g at Luxor,
and has already been described. Both of them show a peculiarity in
their lines, which could only be noticed effectually when the pair
stood together. This peculiarity is a convexity, or _entasis_, as it
is called, on the inner faces. Even to the untrained eye its sides
seem not of equal dimensions; and actual measurement shows the
irregularity more clearly. This is said, however, to be exceptional to
the general rule, and to be foreign to the design of an obelisk in the
best period of the Pharaonic art. Still, several magnificent
specimens, such as the Luxor and Flaminian obelisks, exhibit it. And
they are an illustration of what was a marked characteristic of all
classic architecture, which shows a slight curvature or entasis in its
long lines.

It was early found out that mathematical exactness and beauty were not
the same. By making its two sides geometrically equal, the living
expression of the most beautiful marble statue is destroyed, and it
becomes simply a piece of architecture. It is well known that the two
sides of the human face are not precisely the same; the irregularity
of the one modifies the irregularity of the other, and thus a higher
symmetry and harmony is the result. The two sides of the leaf of the
begonia are unequal, and if folded together will not correspond. The
same is true of the leaf of the elm and the lime. But when the mass of
the foliage is seen together, this irregularity gives an added charm
to the whole. Every object in nature has some imperfection, which
indicates that it has a relation to some other object, and is but a
part of a greater whole. The intentional irregularity of the windows
in the Doge's Palace at Venice enhances the effect of the marvellous
facade. By comparing the Parthenon at Athens, with its curves and
inclinations, with the Madeleine at Paris, we see how far short the
copy comes of the original in beauty and expressiveness, because of
the exact formality of its right angles. The ancient Egyptians
understood this well; and in their architecture they sought to rise to
a higher symmetry through irregularity; and we can see in their
frequent departure from upright and parallel lines in the construction
of their temples, an effort to escape from formal exactness, and a
longing for the nobler unity which is realised to the full in the rich
variety of the Gothic. We may be sure that "every attempt in art that
seeks a theoretical completeness, in so doing sinks