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. 36., 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.
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
