten nor less than nine inches; for then the ascent will not be difficult. The treads of the steps ought to be made not less than a foot and a half, and not more than two feet deep. If there are to be steps running all round the temple, they should be built of the same size.

5. But if a podium is to be built on three sides round the temple, it should be so constructed that its plinths, bases, dies, coronae, and cymatiumare appropriate to the actual stylobate which is to be under the bases of the columns.

[Ill.u.s.tration: FRA GIOCONDO'S IDEA OF THE "SCAMILLI IMPARES"

(From his edition of Vitruvius, Venice, 1511)]

The level of the stylobate must be increased along the middle by the scamilli impares; for if it is laid perfectly level, it will look to the eye as though it were hollowed a little. At the end of the book a figure will be found, with a description showing how the scamilli may be made to suit this purpose.

CHAPTER V

PROPORTIONS OF THE BASE, CAPITALS, AND ENTABLATURE IN THE IONIC ORDER

1. This finished, let the bases of the columns be set in place, and constructed in such proportions that their height, including the plinth, may be half the thickness of a column, and their projection (called in Greek [Greek: ekphora]) the same.[1] Thus in both length and breadth it will be one and one half thicknesses of a column.

[Note 1: Reading _aeque tantam_ as in new _Rose._ Codd. _s.e.xtantem;_ Schn. _quadrantem._]

2. If the base is to be in the Attic style, let its height be so divided that the upper part shall be one third part of the thickness of the column, and the rest left for the plinth. Then, excluding the plinth, let the rest be divided into four parts, and of these let one fourth const.i.tute the upper torus, and let the other three be divided equally, one part composing the lower torus, and the other, with its fillets, the scotia, which the Greeks call [Greek: trochilos].

3. But if Ionic bases are to be built, their proportions shall be so determined that the base may be each way equal in breadth to the thickness of a column plus three eighths of the thickness; its height that of the Attic base, and so too its plinth; excluding the plinth, let the rest, which will be a third part of the thickness of a column, be divided into seven parts. Three of these parts const.i.tute the torus at the top, and the other four are to be divided equally, one part const.i.tuting the upper trochilus with its astragals and overhang, the other left for the lower trochilus. But the lower will seem to be larger, because it will project to the edge of the plinth. The astragals must be one eighth of the trochilus. The projection of the base will be three sixteenths of the thickness of a column.

[Ill.u.s.tration: THE IONIC ORDER ACCORDING TO VITRUVIUS COMPARED WITH THE ORDER OF THE MAUSOLEUM AT HALICARNa.s.sUS

The difference between the Roman and the Greek relation of the bal.u.s.ter-side of the capital to the echinus is to be noted.]

4. The bases being thus finished and put in place, the columns are to be put in place: the middle columns of the front and rear porticoes perpendicular to their own centre; the corner columns, and those which are to extend in a line from them along the sides of the temple to the right and left, are to be set so that their inner sides, which face toward the cella wall, are perpendicular, but their outer sides in the manner which I have described in speaking of their diminution. Thus, in the design of the temple the lines will be adjusted with due regard to the diminution.

5. The shafts of the columns having been erected, the rule for the capitals will be as follows. If they are to be cushion-shaped, they should be so proportioned that the abacus is in length and breadth equivalent to the thickness of the shaft at its bottom plus one eighteenth thereof, and the height of the capital, including the volutes, one half of that amount. The faces of the volutes must recede from the edge of the abacus inwards by one and a half eighteenths of that same amount. Then, the height of the capital is to be divided into nine and a half parts, and down along the abacus on the four sides of the volutes, down along the fillet at the edge of the abacus, lines called "catheti" are to be let fall. Then, of the nine and a half parts let one and a half be reserved for the height of the abacus, and let the other eight be used for the volutes.

6. Then let another line be drawn, beginning at a point situated at a distance of one and a half parts toward the inside from the line previously let fall down along the edge of the abacus. Next, let these lines be divided in such a way as to leave four and a half parts under the abacus; then, at the point which forms the division between the four and a half parts and the remaining three and a half, fix the centre of the eye, and from that centre describe a circle with a diameter equal to one of the eight parts. This will be the size of the eye, and in it draw a diameter on the line of the "cathetus." Then, in describing the quadrants, let the size of each be successively less, by half the diameter of the eye, than that which begins under the abacus, and proceed from the eye until that same quadrant under the abacus is reached.

7. The height of the capital is to be such that, of the nine and a half parts, three parts are below the level of the astragal at the top of the shaft, and the rest, omitting the abacus and the channel, belongs to its echinus. The projection of the echinus beyond the fillet of the abacus should be equal to the size of the eye. The projection of the bands of the cushions should be thus obtained: place one leg of a pair of compa.s.ses in the centre of the capital and open out the other to the edge of the echinus; bring this leg round and it will touch the outer edge of the bands. The axes of the volutes should not be thicker than the size of the eye, and the volutes themselves should be channelled out to a depth which is one twelfth of their height. These will be the symmetrical proportions for capitals of columns twenty-five feet high and less. For higher columns the other proportions will be the same, but the length and breadth of the abacus will be the thickness of the lower diameter of a column plus one ninth part thereof; thus, just as the higher the column the less the diminution, so the projection of its capital is proportionately increased and its breadth[2] is correspondingly enlarged.

