of both were equal, the second rib should be set out with its back line at an equal distance from the points at which the plans of the adjoining lines would intersect; for, in following the curve, both would at a given height reach a point vertically over that intersection, and so the filling in would have a proper starting-point, which would not be the case if they reached that vertical line at different heights. As, however, the diagonal rib (where the ridges are level) has to travel farther to reach a given height, its springing section has to be set _farther back_ to make it reach the vertical line over this point of intersection at an equal level with the transverse rib. The wall rib in a square vault would be similarly placed with the transverse rib; but in an oblong vault, as it would travel a _less_ distance to reach a given level, its springing section must be placed _forwarder_ than that of the transverse rib, and, of course, _greatly_ forwarder than the diagonal. This is easily adjusted by drawing the curve of the back of the rib, whose position is first determined, drawing against it the vertical line of its intersection with the next rib, and then, from the apex point of the adjoining rib, to draw its curve through the point of intersection, which will give on the springing line the distance _backward or forward_ at which the springing section of that rib should be placed (Fig. 361). The ribs of all vaulting of early date are square and flat at the back; the vaulting, which is often very thick, passing over and resting upon their backs. In later works the ribs were usually deeper from intrados to extrados, and were notched, or as it is technically called, “rebated,” to receive the vaulting, or at least the lower part of its thickness (Fig. 362); for where the surface was not intended to be plastered, the wrought stonework was often a thin casing covered over above by a thicker mass of rough work. The curvature of the courses of wrought stone enabled them to be set without the use of continuous timber centering, and this inner facing, once finished, would itself form a substantial centering for the outer rough vault. At a later period this outer thickness was dispensed with as a superfluous load. In all cases the hollow space against the wall behind was filled in solid to a certain height to strengthen the haunches of the vault.