Plate X., Fig. 5, shows a _collar_ principal with curved braces. The tendency of all roof principals is to _spread_ at the walls; this has been met by modern church-builders by introducing an iron tie-rod in place of a tie-beam, thus forming a triangle, the only form of absolute stability, for the whole of the principal, as indicated by the dotted line connecting the hammer-beams in Plate X., Fig. 7. Plate X., Fig. 6, shows a low-pitched Perpendicular roof with principals and half-principal. The common rafters are concealed by a panelled ceiling, the panels being formed by principal rafters and purlins. The arched trusses bring part of the thrust low down on to the walls, which are strengthened by heavy buttresses on the outside. The _half-principal_ is placed over a window arch. Plate X., Fig. 3, shows a low-pitched roof and ceiling supported by a tie-beam only, strengthened at its bearings by _wall posts_ and _braces_. PLATE XI GOTHIC VAULTS [Illustration: PLATE XI] PLATE XII GOTHIC VAULTS [Illustration: PLATE XII] PLATES XI AND XII GOTHIC VAULTS Stone-vaulted roofs became necessary in church building early in the Norman period for security against fire. They were made after the Roman manner, semicircular, with similar vaults intersecting at right angles. The lines of their intersections are the _groins_. When two intersecting vaults are of equal semicircles, each groin is a semi-ellipse. This groin is the weakest part of the vault; in order to strengthen it the Normans built an arch called the _groin rib_, underneath the groin, to support it. Difficulties were met in forming intersecting vaults of unequal span, clumsy contrivances were resorted to, until, in the Transition period, 1145-1190, the introduction of the pointed arch solved the problem, and led the way to the development of Gothic vaulting. The Roman and Norman vaults were built upon temporary _centering_. A _centre_ is a timber frame made like a roof-truss shaped to the form of the arch; a series of _centres_ were placed at convenient distances apart and covered with strong boarding upon which the vault was built. After the masonry was completely _set_, the temporary centering was removed, leaving the vault to carry itself. As the system of vaulting developed, _cross ribs_ and _wall ribs_ (Plate XI., Fig. 3) were added, and much of the temporary centering was dispensed with; ornamental arrangements were designed by introducing more ribs, and _the web_--the covering surface of masonry--was reduced to small panels in the Decorated and Perpendicular periods. In the Tudor period, 1485-1558, the _web_ became the principal part, the ribs being mere mouldings worked upon its surface in the form of _fan-vaulting_, a simple example of which can be studied in the south porch of Chester Cathedral, and the most elaborate in the roof of the Chapel of Henry VII., Westminster Abbey.