delightful to the eye.

[Illustration: Fig. 11. Broken Curves.]

144. Let us take then the simple form _a b c d_, interrupting the curve
_c e_ [fig. 11, A]. Now, the eye will always continue the principal
lines of such an object for itself, until they cut the main curve; that
is, it will carry on _a b_ to _e_, and the total effect of the
interruption will be that of the form _c d e_. Had the line _b d_ been
nearer to _a c_, the effect would have been just the same. Now, every
curve may be considered as composed of an infinite number of lines at
right angles to each other, as _m n_ is made up of _o p, p q_, etc.,
(fig. B), whose ratio to each other varies with the direction of the
curve. Then, if the right lines which form the curve at _c_ (fig. A) be
increased, we have the figure _c d e_, that is, the apparent
interruption of the curve is an increased part of the curve itself. To
the mathematical reader we can explain our meaning more clearly, by
pointing out that, taking _c_ for our origin, we have _a c_, _a e_, for
the co-ordinates of _e_, and that, therefore, their ratio is the
equation to the curve. Whence it appears, that, when any curve is broken
in upon by a building composed of simple vertical and horizontal lines,
the eye is furnished, by the interruption, with the equation to that
part of the curve which is interrupted. If, instead of square forms, we
take obliquity, as _r s t_ (fig. C), we have one line, _s t_, an
absolute break, and the other _r s_, in false proportion. If we take
another curve, we have an infinite number of lines, only two of which
are where they ought to be. And this is the true reason for the constant
introduction of features which appear to be somewhat formal, into the
most perfect imaginations of the old masters, and the true cause of the
extreme beauty of the groups formed by Italian villages in general.

145. Thus much for the mere effect on the eye. Of correspondence with
national character, we have shown that we must not be disappointed, if
we find little in the villa. The unfrequency of windows in the body of
the building is partly attributed to the climate; but the total
exclusion of light from some parts, as the base of the central tower,
carries our thoughts back to the ancient system of Italian life, when
every man's home had its dark, secret places, the abodes of his worst
passions; whose shadows were alone intrusted with the motion of his
thoughts; whose walls became the