The bases of a thirteenth century church indicate the plan and construction of the vaulting--The system of mouldings--Windows, their development--Rationale of stained glass--A general principle of ornamentation common to all good architecture--The roof--Secular buildings--Cloth market Yprès--Warehouses, Nuremburg--Windows in secular and ecclesiastical buildings--Trabeated architecture in its truest forms--Fireplaces--Chimney-shafts--Oriel and Dormer windows--Ceilings--Subordination of external design to internal requirements--Designs adapted to the materials most readily obtained--Conditions demanded of our future architecture--Gothic architecture well fitted to unite these conditions. In my last lecture I traced out the _rationale_ of a number of the leading features, both of Romanesque as distinguished from Roman architecture, and subsequently of Gothic as distinguished from Romanesque. I will endeavour to avoid wearying you by carrying the inquiry into too great a multiplicity of details, but I must, nevertheless, ask your indulgence while I pursue them somewhat further than I have yet done. Nothing would, perhaps, do more to show the reasonableness of the various developments in question than to trace out the details of the vaulting system; to show the varieties it exhibited in different countries and provinces and at different periods, the various modes adopted for effecting a given purpose and the many mechanical and other difficulties to be contended with, and the methods adopted of meeting them. This is, however, so extensive and so intricate a subject, that, if I had devoted these two lectures exclusively to it, I could barely have done it justice. I will, therefore, at present content myself with referring those of you who are anxious to make yourselves acquainted with it, to an admirable and elaborate essay on the subject by Professor Willis, in the Transactions of the Institute of British Architects, and to the article “Construction,” in the fourth volume of Viollet le Duc’s Dictionary. No one who has not gone carefully and practically into the subject can have any idea of the amount of forethought which it demands; so much so that, as Viollet le Duc says, the design for a vaulted building has to be commenced at the top and worked downwards; and we may often form a pretty correct idea, from the bases of a thirteenth century church, of what was the plan and construction of its vaulting. This principle of designing each part from the first with reference to its ultimate intention is very strongly marked in French works of the twelfth and thirteenth centuries, and in those of the transitional period in England. The form, not only of the capital, but even of the base of each shaft, usually indicates the direction of the arched rib or order which it is destined to carry.