1. _Widening of the Nave_ in a vertical direction. Where this occurs, each side of the nave leans outward; three methods being employed, though not more than one appears in a given church. In one case, there is a continuous and absolutely straight outward inclination from floor to vaulting. In another, the outward inclinations recede from floor to vaulting in delicate vertical curves. In the third, the piers are perpendicular up to the arcade capitals, where the inclination begins and is continued in straight lines through the triforium and clerestories. In this last case, the angle, formed by the two lines, produces in the large scale of the building the effect of a curve. The widening in all cases tends to offset the perspective illusion of vertical lines converging toward the vaulting; but also appears to have been preferred for other aesthetic reasons. Instances of continuous widening in straight lines are found in the =Cathedral= and =Church of St. Ouen=, in =Rouen=. Continuous widening combined with vertical curvature occurs at =Canterbury=; while the perpendicular pier, combined with inclined vaulting-shafts, triforium and clerestories is found in =Amiens= and =Rheims=. 2. _Horizontal Curvature in Plan._ Where this occurs, one of five methods is adopted. In the first, the piers are set on parallel curves, which consequently are convex to the nave on one side and concave to the nave on the other. In the second, both curves are concave to the nave, which thus widens slightly from both ends toward the centre. In the third, both curves are convex to the centre. In the fourth, the curves are parallel, but reverse their direction at or near the choir, in the form of an attenuated S, or “Hogarth’s line of beauty.” In all the above instances the curves start at the bases of the piers and continue in the triforium, clerestory and roof parapets; in certain cases being also repeated in the outer aisle walls. The fifth system is connected with a special phase of the Widening. For, in this case, the piers are set on a straight line and with the triforium and clerestory are perpendicular from floor to ceiling. That is to say, at the west end and the crossing; but, in between, from both ends, the piers gradually lean outward with an increasing inclination toward the centre of the nave. Thus result curves, concave to the interior, which, however, since the bases of the piers are on straight lines, are found only in the triforium, clerestory and parapet walls. =Lichfield Cathedral= presents an example; =Rheims= another, but with a difference. For while the widening in Lichfield begins at the pavement, that of Rheims starts at the arcade capitals. 3. _So-called Perspective illusions._ These were intended to emphasise the effect of the choir and generally to increase the suggestion of size and distance. This was accomplished in three ways. a. By making the nave arcade and the outside walls converge toward the choir.