THEORY OF OPTICAL CORRECTIONS ADOPTED BY GREEK ARCHITECTS

107

The attenuated appearance of a tapering column built with straight sides seems to be owing to
several and independent causes, which may be considered separately.

I. The apparent hollowncss in the sides of a frustum of a cone or pyramid in any position.

II. An additional feeling of the same kind when that figure is employed as a column or pilaster
to support weight.

III. Inequalities of chiaro-oscuro.

Firstly, The attenuated appearance of a conical or pyramidal frustum in the abstract, although
it depends upon the convergence of the sides, seems to be confined to cases where the angle at
the apex is sensible, but small ; for on the one hand it seems to be inappreciable in a cylinder or
prism, and on the other is but little felt in the Gothic spire, and still less, if at all, in the Egyptian
pyramid. The proof of this, least liable to objection, is the appeal to experiment.1

Secondly, In the case of the column or pilaster used to support a weight, both the upper
and the lower diameters, owing to the greater importance of their situations, detain the eye longer,
and thereby produce a greater impression of size than any of the intermediate diameters, which
consequently appear relatively smaller, and the shaft concave.

Thirdly, The last and by no means the least cause of the apparent attenuation in the shaft
of a straight-sided column, is the effect produced by the inequalities of chiaro-oscuro both of the
column and of the back ground.

Of a column which stands detached in a portico, the upper part, by reason of the light being
enhanced by the deep shade under the portico, and the lower part, by reason of the greater amount
of light actually reflected upon it from the ground, will appear brighter than the intermediate parts,
and therefore, according to the universally admitted theory," will appear relatively broader.

The above reasons for an appearance of contraction and weakness in the central parts of the
shafts, as well as the real monotony of a perfectly straight line, seem sufficient to have led the Greek
architects to the use of the entasis, which, as has been before observed, does not seem by them to
have been applied to a greater extent than just to balance the effects of the optical illusions.3

The amount of entasis depended also in some degree on the absolute height, for it is found
to be relatively less in smaller than in larger columns. Those of the Parthenon and Theseum
have in all other respects nearly the same proportions, but it will be seen from the table in page 43
that their relative entasis, in terms of the length of the shaft, is about in the proportion of 9 : 7.
That of the two orders of the Propylaea as 5 : 4. The influence of this modification of the en-
tasis is most felt when the columns are under 20 feet in height; in those of the Temple of Nike
Apteros, which do not exceed 12, there seems to be no entasis whatever. I have endeavoured in
Appendix vi. Art. 19, to deduce a rule for calculating the entasis of any column, of which the height

1 The following explanation of the cause of this appearance in a tapering
shaft in any position may be proposed, but with considerable diffidence,
ft will be readily admitted that the eye becomes sensible of an object
presented to it, not all at once, but by passing very rapidly over it from
point to point. It is therefore reasonable to suppose that it will pass from
a small figure to a larger with greater ease than the converse, and will
accept the impression which it derives from the former rather than that
which is the result of the latter process. Thus in passing from the smaller
to the larger diameter of a tapering shaft, and endeavouring to grasp both
sides at once, it will receive by contrast a greater impression of the divergence
of the bounding lines than they really have ; and as this feeling will con-
tinue to accumulate as the eye travels along the shaft, the result will be a
slight appearant e of hollowness. From the comparative difficulty in passing
from large to small, this impression will not be entirely counteracted by
the opposite feeling generated in retracing the course from the base to the
neck. That this effect does not take place when the angle at the apex is
large may be partly assigned to the divergence being in this case so marked
as to be more correctly estimated, and partly because the eye in its
instantaneous action can no longer follow both lines at once, and ceases
to be influenced in the same degree by their contrast.

- A. good illustration of the effect of different degrees of irradiation

upon the apparent size of objects, is the seeming alternate dilation and
collapse in the full moon when "stooping through a fleecy cloud." The
apparent attenuation to which a pilaster with parallel sides is liable is solely
owing to the causes treated of under the two last heads. How inconsider-
able this must be may be gathered from the fact that in the columns
of the Erechtheum, of which the diminution is but small, an entasis of only
nrVrr °^ tne shaft, equivalent to an increment of curvature of .%$%, is found
to be sufficient to correct all the causes of illusion combined.

3 Without entering into the question of the propriety of the use of
single columns, we may see that they are removed from many of the
influences above mentioned, and do not require so much diminution or
entasis. I think it will be generally felt, in respect of entasis, that of the
shafts of two monumental columns recently erected in London, namely the
column at the bottom of Regent Street and that in Trafalgar Square, the
one wFhich has the least entasis is the most pleasing; and we may even
extend these remarks to the columns of Trajan and Antoninus at Rome
of course without any disparagement to the superiority of the sculpture of
the Trajan column over that of the Antonine. It follows also from what
has been said that rusticated columns, in the few situations in which they
are admissible, do not require entasis so much as columns with smooth
shafts.