The Greeks, in proportioning their Doric columns, arrived at an apparent system of entasis that is radically different from the more customary method employed on all Roman columns.

No part of the outline of the Doric column is parallel with its axis or center line. From the very bottom, the shaft slopes in towards the center, this slope increasing as it nears the neck of the column, in portions of arcs of circles of a varying though large radius. This could not be described as a true arc, however, inasmuch as at the bottom the line is almost straight for some distance. By referring to Fig. 87, the column from the Parthenon, shown in Plate XXXVII, will be found drawn out with special reference to its outline or entasis. In the middle of the sheet, at the top, the plans of the column at the neck and base are shown enlarged to one and one-half times the size of the column shown in elevation, and here the diameters through the column at the points marked on the shaft are shown more exactly. The total height of the shaft of the column is divided into six equal parts, and numbered from one, beginning at the neck, to seven at the base. The difference between the diameter of the column at the neck and at the base is divided, on the radial line, into an equal number of parts, and numbered correspondingly from one at the neck to seven at the base, these lines being extended parallel to the line of axis until they intersect the lines at right angles to them that divide the column into the six parts just referred to. It will then be found that, as is shown at the right of the column shaft, these points will coincide with the outline of the column which passes through them, except at the two points numbered four and five. As is shown more clearly on the other side of the column, where the dotted line indicates a straight line drawn between the points one and seven, the swelling of the column occurs between points six and three; and therefore, at the points numbered four and five, the outline of the column is slightly beyond the point of intersection of the two lines that we have just described. This will in the main determine a general scheme for arranging with some correctness the entasis of the column outline of the Greek Doric Order, although it varies somewhat in each of the different old examples.

STELE-CRESTS Fig. 86.

A-METHOD-OF-DETERMINING -THE- -ENTASIS - PLANS-ENLARGED- OF- GREEK- DORIC- &-IONIC-SHAFTS.

Fig. 87.

The Greek Ionic column follows a different system. This shaft also has no portion of its outline that is parallel with the axis of the column, but the outline is at all points more nearly parallel than was true of the Doric shaft. This is not only because of the slight difference between the diameter at the neck and base, and the greater height of the column, but also because the lower portion of the shaft more nearly approximates a perpendicular line than in the earlier Order. As we have already mentioned, in one instance there is a very light belly on the Ionic shaft, whereby its diameter at a point one-third the height of the shaft above the base is 1/134 greater than it is at its lower diameter. This is the exception, however, and the shaft shown in Fig. 87 is dimensioned after the more general Greek custom.

This shaft is also divided into six equal parts, and the line of the diameter at the neck is set off on the circle expressing the plan at the base. The distance on this circle is then divided into six equal parts, and is numbered correspondingly with the divisions on the shaft of the column, as we have already done in working out the Doric entasis. The points determined on this plan of the column at the base are then extended, as before, until they intersect the lines dividing, at right angles to them, the shaft of the column, which will determine the points through which the column outline should pass. This method determines of itself the exact increase of the "tumble-home" of the column in its upper portions. The arc described by this outline approximates, although it does not exactly coincide with, a hyperbolic curve.

The Greek Corinthian shaft has no set and determined entasis.

Each of the three examples shown in Plate XLVIII follows a different method. The shaft of the column from the Temple of the Winds should be laid out by the Doric method, the different effect being given by the comparatively small difference between the diameter at the neck and at the base, as well as by the extra height of the shaft and the form of the capital. The shaft from the Monument of Lysicrates follows very nearly the Ionic method, differing from it, however, in that the lower one-third of the column is in outline more nearly parallel to the line of the axis than the method we have described for determining the Ionic shaft. The column from the Tholos at Epidauros follows the method afterwards used by the Romans, the lower one-third of the column being straight and perpendicular, with the outline parallel with the line of axis, while above this point the diminution is determined by the same process as we employed on the shaft of the Ionic column, being restricted in its application, however, to the upper two-thirds of the column shaft.