Pennethorne, John; Robinson, John [Ill.]: The geometry and optics of ancient architecture: illustrated by examples from Thebes, Athens, and Rome (London [u.a.], 1878)

THE CITBVES OF THE HORIZONTAL LINES. 85

CHAPTER III.

THE CALCULATION OF
THE HORIZONTAL CURVED LINES.

So long as we were under the impression that the horizontal curved lines in the Entablatures
of the Parthenon and of the Temple of Theseus varied from the curved lines of the Upper
Steps, we had every reason to suppose that the horizontal curved lines were separately
corrected, according to some Greek Optical Theory, and such for a long time was my own
impression, but now that we can deduce from Mr. Penrose's measurements the facts, that the
observed variations in the lines of the Entablatures are due to concussions which have
shaken the stones, and thus flattened the curves, as well as caused the Entablatures to
bend inwards, that when the lines are restored, originally there was no difference in the
curvature of the lines of any given Portico, whether they were seen at 10 feet or at 50 feet
above the level of the eye, and that the curvature of the Upper Step in the Portico regulated
the curvature of the Upper Step on the return sides as well as all the lines in the Entablatures,
we at once perceive that the Greeks never attempted to correct these lines according to any
optical law, so as to make them all appear as perfectly straight lines when viewed from the
point of sight, which it would have been impossible to do without a great disturbance in the
general dimensions, but that the Greek Architects laid aside the straight lines, in their larger
works of Architecture, as apparently imperfect lines, when the design was viewed upon the
angle of the building from a point of sight below the Upper Step, as in the case of the
Parthenon and of the Temple of Theseus, owing to the lines appearing to the eye, as stated
by Vitruvius, to be concave lines, and that they substituted instead convex lines, tracing their
horizontal lines as the arcs of true circles, and giving as much convexity to them as they could
venture upon without disturbing the symmetry of the design.

*

The actual amount of curvature to be given to the horizontal lines in any Portico had
to be decided by the judgment of each Architect, who may have been guided to a certain
extent by works previously executed, and possibly also, as we shall see, within certain limits,
by the calculated concave appearance of the lines of the Portico when viewed from the given