Improved scientific construction is most evident in the walls. The development of stone-vaulted roofs (a protection against fire) carried by arched ribs brought down the incumbent load on to the walls, producing thrusts upon them which had to be provided against. The old manner of making the wall of great thickness was wasteful and unsatisfactory. The happy idea of the Gothic _buttress_ fulfilled all the requirements, and produced one of the most beautiful features of the Gothic style. It was built in diminishing stages, its outline enclosing the graceful parabolic curve of nature--the path of the combined thrusts and their opposing reactions. This structure was carried to perfection when combined with the _flying-buttress_ (Plate VII., Fig. 10), which conducted the thrust from the lofty wall of the nave over the external roof of the aisle by an arch on the _wall-buttress_, which was strengthened to do its work by the addition of a heavy _pinnacle_. Plate V., Fig. 9, from Lichfield Cathedral, shows two buttresses of the Lancet period built to meet the thrust of the ribs carrying the vaulting of the Chapter-house and Library over. In one of these the approximate direction of the thrusts is indicated by the arrows _a_, _b_, which, if unopposed, would cause a collapse; the ultimate deflection of their path by the weight of the superincumbent masonry is indicated by dotted lines within the _buttress_, thereby producing equilibrium through the opposing resistance from the foundations along the same path. In Plate V., Figs. 10 and 11, the piers had columns surrounding them whose shafts in the Lancet period were _detached_, but connected at their extremities by moulded _stone bands_ (A, B), and at the bases and capitals. These piers were sometimes carried to a great height, as those in Westminster Abbey, which have three of these _stone bands_ in their height. In the Geometrical period the shafts formed part of the main pier, were not detached, and resembled mouldings (Plate V., Fig. 11). Such shafts were described as _engaged_. Plate V., Fig. 7, shows a tower with a _broach-spire_ belonging to the Early English period. In the figure the four broaches are the small pyramids covering the _squinch arches_ or _squinch corbels_, which carried four of the eight sides of the octagonal spire across the angles of the tower.