128 NOTICES OF THE MEETINGS [ Feb. 20, 
other causes united, the tapering shaft of the column will appear 
attenuated, unless its contour be made just so much convex, as to 
counterbalance these optical illusions. This entasis as it is called, 
literally bow-stretching, as applied in the columns of the Parthenon 
is formed by an accurate hyperbolic curve, which increases the 
diameters a little below the middle by the amount of .114 ft. in a 
shaft 31.4 ft. long. The directions of the axes of this hyperbola 
are vertical and horizontal; the constant number which expresses 
the eccentricity is 30; and the principal axis one Greek foot; the 
vertex does not occur in the shaft and is just two diameters of the 
column below the base. 
The columns of the Propylea are also hyperbolic, but differ from 
the last mentioned, in that the vertex of the hyperbola occurs near 
the middle. 
When this difference had been pointed out by measurement, the 
variation of character resulting therefrom to the two columns be- 
came appreciable ; but in all the Athenian examples the entasis is so 
slight, that the first investigators of the remains of Greek architec- 
ture, whose eyes were accustomed to the palpable bulging of the 
columns built by the architects of the 16th and 17th centuries, were 
deceived by its delicacy, and reported that the Greek columns had 
no entasis. 
Table of Entasis of different columns at Athens. 
Actual measurement In terms of length 
in Feet. of Shaft. 
Erechtheum . .. + 0195 «feocath in Webelcas eects 
Wiiaiatinny 6 ey aS .023 Pete Wamton Hens 
Parthenon .e0 2 0.0) 2: .057 aby Sealey oy giewes ae eae 
Propyleea 
Small order at ee ees MOR | flo weve 76, oN Toallsehaareer 
Large order . . + - .0627 spear neh: mimes Daoeioes 
The entasis being established, a second process of refinement 
would lead to the inclination of the axes of the columns. 
The diminution is so entirely in conformity with Nature, that the 
artifice more or less escapes observation, and the upper diameter 
does not appear so much smaller than the lower as it really is. 
This circumstance may combine with the others before mentioned, 
to demand the entasis, but it immediately produces the effect which 
the inclination of the columns seeks to remedy. For by how much 
so ever the sum of the upper diameters is apparently increased, by 
so much is the appearance of length in the architrave greater than 
in the stylobate (or step on which the columns stand), and the 
columns appear to have a fan-like divergence from the base line, 
unless the length of the architrave be reduced. This was effected 
by the Greeks by contracting the distance between the capitals of 
the extreme intercolumniations. This contraction in the Parthenon 
produces an inclination of .228 ft. in the angle columns in each 
direction, entailing a parallel inclination inwards in all the interme- 
diate columns of each colonnade. Several subordinate inclinations 
