We find the same cause regulating the geometrical system adopted for setting out the stones forming the bosses, which had also to contain a short piece of the impinging ribs. Professor Willis, in his admirable papers on vaulting, gives in minute detail the method adopted, showing that, to facilitate the operation, they made the upper surface of the boss-stone _horizontal_, to serve as a sort of drawing-board on which to draw the plan of the intersecting ribs. I have tested this in several instances. In the western part of the nave at Westminster, there being no outer thickness of stone vaulting, the boss-stones appear, and their surfaces are horizontal. On sweeping away the accumulation of dust and rubbish which covers them, I found, sure enough, the centre and side lines of all the ribs carefully drawn upon them. In the lierne vaulting at Ely, though there has been an outer thickness of stonework, it was cleared away in the last century for the sake of lightness, so that the boss-stones, once concealed, are now visible. On clearing them from obstructions, I again found, as at Westminster, the lines of the ribs (here much more complex), carefully set out upon the top of the stones. Each of these little stone tables, in fact, has drawn out upon it the bit of the full-size plan of the vaulting which its surface would contain. The lierne vaulting, though commencing as early as the first quarter of the fourteenth century, was so popular as to be continued throughout the remaining periods of Gothic architecture, used side by side, and often in union with other and later systems. The same was naturally the case with ordinary rib vaulting, so that in later times we have at least _three_ systems used contemporaneously. I know of no specimens of lierne vaulting more charming than what we see in the oriels of the halls of Crosby Hall (Fig. 386), and Eltham Palace (Fig. 387), two sister works, unquestionably the work of the same architect, in the reign of Edward IV. They are of different plans. The one consists of five sides of an octagon, the other of a double square. The latter is on the system I have mentioned as having its central compartment raised like a square dome, to allow of the passage of the arch by which it opens into the hall. Both are carried out with the depressed arch belonging to their late period, and are treated with exquisite care and taste. At Gloucester, in the choir, and Winchester, in the nave, this manner of vaulting assumes a very peculiar form; the side cells falling in at a low level, as what are called “_Welsh_” groins, leaving a width of barrel-vault above, which is richly decorated by surface ribs and liernes. [Illustration: Fig. 386.--Oriel, Crosby Hall, London.]