This regret, however, is diminished by the abundant evidence we possess that the dome, though absent from English buildings, was by no means held to be alien from the contemporary architecture of neighbouring countries, inasmuch as we possess it in highly developed forms over a large part of France, in Germany, and in Italy, erected at the same periods with many of our great Mediæval edifices. If, then, I am departing from the line I had been taking in tracing out the history of old English architecture, I am not only supplying a hiatus in that history, but I trust that I may be able to offer suggestions for a more practical object--the supplying of that hiatus in our revived and redeveloped Neo-mediæval style. In a former lecture, after defining a vault as the covering of a rectilinear space produced by the motion of an arch parallel to itself, I defined a dome as the covering of a circular space produced by the revolution of an arch round its central vertical axis. It follows that, if the arch so revolving is semicircular, the resulting dome is a hemisphere. The revolving arch may, however, be of any form which an arch can assume. It may be elliptical, parabolic, hyperbolic, cycloidal; or it may be a pointed, a horse-shoe, or an ogee arch. Any one of these, or other forms of arch revolving on its centre, will generate a dome of its own sectional form. The _plan_, too, in spite of my definition, need not be a circle; it may be an ellipse, or of other forms. I will not at this stage admit of square-planned, polygonal, or other straight-sided domes, because it may be doubted whether they are genuine domes at all, or whether they are not figures resulting from the intersection of a certain number of ordinary vaults. Anyhow, these are not generated by the revolution of an arch, so that if they are domes, my definition is at fault. Simple, however, as is the hemispherical dome, it does not appear to have been historically the primeval type; for, strange to say, the earliest known domes assume, in section, the form of a lofty pointed arch. I refer specially to that of the supposed tomb of Agamemnon at Mycenæ, and also to some portrayed on the Assyrian sculptures. These would hardly come within the range of this lecture, were it not so curious a fact that the earliest form of the dome foreshadows the very use to which I would now especially desire to accommodate it. It is easy to perceive why the pointed arch was adopted in these primeval domes. They were not built with radiating joints, but in overhanging courses; and it will readily be seen on comparing their sections, that for this mode of construction the pointed arch is much more favourable than the circular; while, as soon as ever the radiating system was adopted, the semicircle at once became the simplest and most obvious section.