to repulse, and still do repulse, the study of the architecture of the Middle Ages as having been only produced by chance?” It will be seen from what I have above stated that the order in which the pointed arch was successively adopted for different parts of a building, and the motives which led to its adoption, may be roughly classified under the heads of _Statical_, _Geometrical_, and _Æsthetical_, or positions in which it was demanded for soundness of construction, for the mathematical agreement of parts, and for harmony and beauty of effect. The first head embraces all wide-spanned arches, especially those I have pointed out as the first in which it made its appearance: the transverse arches of wide vaulting, also arches carrying towers, and others bearing great weight on their crown, and all which are defective in abutment, or demand the addition of buttresses (for remember that, though buttresses were rendered sources of beauty, they originated in _necessity_, and the aim was to keep their projection within bounds, rather than unduly to increase it). The second, or geometrical class, includes, primarily, the narrower arches of oblong vaulting; for, even had the transverse section continued round, the pointed arch must soon have suggested itself for the narrow arches of the sides; and though for a time the idea did not occur, the necessity of it is only the more apparent in the want of harmony, the undue stilting, and the loss of clerestory space which arose from its neglect. Under the same head come all other cases of irregularly formed vaulting in which the sides differ in width, and arches of varied proportion are therefore needed. Of the same kind are many other cases in which arches of different widths are in the same range, and where--though the _statical_ view would demand that the widest span should have the strongest arch--_geometrical_ agreement suggests the contrary; as, for instance, in the choir of St. Germain des Pres, at Paris, and many others, where the side arches are all round; but those of the apse, being narrower, are pointed. These two pressing necessities having once established the use of the pointed arch in a large number of the most important positions, a natural feeling for harmony would come in to suggest its use in many others. First we may mention windows under the narrow compartments of groining--as in clerestories, apsidal chapels, etc.,--where, as soon as the pointed arch was used for the vaulting, the round-topped window would present a certain degree of discord, as we see at St. Cross,[8] and at St. Joseph’s Chapel[9] at Glastonbury. Then again, as windows became more elongated, the round arch became ill-proportioned to the jambs; and generally, as the architecture acquired a more aspiring tendency, the pointed arch was found more congenial with its spirit; so that, little by little, from being an exception, used from mere constructional expediency, it became the prevailing feature of the style; the