Perhaps the earliest method was simply to occupy those triangular spaces with pyramidal masses of masonry, sloping back against the adjacent faces of the tower,—­an expedient which Nature herself might have suggested in the first snow-storm.  Then they boldly cut the Gordian knot by shaving off the corners of the tower at the top, thus creating there an octagonal platform, to which the spire would exactly correspond.  Still oftener they chamfered the spire upwards from the corners of the tower:  in other words, they placed, as it were, a square spire on their tower, occupying the whole of its summit, and then obtained the necessary octangularity by shaving off the angles of the spire from the apex to a certain point near the base, where the cutting was continued obliquely to the corners of the tower.  The latest method was to build pinnacles on the triangular territory.  In such cases the spire usually stood wholly within the outer boundaries, and parapets assisted to conceal the first springing of the spire.

The first of these methods is usually considered the most perfect and beautiful, on account of its simplicity and candor.  This is called the broach; and it is the only form thus far spoken of wherein the tapering surfaces rise directly from the tower-cornice, without mutilating the tower or violating the pure outlines of the spire.  The heavenward aspiration, as it were, ascends without effort from the solidity of the tower.  It seems to typify a certain fitness and adaptability to heavenly things even in the gross and earthly nature of man.  One cannot fail to admire its unaffected dignity, its harmonious balance, its graceful proportions.

It would be impossible within the limits of this article to give any idea of the wonderful diversity of treatment these simple generic forms received at the hands of the early builders.  The changes of combination, proportion, and ornamentation were endless.  For the mediaeval spirit was eminently earnest in its labor, and would not be content with copying an old shape merely because it was a good shape.  It would not be satisfied with the cold repetition of a written litany of architectural forms; but its ardent piety, its thoughtful zeal, the life of its love, demanded an ever-varying expression in these visible prayers.  Emerson himself might find nought to censure there, in the way of undue conformities and consistencies.  Its language was written with the infinite alphabet of Nature.

We are speaking now especially of England; and we, her children, may well be proud that these divine enthusiasms of antiquity, which we thought so quaint, so rare, so far away from us, nowhere else found fairer demonstrations.  The English spires bear especial witness to the zeal and aspiration of their builders.  They belted them with bands of ornament, cut at first in imitation of tiles, and afterwards beautifully panelled with foliations.  Moulded ribs began to run up the angles of the spires, and, when they met