In the thirteenth century the style was formed in all its purity; it was characterized by great simplicity and beauty, and in these respects was never surpassed. The arch had few mouldings, and these clearly defined and graceful; the shafts of columns were of slender and charming proportions, and the foliage employed for the decoration of their capitals, while conventional, departed entirely from the acanthus leaves of Classic origin, and assumed forms suggested by Western plants. Piers were reduced to the precise dimensions needful, and were formed of slender shafts, grouped together, which received the arch mouldings on either side, and rose in the front and rear to the height necessary to take the springing of the vault. In practice, the thrust of the vault was found not to be transmitted directly to a point to be received by an arch, but to two points above and below this theoretical one, which necessitated the employment of two flying buttresses, the one above the other. In Chartres Cathedral these are connected by radiating columns, and there are many examples where the intervening space is occupied by an open arcade. The French generally built their vertical buttresses very massively, but in England the pinnacle was more frequently used to counteract the thrust of the arch. For this purpose it was eminently appropriate, and might be considered ornamental, but the placing of pinnacles upon the corners of the towers and elsewhere where they served no end, which was often done, was always a mistake; and a defect which mars the effect of many beautiful English buildings. In Notre Dame of Paris, we find the single round column still occupying the first story, with the more complex arrangement of pier and connected shafts starting above the abacus of its capital, but as a general thing, a distinct shaft was provided for each set of mouldings. In time this was replaced by a continuation of the vault mouldings down to the floor, interrupted only by an occasional string-course, or a band of foliage replacing the capital. [Illustration: PLAN OF AN ENGLISH CATHEDRAL. (_From Rickman._)]