[Note 2: Codd. _alt.i.tudo_.]

8. With regard to the method of describing volutes, at the end of the book a figure will be subjoined and a calculation showing how they may be described so that their spirals may be true to the compa.s.s.

The capitals having been finished and set up in due proportion to the columns (not exactly level on the columns, however, but with the same measured adjustment, so that in the upper members there may be an increase corresponding to that which was made in the stylobates), the rule for the architraves is to be as follows. If the columns are at least twelve feet and not more than fifteen feet high, let the height of the architrave be equal to half the thickness of a column at the bottom.

If they are from fifteen feet to twenty, let the height of a column be measured off into thirteen parts, and let one of these be the height of the architrave. If they are from twenty to twenty-five feet, let this height be divided into twelve and one half parts, and let one of them form the height of the architrave. If they are from twenty-five feet to thirty, let it be divided into twelve parts, and let one of them form the height. If they are higher, the heights of the architraves are to be worked out proportionately in the same manner from the height of the columns.

9. For the higher that the eye has to climb, the less easily can it make its way through the thicker and thicker ma.s.s of air. So it fails when the height is great, its strength is sucked out of it, and it conveys to the mind only a confused estimate of the dimensions. Hence there must always be a corresponding increase in the symmetrical proportions of the members, so that whether the buildings are on unusually lofty sites or are themselves somewhat colossal, the size of the parts may seem in due proportion. The depth of the architrave on its under side just above the capital, is to be equivalent to the thickness of the top of the column just under the capital, and on its uppermost side equivalent to the foot of the shaft.

10. The cymatium of the architrave should be one seventh of the height of the whole architrave, and its projection the same. Omitting the cymatium, the rest of the architrave is to be divided into twelve parts, and three of these will form the lowest fascia, four, the next, and five, the highest fascia. The frieze, above the architrave, is one fourth less high than the architrave, but if there are to be reliefs upon it, it is one fourth higher than the architrave, so that the sculptures may be more imposing. Its cymatium is one seventh of the whole height of the frieze, and the projection of the cymatium is the same as its height.

11. Over the frieze comes the line of dentils, made of the same height as the middle fascia of the architrave and with a projection equal to their height. The intersection (or in Greek [Greek: metope]) is apportioned so that the face of each dentil is half as wide as its height and the cavity of each intersection two thirds of this face in width. The cymatium here is one sixth of the whole height of this part.

The corona with its cymatium, but not including the sima, has the height of the middle fascia of the architrave, and the total projection of the corona and dentils should be equal to the height from the frieze to the cymatium at the top of the corona.

[Ill.u.s.tration: A COMPARISON OF THE IONIC ORDER ACCORDING TO VITRUVIUS WITH ACTUAL EXAMPLES AND WITH VIGNOLA'S ORDER

A: Showing the orders reduced to equal lower diameters. B: Showing the orders to a uniform scale.]

And as a general rule, all projecting parts have greater beauty when their projection is equal to their height.

12. The height of the tympanum, which is in the pediment, is to be obtained thus: let the front of the corona, from the two ends of its cymatium, be measured off into nine parts, and let one of these parts be set up in the middle at the peak of the tympanum, taking care that it is perpendicular to the entablature and the neckings of the columns. The coronae over the tympanum are to be made of equal size with the coronae under it, not including the simae. Above the coronae are the simae (in Greek [Greek: epaietides]), which should be made one eighth higher than the height of the coronae. The acroteria at the corners have the height of the centre of the tympanum, and those in the middle are one eighth part higher than those at the corners.

13. All the members which are to be above the capitals of the columns, that is, architraves, friezes, coronae, tympana, gables, and acroteria, should be inclined to the front a twelfth part of their own height, for the reason that when we stand in front of them, if two lines are drawn from the eye, one reaching to the bottom of the building and the other to the top, that which reaches to the top will be the longer. Hence, as the line of sight to the upper part is the longer, it makes that part look as if it were leaning back. But when the members are inclined to the front, as described above, they will seem to the beholder to be plumb and perpendicular.

14. Each column should have twenty-four flutes, channelled out in such a way that if a carpenter's square be placed in the hollow of a flute and turned, the arm will touch the corners of the fillets on the right and left, and the tip of the square may keep touching some point in the concave surface as it moves through it. The breadth of the flutes is to be equivalent to the enlargement in the middle of a column, which will be found in the figure.

15. In the simae which are over the coronae on the sides of the temple, lion's heads are to be carved and arranged at intervals thus: First one head is marked out directly over the axis of each column, and then the others are arranged at equal distances apart, and so that there shall be one at the middle of every roof-tiling. Those that are over the columns should have holes bored through them to the gutter which receives the rainwater from the tiles, but those between them should be solid. Thus the ma.s.s of water that falls by way of the tiles into the gutter will not be thrown down along the intercolumniations nor drench people who are pa.s.sing through them, while the lion's heads that are over the columns will appear to be vomiting as they discharge streams of water from their mouths.

In this book I have written as clearly as I could on the arrangements of Ionic temples. In the next I shall explain the proportions of Doric and Corinthian temples.

BOOK IV