Considering the growth of the spire from the tower-roof, it might naturally be supposed that the earliest forms would be square or round, in plan. But no sooner had the roof passed into this new sphere of existence, than the fine intelligence of the builders perceived that it needed refinement. They saw that in a square spire there was so coarse a distinction between the tapering mass of light and the tapering mass of shadow, that the delicacy and lightness necessary to express the sentiment they desired to convey did not exist in the new feature;--in a round spire, on the other hand, they found that this distinction of light and shade was too little marked; it was vapid and effeminate, and quite without that delicious crispiness of effect which they at once obtained by cutting off the corners of the square spire, and reducing it to an octagon. With very rare exceptions, as in the southwest spire of Chartres Cathedral, this form was always used. Now it will be seen that a difficulty arises in the beginning, how to unite the octagon of the spire with the square of the tower. There are four triangular spaces at the summit of the tower left uncovered by the superstructure; and how best to treat these, simple as the task may seem, constitutes what may be called the touchstone of architectural genius in spire-building. There are several general ways of effecting this, each of them subject to such modifications, in individual instances, as to give them an ever-varying character. 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.