ENGLISH GOTHIC. 287 orm, but often had winding surfaces, and were constructed so that their pressure was directed towards the piers and not the wall rib. The ^^ploughshare t-wist, so called from its resemblance to a ploughshare, was produced by stilting or raising the springing of the wall rib, when forming the window arch bordering on a vaulting compartment, above that of the diagonal and transverse ribs (No. 109 a). This was a common arrangement, and was necessary in order to obtain greater height for the clerestory windows. The geometry of the Gothic system was a rough use of mathe- matical truths in which beauty was sought for, and not a strict regard for the exactitude of scientific demonstration. The curva- ture of the ribs was obtained from arcs struck from one or more centres, and designed without reference to the curvature of adjoining ones, as is seen in the setting out of Gothic vaulting compartment (No. 11 1 d). In this lies the whole difference between the Roman and mediaeval systems, for in the former the vaulting surface is everywhere level in a direction parallel to the axis of the vault, and any horizontal section of a spandrel or meeting of two cross vaults would be a rectangle. In the ribbed Gothic vault, however, the plan thus formed would have as many angles as ribs, varying according to the curve of the latter. The plain four-part (quadripartite) ribbed vault, primarily constructed as a skeleton framework oi diagonal a.nd transverse ribs, was chieily used in this period, as in the naves of Durham, Salisbury (No. 112 j, l), and Gloucester, and the aisles of Peterborough. Later in the century intermediate ribs, known as tiercerons, were introduced between the transverse and diagonal ribs as in the vaulting of the nave of Westminster Abbey (No. 112 k, m), and were especially needed to strengthen the vaulting surfaces by decreasing the space between the ribs. In such cases ridge ribs were introduced in order to take the thrust of the tierceronse which abut at their summit at an angle, and would have a tendency to fall towards the centre of the compartment unless resisted by the ridge rib. In Continental examples the ridge rib is often not continuous, but only extends to the last pair of arches which abut against it obliquely. Ridge ribs are generally horizontal in England and arched on the Continent, the "infilling" or " severy " having its courses meeting at the ridge in zigzag lines as in the nave of Westminster Abbey (No. 127 c), and the naves and choirs of Lincoln, Exeter and Lichfield Cathedrals, and as found in the churches of South- West France. A wall-rib, called a "formeret," because forming a boundary for each compartment, was also introduced. •Decorated (Fourteenth Century). — During this period there was an increase and elaboration of intermediate ribs
