The whole tendency, too, of the onward movement of the art was towards increased height; and, while walls and pillars might avail themselves to the full of this upward striving, it was hard that the arch--the very essence of the style--should be condemned to unalterable stuntiness. Proportion evidently claimed that the arch should have its fair share in the increasing height of the buildings, yet the inexorable semicircle said, “Nay, my proportions are fixed. You may lengthen your straight lines as you please; but by no law of science can my height exceed one-half of my width.” A geometrician might reply that the semicircle might be stretched upwards into a semi-ellipse with its major axis upright. I do not think that our Mediæval builders ever tried this dismal experiment, nor do I know that it was ever attempted, except by the barbarous Parthians, in a building you will find figured in Mr. Fergusson’s _Handbook_; and so hideous was the result that one may well suppose it to have been handed down as a warning to subsequent generations! Nor was this craving after a loftier arch the result of taste alone. Constructive motives pointed in the same direction; for it was found that round arches, when carrying great loads, as those sustaining towers, etc., were apt to overcome the resistance of their piers; and many failures were the result. The same was found to result from _vaulting_ over wide spaces. True it is that the Romans, in the great halls of their baths, had vaulted over spans of double the width of the naves of our Norman cathedrals; but this had been effected at the expense of the utility of their aisles, which were cut up into short lengths by the ponderous abutments needed to sustain the tremendous pressure of the central vault. Besides which, the Mediæval builders aimed at raising the springing of these vaulted naves to a height out of the reach of the abutment of the aisles. An arch of less lateral pressure was therefore desired. Another motive might have led to a similar aim. We have seen what difficulties and contrivances resulted from the exigencies of vaulting over irregular spaces where it was desirable that the crowns and springers of the surrounding arches should range on the same levels, though their spans might differ to any extent. It was clear, then, that an arch of more elastic proportions was the grand _desideratum_. The claims, then, of _proportion_, of construction, and of geometrical convenience, all took the same direction, and demanded an arch of variable proportions. This three-fold demand was met by the introduction of the _Pointed arch_.