Having said enough upon this simple case of groined vaulting to show that it may be made both the source and the vehicle for architectural treatment of a most reasonable kind; and, as you will readily imagine that its ribs and their supporting capitals, corbels, and colonnettes, may receive _any amount_ of sculptured enrichment, and its vaulted surfaces any degree of decoration in the form of painting or mosaic work, I will here close my lecture, hoping that, though its subject-matter may have appeared somewhat dull and its arguments almost self-evident, it may, nevertheless, have placed simple and familiar facts before you in a form more systematic than that in which they might otherwise have presented themselves; and that, like the definitions and axioms of Euclid, it may be serviceable in preparing the way for more intricate and less obvious matters of consideration which I shall have to bring under your notice while following out, in my succeeding lectures, the principles of vaulting into those more difficult and ornate forms which became so important an artistic element in the subsequent developments of Mediæval architecture. LECTURE XIV. The Principles of Vaulting. Vaulting of spaces of other forms than the mere square--Apsidal aisles, St. John’s Chapel Tower, and St. Bartholomew’s Church, Smithfield--Chapter-house and crypt, Worcester--Round-arched vaulting in its most normal form, as resulting from the _barrel_ vault and its intersections--Short digression on another simple form of vault, the _dome_--“Domed up” vaults--“Welsh” groining--The square or polygonal dome--The Round-arched style of the twelfth century almost perfect--First introduction of the Pointed arch into vaulting--Names of the parts of groined vaulting--Two specimens in London of the apsidal aisle, one in the Round-arched, the other in the Pointed-arched style--Vaulting a polygon with a central pillar--_Ploughshare_ vaulting--The artistic sentiment and character of early Gothic vaulting. In my last lecture I explained the general principles of groined or intersecting vaulting, and just carried on the subject through its simplest case,--the covering of a square space, or any repetition of square spaces, by the intersection of semi-cylindrical vaults; and I just showed how, by emphasising the outlines of the squares so covered by means of transverse ribs or angles, and by placing impost mouldings, pilasters, columns, or colonnettes in the sustaining piers, such a mode of covering a space might be readily made at once susceptible and suggestive of architectural treatment. Let us now proceed to consider the application of the same principles to the vaulting of spaces of other forms than the mere square.