Chap. XXXT.

PRINCIPLES OF PROPORTION.

1581

out; the eye is satisfied that the load cannot distress its supports, and the spaces betweenthe supporting masses are again proportioned and made equal to either, so that we have atriple division, — one, the per-pendicular arrangements of thesupports, another their justdistribution or equal distances,and the third, the entablatureproportioned to the strengththat is to carry it, all of whichare comprised within the boun-dary of a square. The tetra-style porticoes that remain arenot numerous, and none areperfect; three have been se-lected, which will enable us totest the idea we have attemptedto define. First, that at Eleusis,the entire width of which is

20 feet 6 inches, the height ,

21 feet 6 inches; and if wereject half the height of thepediment we shall have asquare : the united dia-meter of the columns onlyvaries 5 inches in widthfrom those of the intercolum-niations.

Fig. 2909.

TKTIUSTYLE PORTICOES.

If we divide the height into three, rejecting, as already observed, half the pediment, whichin this case is 1 foot 1^ inch, we have for the height of the square 20 feet 4 inches, whilstthe entire width is 20 feet 6 inches, a difference not very great: this divided into three, andgiving two-thirds to the height of the columns, would make them only 13 feet 6 inches and8 seconds, whilst they really are 14 feet 2£ inches in height. In this example the entireheight, which we may call 21 feet 5J inches, is divided into three, two parts of whichconstitute the height of the columns.

In the Temple of Themis at Rhamnus , the width is 20 feet 11 inches, and the heightthe same, the diameters of the columns being in excess 3 inches only above the width ofthe intercolumniations.

In the Doric Portico at Athens , the entire height equals nearly the width.

Hexastyle Porticoes. — The practice of the Dorian architects, in setting out a templewith six columns in front, appears sometimes to have been to divide the width into twelveparts, the height without the pediment being made equal to eight of them; thus forminga fa 9 ade within a parallelogram or a square and a half: as the ninth division in height cutsthe pediment in half, we have thirty-six squares for the entablature or mass supported, 1being the same quantity found in the six columns and the five intercolumniations; at othertimes we find the entire width divided into nine parts, and six given to the height, one ofwhich indicates the pediment, thus rising a ninth : if a circle be described in the tympanum,and a horizontal line drawn through the centre, cutting off a twelfth of the height, theremaining being divided into three equal parts, the upper third, or entablature, beingthe part supported, the remaining | are divided between the columns and their interspaces;thus making the columns equal to | of the height comprised between the centre of thetympanum and the platform upon which they were placed.

If we take each of these nine parts as 5 feet, we have 45 feet for the width, 30 for theheight, including the 5 feet for the rise of the pediment, which if we divide by the horizontalline, to obtain its true area or quantity, we shall have 2 feet 6 inches for its mean height,and 6 feet 8 inches for that of the level entablature: for as we have observed, these twodimensions, which make 9 feet 2 inches, must be equal to half the height of the columns, orthe whole will not be divided into three parts; or, which is the same thing, the height fromthe centre of the pediment must be divided into three parts, and the upper division takenfor the entablature. These proportions are exceedingly simple in their application; if itwere intended that the columns and the spaces between them should be equal, half the widthof the fa 5 ade, or 22 feet 6 inches, should be distributed among the intercolumniations,and the other half divided among the columns.

The Temple of Theseus at Athens is one of the best preserved as well as the most admired,and was probably erected soon after the Parthenon ; it is of Pentelican marble, adornedwith admirable sculptures. The total width of its hexastyle portico is 45 feet; and its height,instead of 30, is 31 feet; the extra foot, which prevents it being an exact square and a half, isgiven to the pediment, which probably has undergone some change, as it rises much morethan the ninth of its whole extent. *