We shall presently see how this was effected in subsequent times, and I will not anticipate that subject, but will content myself with mentioning that this seems to anticipate the Byzantine domes of the succeeding century, as had been the case in two other instances to which I shall have to refer, and as had been nearly the case in the Temple of Minerva Medica.
Fig. 405.—Baptistery at Ravenna. Plan and Section.
The domes which we have hitherto considered are exclusively and of necessity carried by circular or other continuous walls. They are consequently supported uniformly throughout their entire circumference, and their use is necessarily limited to the coverings of circular or quasi-circular or polygonal buildings. Had no further development been attained, it would ever have been felt to be a sad deficiency in the scope of architectural facilities that the noblest form of covering should be limited to the least usual and, for most purposes, the least convenient form of apartment. We are happily as far as possible from being left in this dilemma. A very simple application of geometrical thought opened a way by which almost any reasonable form of building may be covered by a dome, or by a series or group of domes.
I will endeavour, as simply as I am able, to explain this important development.
It is a property of the sphere that every possible plane section of it is a circle. It follows that every vertical section of a hemispherical or segmental dome assumes the form of a semicircular or segmental arch. If, therefore, a square be inscribed in the base of a dome, and walls be built on that square, and continued up till they meet the dome, they will intersect with it in four semicircles ([Fig. 406]). If, instead of walls, you build arches on the sides of that square, these arches will coincide with the curve of the dome where they meet it, and, if strong enough, will carry the portion of the dome remaining between them. If, again, instead of arches, you suppose the dome intersected on the lines of the inscribed square by vaults at right angles to those sides, the result will be the same.
Fig. 406.